-
The invention relates to the field of signal processing, and more particularly
to a technique for deriving automatically high level information expressed by an
electronic input signal by analysing the signal's low-level characteristics. In this
context, the term high-level refers to the global characteristics of the signal content,
while the term low-level refers to the fine grain structure of the signal itself,
typically at the level of its temporal or spatial modulation.
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For instance, in the case of audio signals corresponding a given music title,
such as contained in an audio file readable by a music player, examples of its high-level
expression would be an indication of whether the title pertains to a sung or
instrumental piece of music, the musical genre, musical complexity, overall timbre,
tempo, or the rhythm structure, etc., while the low-level characteristics would be the
signal's time-dependent parameters such as amplitude, pitch, etc. analysed over
successive short sampling periods. The signals in question can thus be in the form
of digital data accessed from a memory or inputted as a digital stream, or they can
be in analogue form.
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In such audio applications, the high-level information is normally known by
the term "descriptor". Generally, a descriptor expresses a quality, or dimension, of
the content represented by the signal, and which is meaningful to a human or to a
machine for processing high-level information. Depending on what they express,
descriptors attribute a value which can be of different types:
- a Boolean, e.g. true/false to indicate whether or not a music title is sung,
- a number to express information quantitatively against a reference scale,
e.g. 7.3 against a scale of 1 to 10 for a global music energy descriptor,
- an indication of a selection from a list of labels, e.g. "military music" to
indicate a musical genre from a preset list.
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In the field of music, descriptors are of interest notably in the expanding
field of music access systems and Electronic Music Distribution (EMD). To
facilitate user access to large music databases, descriptors of music titles are needed.
EMD belongs to the more general concept of music information retrieval (MIR),
which is the technique of intelligently searching and accessing musical information
in large music databases.
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Traditionally, EMD systems use either manually entered descriptors (e.g.
using software systems developed commercially by the companies "Moodlogic" and
"AllMusicGuide". The descriptors are then used for accessing music browsers,
using a search by similarity, or a search by example, or any other known database
searching technique.
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A key issue in extracting automatically descriptors for audio signals is that it
is very difficult to map signal properties with perceptive categories. In the prior art,
attempts have been made to extract specific descriptors from a sound signal, these
being documented notably in:
- Scheirer, Eric D., "Tempo and Beat Analysis of Acoustic Musical Signals",
J. Acoust. Soc. Am. (JASA) 103:1 (Jan 1998), pp 588-601., for tempo,
- Aucouturier Jean-Julien, Pachet Francois, "Music Similarity Measures:
What's the Use? ", Proceedings of the 3rd International Symposium on Music
Information Retrieval (ISMIR02), Paris - France, October 2002, for timbre,
- Pachet, F., Delerue, O. ,Gouyon, F., "Extracting Rhythm from Audio
Signals ", SONY Research Forum, Tokyo, December 2000, for rhythm, and.
- Berenzweig A.L., Ellis D. P. W., "Locating Singing Voice Segments
within Music Signals", IEEE Workshop on Applications of Signal
Processing to Acoustics and Audio (WASPAA01), Mohonk NY, October
2001.
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There are however many other dimensions, i.e. descriptors, of music that can
be extracted from the signal. For instance:
- danceability
- music for children
- military music
- music for slow
- global energy
- sung versus instrumental
- original versus remix
- acoustic versus electr(on)ic
- live versus studio
- musical complexity
- musical density
- etc.
-
-
While such descriptors are readily discernible by a human listener, the
technical problem of producing them electronically from raw music data signals is
reputed to be particularly difficult. For instance, there is no immediately apparent
low-level characteristic of a raw music signal from which it is possible to identify
whether it pertains to a sung piece or to an instrumental. This is particularly true
when the sung voice is mixed with music. Even the global energy descriptor has no
straightforward link with the energy level of the raw signal.
-
Some descriptors, such as the musical genre, are influenced by cultural
references and therefore require criteria to be entered from a specific population
sample.
-
In view of the foregoing, the invention provides for an automated tool which
takes for input a test database containing a set of reference signals, for instance
audio files readable by a music player, at least one arbitrary descriptor that can be
potentially correlated to the signals, a grounded truth value of that descriptor for
each of the database signals and a set of elementary signal processing functions.
The tool then selects functions of that set to construct one compound function or
more, and automatically applies it on the signals of the database. Depending the
correlations between the value returned by the function and grounded truths, new
compound functions are created and tried, until an arbitrary end condition is
reached.
-
More particularly, according to a first aspect, the present invention relates to
a method of generating a general extraction function which can operate on an input
signal to extract therefrom a predetermined global characteristic value expressing a
feature of the information conveyed by that signal,
characterised in that it comprises the steps of:
- generating automatically compound functions, each compound function
being composed of at least one of a set of elementary functions, by using means that
handle the elementary functions as symbolic objects,
- operating said compound functions on at least one reference signal having
a pre-attributed global characteristic value and serving for evaluation, by using
means that process the elementary functions as executable operators,
- determining the correlation between the values extracted by those
compound functions as a result of operating on the reference signal and the pre-attributed
global characteristic value of the reference signal, and
- selecting the general extraction function among those compound functions
for which the correlation is relatively high.
-
The invention provides for many advantageous optional embodiments,
which are outlined below.
-
The compound functions are preferably generated in successive populations,
wherein each new population of functions takes as a basis earlier population
functions which produce a relatively high correlation.
-
The method can be performed by the steps of:
- a) preparing at least one reference signal for which the predetermined global
characteristic value is pre-attributed,
- b) preparing a population of compound functions each composed of at least
one elementary function,
- c) modifying compound functions of the current population using the means
that handle their elementary functions as symbolic objects,
- d) operating the compound functions of the population on at least one
reference signal using the means that exploit the elementary functions as executable
operators, to obtain a calculated value for each compound function of the population
in respect of the reference signal,
- e) for at least some compound functions of the population, determining the
degree of matching between its calculated value and the pre-attributed value for the
signal from which that value has been calculated,
- f) selecting compound functions of the population producing the best
matches to form a new population of functions,
- g) if an ending criterion is not satisfied, returning to step c), where the new
population becomes the current population,
- h) if an ending criterion is satisfied, outputting at least one compound
function of the current new population as a general function.
-
-
The compound functions are preferably produced by random choices guided
by rules and/or heuristics.
-
The rules and/or heuristics can comprise at least one rule which forbids,
from a random draw for selecting an elementary function to be associated with a
part of a compound function under construction, an elementary function that would
be formally inappropriate for that part.
-
The rules and/or heuristics can comprise at least one heuristic which favours,
in a random draw for selecting an elementary function to be associated with a part
of a compound function under construction, an elementary function which is
considered to produce potentially useful technical effects in association with that
part, and/or which discourages from the random draw an elementary function
considered to produce technical effects of little or no use in association with that
part.
-
The rules and/or heuristics can comprise at least one heuristic which ensures
that a compound function comprises only elementary functions that each produce a
meaningful technical effect in their context.
-
The rules and/or heuristics can comprise at least one heuristic which takes
into account at least one overall characteristic of the reference signals.
-
Advantageously, a new population of functions is produced using genetic
programming techniques.
-
The genetic programming techniques comprise at least one of following:
- crossover,
- mutation,
- cloning.
-
A crossover operation and/or a mutation operation can be guided by at least
one heuristic cited above.
-
The means that handle the elementary functions as symbolic objects
preferably manage the functions in accordance with a tree structure comprising
nodes and connecting branches, in which each node corresponds to a symbolic
representation of a constituent unit function, the tree having a topography in
accordance with the structure of the function.
-
Advantageously, the method further comprises a step of submitting a
compound function to at least one rewriting rule executed by processing means to
ensure that said compound function is cast in its most rational form or most efficient
form in respect of execution efficiency.
-
Preferably the method uses a caching technique for evaluating a function, in
which results of previously calculated parts of functions are stored in
correspondence with those parts, and a function currently under calculation is
initially analysed to determine whether at least a part of said function can be
replaced by a corresponding stored result, said part being replaced by its
corresponding result if such is the case.
-
The method can then comprise the steps of checking the usefulness of results
stored according to a determined criterion, and of erasing those found not to be
useful, the criterion for keeping a result Ri being a function which takes into
account: i) the calculation time to produce Ri, ii) the frequency of use of Ri and,
optionally, iii) the size (in bytes) of Ri.
-
The elementary functions can comprise signal processing operators and
mathematical operators.
-
The method can further comprise a step of validating a general function
against at least one reference signal having a known value for the general
characteristic, and which was not used to serve as the reference.
-
The signal can express an audio content, and the global characteristic can be
a descriptor of the audio content.
-
The audio content can be in the form of an audio file, the signal being the
signal data of the file.
-
Examples of descriptors for which the invention can be use are:
- a global energy indication,
- a sung or instrumental audio content,
- an evaluation of the danceability,
- an acoustic or electric sounding audio content,
- presence or absence of a solo instrument, e.g. guitar or saxophone solo.
-
According to a second aspect, the invention relates to a method of extracting
a global characteristic value expressing a feature of the information conveyed by a
signal, characterised in that it comprises calculating for that signal the value of a
general function produced specifically by the method according to the first aspect
for that global characteristic.
-
According to a third aspect, the invention relates an apparatus for generating
a general function which can operate on an input signal to extract therefrom a
predetermined global characteristic value expressing a feature of the information
conveyed by that signal,
characterised in that it comprises:
- means for generating automatically compound functions, each compound
function being composed of at least one of a set of elementary functions, the means
handling the elementary functions as symbolic objects,
- means for operating the compound functions on at least one reference
signal having a pre-attributed global characteristic value serving for evaluation, the
means processing the elementary functions as executable operators,
- means for determining the correlation between the values extracted by
those compound functions as a result of operating on the reference signal and the
pre-attributed global characteristic value of the reference signal, and
- means for selecting the general extraction function among those compound
functions for which the correlation is relatively high.
-
According to a third aspect, the invention relates to an apparatus according
to the third aspect configured to execute any one of the optional aspects of the
method set out above, it being understood that the features defined in the context of
the method can be implemented mutatis mutandis to the apparatus.
-
According to an fourth aspect, the invention relates to the use of the
apparatus according to the third aspect as a fully autonomous automatic descriptor
extraction function generating system.
-
According to a fifth aspect, the invention relates to the use of the apparatus
according to the third aspect as a descriptor extraction means.
-
According to a sixth aspect, the invention relates to the use of the apparatus
according to the third aspect as an authoring tool for producing descriptor extraction
functions.
-
According to a seventh aspect, the invention relates to the use of the
apparatus according to the third aspect as an evaluation tool for externally produced
descriptor extraction functions.
-
According to an eighth aspect, the invention relates to a general function in a
form exploitable by an electronic machine, produced specifically by the apparatus
according to the third aspect.
-
According to a ninth aspect, the invention relates to a software product
containing executable code which, when loaded in a data processing apparatus,
enables the latter to perform the method according to the first aspect.
-
In the preferred embodiment, the above iterative search procedure through
successive populations is implemented by what is known as genetic programming.
The functions ― which typically take the form of executable code ― are tried and the
results serve to automatically create new populations of functions in accordance
with genetic programming techniques, taking the best fitting functions in a manner
somewhat analogous to selection and submitting those selected functions to actions
corresponding e.g. to crossover and mutation phenomena occurring in biological
processes at chromosome level. The remarkable aspect here resides in applying a
genetic programming technique on functions which take for argument raw
electronic signals.
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When applied to the field of music files, the proposed invention allows to
extract arbitrary descriptors from music signals. More precisely, the embodiment
does not extract a particular descriptor, but rather, given a set of music titles
containing both examples (and possibly counter-examples) for a given descriptor,
builds automatically a function that extracts from audio signals an optimum value.
The same system can be used to produce a function associated to an arbitrary
descriptor such as one listed in the earlier part of the introduction, which can then be
exploited as a general function for that associated descriptor, in the sense that it can
be made to operate subsequently on any music file to extract the value of the
descriptor for that file (assuming its signals are compatible).
-
The design of the system is based on extended experiments in the field of
audio/music description extraction. During these experiments the applicant
observed that a deep knowledge of signal processing was required to design
accurate and robust signal processing extractors. Each extractor can be seen here as
a function that takes as argument a given music signal (typically 3 minutes of
audio), and outputs a value. This value can be of various types: a float (for the
tempo), a vector (for the timbre), a symbol (for instrumental versus song
discrimination), etc.
-
The main task of extractor design is to find the right composition of basic,
low-level signal processing functions to yield a value that is as correlated as
possible to the values obtained by psycho-acoustic tests.
-
The preferred embodiment contains a representation of a human expertise in
signal processing: it will try different combinations of signal processing functions,
evaluate them, and compare them against human perceptive values. Using an
algorithm based on genetic programming, different signal processing functions will
be tried concurrently, and modified to find a satisfying extractor function.
-
Compared to existing approaches in music extraction, the system is one step
higher: its primary function is not to produce a descriptor for a signal, but rather a
function which itself will produce the descriptor, when applied on other music file
signals e.g. taken from a database of signals.
-
The invention and its advantages shall become more apparent from reading
the following description of the preferred embodiments, given purely as nonlimiting
examples, with reference to the appended drawings in which:
- figure 1 is a diagram showing the basic user input and output of a
programmed system for automatically generating descriptor extraction functions in
accordance with the invention;
- figure 2 is a simplified block diagram showing the main functional units of
the system shown in figure 1;
- figure 3 is a symbolic illustration showing the formal compatibility
requirements for two grouped elementary functions forming part of a compound
function produced by the system of figure 2;
- figure 4 is a symbolic illustration of an elementary function for performing
a low-pass filtering operation on a signal;
- figure 5 is a symbolic illustration of an elementary function for performing
a short-time fast Fourier transform operation on a signal;
- figure 6 is a symbolic illustration of a grouping of elementary functions
forming a term in a compound function;
- figure 7 is a diagram showing an example of a tree structure symbolic
representation of a compound function;
- figure 8 is a diagram showing a matrix of values calculated on a set of
reference signals for a population of compound functions, and how those values are
used to determine the fit of those functions with respect to a descriptor associated
with the music contents of those signals;
- figure 9 is a diagram showing, through a tree structure representation, how
parts of two compound functions are combined to form a new compound function
using a crossover operation according to a genetic programming technique;
- figure 10 is a diagram showing, through a tree structure representation,
how a compound function is mutated into a new compound function using a
mutation operation according to a genetic programming technique;
- figure 11 is a diagram showing, through a tree structure representation,
how a caching technique is implemented to acquire results data for a prior-results
data cache and to substitute a part of a function under calculation with a previously
calculated result;
- figure 12 is a flow chart showing the general steps performed by the system
of figure 2 for producing a descriptor extraction function;
- figure 13 is an example of different functions and their fitness produced
automatically by the system of figure 2 for evaluating the presence of voice in
music title; and
- figure 14 is an example of different compositions of descriptor extraction
functions in terms of elementary functions, and their fitness produced automatically
by the system to evaluate the global energy of music titles.
-
Figure 1 depicts a system 2 in accordance with the invention to indicate the
raw data on which it operates (user data input) and the output (user data output) it
produces from the latter. The example is based on a music data application, in
which the system 2 generates as its user data output an executable function 4,
referred to as a descriptor extractor function (DE function). This function is then
packaged in a data carrier 5 in a form suitable to be exploited for extracting a given
descriptor from an arbitrary audio file 6. The latter is typically formatted according
to a recognised standard such as CD audio, MP3, MPEG7, WAV, etc exploitable by
a music player, and contains a musical piece to which a descriptor value Dx is to be
associated. The DE function 4 operates on the raw data signal Sx of the audio file
6, i.e. it takes the latter as its argument or operand and returns the descriptor value
DVex for that file. Naturally, the signal Sx is assumed to be compatible with the
DE function 4 as regards data format. As mentioned in the introductory portion, the
descriptor value is typically a number, a Boolean, or a statement, and generally
belongs to the class or real objects Rn.
-
The above data carrier 5 typically comprises a software package which can
contain other DE functions, e.g. for extracting other descriptor values, and possibly
auxiliary software code, e.g. for management and user assistance. The data carrier 5
can be a physical entity, such as a CD ROM, or it can be in immaterial form, e.g. as
downloadable software accessible from the Internet.
-
The system 2 generates the DE function 4 on the basis of both the user data
input and internally programmed parameters, functions and algorithms, as shall be
detailed later.
-
The user data input serves inter alia to feed an internal learning database and
constitutes the raw learning material from which to model the DE function. This
material includes a set of m audio files A1 to Am and, for each one Ai(1 i m), a
given value Dgti of a specific descriptor De for the audio item Ti it contains. The
audio files Ai are formatted as for file 6 above, and thus each produce a respective
signal Si when accessed to reproduce the audio item Ti.
-
The respective descriptor values Dgt1-Dgtm associated to the audio files
are established by a human judge, or a panel of human judges. For instance, if the
descriptor De in question is the "global energy" of the music title, the judge or panel
awards for each respective title Ti a number within a range from a minimum (level
of a lullaby, for instance) to a maximum, and which constitutes the title's descriptor
value Dgti. These values Dgti are referred to "grounded truth" descriptor values.
-
Figure 2 shows the general architecture of the system 2. The system is
preferably implemented using the hardware of a standard personal computer PC.
For ease of understanding, the different types of data used are divided into
respective databases 10-18 under the general control of a data management unit 20,
which further manages the overall data flow of the system 2. The databases
comprise:
- a learning database 10, which stores the signal data S1-Sm of the reference
audio files A1-Am in association their corresponding grounded truth descriptor
values Dgt1- Dgtm, supplied as the user data input (cf. figure 1);
- a library 12 of elementary functions EF1, EF2, EF3, ..., which serve as the
basic building blocks from which compound functions CF are created on a guided -
or constrained ― random basis. A selected compound function, or possibly a
selected group of compound functions, shall become an outputted DE function 4;
- a heuristics database 14, which contains different types of guiding or
constraining rules that come into play in conjunction with random selection events,
notably at different stages in the elaboration of compound functions, as shall be
explained in more detail below;
- a formal rules and rewriting rule database 15, which contains a set of
deterministic rules for recasting automatically-generated compound functions into
their formally correct and most rational form;
- a prior results cache 16, which stores results of previously calculated parts
of compound functions in view of obviating the need to recalculate them when
subsequently encountered; and
- a validation database 18, which contains the same type of data as the
learning database 10, but for other music titles. The audio data contained in that
database are not used as reference for elaborating the compound functions, and thus
constitute a neutral source for ultimately testing the validity of a candidate DE
function 4 selected among the compound functions.
-
The signal processing and overall management of the system are carried out
by a main processor unit 22 which runs programs contained in a main program
memory 24. A user interface 26 associated to a monitor 28, keyboard 30 and mouse
31 allows the user input and output data of figure 1, as well as the internal
programming data, to be entered and extracted.
-
Figure 3 illustrates the principle of an elementary function EF as exploited
by the system 2. Being effectively an operator, the elementary function comprises
executable code and one or a set of parameter(s) which it can receive as input Pin,
and which defines the elementary function's boundary conditions. An elementary
function acts on an operand, or argument 32 ― which can be signal data or the
output of a preceding elementary function ― and generates an output that is the
result of the code executed on the operand data. An elementary function EF is
catalogued in the system inter alia by the type of operand, designated Toper, on
which can operate and on the type of output, designated Tout, it delivers. Types
Toper and Tout can be the same or mutually different for a given elementary
function. Typical types include: signal, numerical (single number, float, range),
vector, or matrix. As explained further, the system 2 treats elementary functions EF
― which can be assimilated to modules ― as symbolic objects or as executable
operators depending on the nature of the processing required in the course of
elaborating a compound function CF.
-
Figure 4 illustrates an example of an elementary function in the form of a
low pass filter (LPF) operator. As such, its executable code comprises a digital LPF
algorithm and its input parameters Pip are the cut-off frequency F and optionally the
attenuation rate (dB/octave). The operand and output types are respectively
Toper=Signal and Tout=Signal.
-
Figure 5 illustrates another example of an elementary function, this time in
the form of a short-time fast Fourier transform (short-time FFT) operator. The
executable code comprises a short time FFT algorithm, and its input parameters Pin
are the sampling window and summation limits. The operand and output types are
respectively Toper=Signal and Tout=matrix.
-
Figure 6 illustrates the principle of a string of elementary functions, the
example concerning three elementary functions EFa, EFb and EFc forming a term
TCF of a compound function that operates on a signal data S of an audio file, the
term being TCF=EFc.EFb.EFa*S. Note that in such a string of elementary
functions, an elementary function also constitutes an argument, or operand, for its
left-hand neighbour (i.e. succeeding function) to which its is joined by "*" function
when the case arises. Also, an output of an elementary function can include
parameter input data for its neighbouring function. This is illustrated in figure 6 by
the output of function EFb, which produces inter alia a signal which conveys a
parameter Pin for its downstream function EFc, for instance the value of a high-pass
cut off frequency if the latter is a high-pass filter function.
-
A compound function CF can contain an arbitrary number of elementary
functions related by different arithmetical operators (+, -, * or ÷). Elementary
functions connected together by a multiplicative or divisional operator form a term;
several terms can be linked by associative operators + and - as the case arises when
constructing a compound function CF.
-
Among the programs stored in the main program memory 24 are:
- a compound function construction program 25, which has the role of
generating compound functions by assembling together a number of elementary
functions EF. The latter are typically signal or data processing functions that can
each be considered as a single unit operator or module that produces a determined
technical effect on the signal data Si of an audio file or on the output of another
elementary function, and
- a function execution program 27, which is composed of the compound
functions themselves, these being exploited no longer as symbolic objects, but as
executable algorithmic entities for producing technically meaningful operations on
signal data S.
-
These two programs 25 and 27 are under the overall control of a master
program 29 which manages the overall system 2.
-
The compound function construction program 25 is based on genetic
programming techniques following an artificial intelligence (AI) approach.
Accordingly, the elementary functions EF are also handled as symbols, whereby
they are treated as first class obj ects in their symbolic representation.
-
Thus, the system 2 is capable of handling the elementary functions both as
objects, when executing the compound function (CF) construction program 25, and
as executable operators, notably for evaluating and testing the compound functions,
when executing the function execution program 27. To this end, these two
programs 25 and 27 use languages adapted respectively to handling objects and to
carrying out numerical calculations, an example of the latter being the "Matlab"
language.
-
Table I gives a non-exhaustive example of elementary functions stored in the
elementary function library 12, together with their operand type Top, output type
Tout and parameters.
sample list of elementary functions used by the system 2. |
I.1 ― Mathematical functions |
Function name | Operation | Param Pin | Toper | Tout |
DERIV | Time derivative | - | Signal | Signal |
MAX | Max value of set | - | set of No.s | No. |
MIN | Min value of set | - | set of No.s | No. |
SQUARE | Raise power 2 | - | No. | No. |
LOG | Logarithm | - | No. | No. |
MEAN | ave value of set | - | set of Nos. | No. |
VAR | variance of set | - | set of Nos. | No.s |
ABS(V) | Absolute value |V| | - | signed V | unsigned V |
SUM | Summation of terms | | No. | set of No |
SQRT | Square root | - | No. | No. |
POWER | Raise power 'i' | Integer i | No. | No. |
I.2 ― Signal processing functions |
Function name | Operation | Param Pi | Toper | Tout |
ENV. | Envelope of signal | - | Signal | Signal |
FFT | Fast Fourier transf. | limits | Signal | Signal |
stFFT | short-time FFT | limits/time | Signal | Matrix/Vector |
AUTOCOR | autocorrelation | - | Signal | Vector |
COR | correlation | - | Signal/Signal | Vector |
LPF | Low-pass filter | Fcutoff/atten. | Signal | Signal |
HPF | High-pass filter | Fcutoff/atten. | Signal | Signal |
BPF | Bandpass filter | Flow/Fhigh/atten. | Signal |
Signal |
FLAT | Flatness | | Signal | No. |
E | Energy | | Signal | No. |
PITCH | Pitch | - | Signal | No. |
1.3- Combining and connecting functions |
Function name | Operation | | Para Pi - |
COMPOSITION o - |
LOOP | Repeat until | No. iterations |
( | bracket |
COMBINATION * | Multiply | | - | - |
÷ | Divide | - | - |
+ | Add | - | - |
- | Subtract | - | - |
-
The last four combination operators are simply arithmetic operators which
join successive functions, but are treated as functions too.
-
Advantageously, when the system handles the elementary functions as
symbols, as in the above construction phase, it uses a tree structure.
-
According to the tree structure, a compound function CF is symbolised in
terms of nodes, where each node corresponds to one elementary function EF, and in
which branches connect the nodes according to the arithmetic operators +, -, *, ÷
used.
-
As an example, figure 7 illustrates the tree structure for the compound
function CF = MAX.DERIV.FFT.FFT.LPF(B1)(S) + ABS.PITCH.LPF(B2)(S) +
PITCH.HPF(VARIANCE(S))(S). The three terms are developed along three
respective branches Br1-Br3. The three branches join at the "+" function, which is
the common link to CF. The order of appearance of the elementary functions is
followed along successive nodes, the first elementary function (i.e. the first to
operate on the signal) being nearest the free end of its branch.
-
The CF construction program 27 initially begins by selecting and
aggregating elementary functions in a random fashion.
-
Elementary rules and heuristics intervene in this random process to govern
the appropriateness of combinations of elementary functions, notably as regards the
incorporation of a potential elementary function in the context of any elementary
function already present in term under construction.
-
Firstly, rules govern the function generation process on a number of different
considerations, among which are:
- i) Formal rules. These rule out the existence of two combined elementary
functions EFbEFa if their types are not compatible. In other words, if for the above
two functions the output type Tout(a) of EFa is not the same as the operand type
Toper(b) of EFb, then EFbEFa, and elementary function EFa has already been
selected, then elementary function EFb is attributed a zero weighting coefficient for
the random draw that is to select an elementary function for which elementary
function EFa is the operand. For example, the formal rule weighting scheme would
forbid the meaningless operator combinations FFT.MAX.DERIVABS(V), etc.
The formal rules also ensure that the right-hand most function of a term in
the compound function has a signal operand type (Toper=S), given that it will
necessarily operate on the signal Si from an audio file.
- ii) Boundary condition rules. These rules serve to impose constraints on
the compound functions or their populations having regard to the system
parameters, such as: length constraint on the compound functions, by weighting the
number of elementary functions used to favour a prescribed median value, the
number of branch points (cf. the tree structure), the number of compound functions
produced to form a first population P, etc..
-
-
Secondly, knowledge-based heuristics generally operate by associating to
each elementary function EF a weighting coefficient affecting its random draw
probability. These coefficients are attributed dynamically according to immediate
context. The heuristics can in this way rule out some combinations of elementary
functions through a zero weighting coefficient, at one extreme, and force
combinations by imposing an absolute maximum value coefficient at the other
extreme. A set of intermediate weighting coefficient values is provided to allow the
random process to determine the construction of compound functions, albeit with
constraints. These heuristics are generally derived from experience in using the
system and the user's formal or intuitive knowledge. They thus allow the user to
inject his or her know-how into the system and afford a degree of personalisation.
They can also be generated by the system itself on an automated basis, using
algorithms that detect similarities between compound functions that have been
recognised as successful.
-
By using the range of attributable weighting coefficients in implementing
these heuristics, the system user can use them:
- i) as a positive influence, i.e. to encourage the presence or combinations of
elementary functions that are of interest. For example, the system uses a knowledge
based heuristic to favour the presence of two successive FFTs on a signal S, i.e.
FFT.FFT(S), this being found to be conducive to interesting results;
- ii) as a negative influence, i.e. that on the contrary to seek to prevent
elementary function combinations that are considered to be ineffective or
technically inappropriate. For instance, it has been found that the presence of three
successive FFTs on a signal S, i.e. FFT.FFT.FFT(S) does not usually produce
interesting results. The corresponding heuristic used by the system will thus give a
low weighting coefficient to an FFT elementary function in the draw for the
elementary function to be the operand on the existing combination of FFT.FFT.
-
-
Before the newly-formed compound functions are processed, they are
advantageously submitted to rewriting by application of rewriting rules stored in
database 15. Rewriting involves recasting compound functions from their initial
form to a mathematically equivalent form that allows them to executed more
efficiently. It is governed by a set of deterministic rewriting rules of varying levels
of complexity which are executed on each function CFi of the population by the
main processor 22, those rules being in machine-readable form.
-
Simple rewriting rules eliminate self-cancelling terms in a compound
function. For instance, if the compound function considered contains the terms
HPF(S, Fa)+FFT(S)- FFT(S), the rewriting rules shall tidy up the expression and
reduce it to HPF(S, Fa).
-
Another category of rewriting rules eliminates elementary functions that are
redundant given their environment, i.e. which do not produce a technical effect. For
instance, if an expression contains a bandpass filtering function with a passband
between frequencies Fb and Fc, then the rules would eliminate any subsequent
function in that term which filter out frequencies outside that passband range, i.e.
which are no longer present.
-
Other rewriting rules conduct simplifications of a more advanced type. For
instance, they will replace systematically the expression E(FFT(S)) by the
equivalent, but more easily calculable, expression E(S).
-
The implementation of the rewriting rules uses the tree structure of the
compound function under consideration. Each node, or section of the tree, is
scanned against the set of rewriting rules. Whenever a rewriting rule is applicable
to a node or a succession of nodes of the part of the tree being analysed, the node or
succession of nodes in question is rewritten according to that rule and replaced by a
new tree section or node that corresponds to the thus rewritten ― and hence
simplified ― form of the compound function.
-
Each time the tree is modified in this way, it is scanned again, as its new
form can create new opportunities for applying rewriting rules that were not
evidenced in the previous form of the tree. Accordingly, the tree scanning is
repeated cyclically until no changes have been brought for a complete scan.
-
To ensure that there is no risk of falling into infinite loops, the rewriting
rules do not produce a change that in itself leads to another change, and conversely,
ad infinitum. For instance, the system would not contain simultaneously a rule to
rewrite A+B as B+A and another rule to rewrite B+A as A+B (in fact, this would be
the same rule, infinitely applicable to the result of its own production, and therefore
yielding an unending loop)
-
Once the population P of compound functions has been formed in
accordance with the above heuristics and rules, the compound functions cease to be
considered as symbolic objects and are treated instead by the function execution
program 27 according to their specified functional definitions.
-
Specifically, a compound function CFi (1≤ i ≤ n) is treated by the system 2
as a calculation routine using "Matlab" language and made to operate on the music
file data signals Sj (1≤j≤m) stored in the learning database 10 to produce an output
value Dij=CFi*(Sj). The signal Sj in question corresponds to a digitised form of an
amplitude (signal level) evolving in time t, the time frame of t typically being on the
order of 200 seconds in the case of a music title.
-
Each of the n compound functions CF1-CFn operates in this way on each of
the m titles stored in the learning database 10, thereby producing a total of n.m
output values Dij (for i=1 to n and j=1 to m) according to a matrix for the
population P. This combination of calculation events is illustrated symbolically in
figure 8.
-
As shown in figure 8, the n.m output values are mapped in matrix MAT(P)
which is stored in a working memory of the main processor 22. These values are
accessed at a subsequent stage of evaluating the overall fit of each of the n
compound functions CF1-CFn with the descriptor De for which the grounded truths
Dgt1-Dgtm were produced. This evaluation is carried out by standard statistical
analysis techniques. In the illustrated example, each of the output m.n output values
of the matrix MAT(P) is compared with its respective corresponding grounded truth
descriptor value Dgti. Specifically, the set of m.n values Dij is analysed against
corresponding grounded truth descriptor values Dgt1-Dgtm for the descriptor De
ascribed to the respective music titles T1-Tm.
-
For a given compound function CFi, the analysis here involves comparing
the value Dij with the Dgtj value for the corresponding audio file. This comparison
is performed for each of the audio files, so yielding m comparison values. These
comparison values are submitted to statistical analysis to obtain a global fit ― or
fitness ― value FIT(afj) with respect to the descriptor De for that function CFi. The
global fitness value FIT(afj) expresses objectively how well overall the descriptor
values generated by the function CFj match ― or correlate ― with the corresponding
grounded truth descriptors Dgt1-Dgtm.
-
The global fit in question is evaluated in the form appropriate for the
descriptor, for instance numerical closeness for a numerical descriptor, Boolean
correspondence for a Boolean descriptor, etc.
-
The above comparisons and statistical analysis are conducted for each of the
n compound functions CF1-CFn, and the respective fitness values FIT(af1)-FIT(afn)
are stored.
-
Then a new population P1 of r compound functions is produced by taking
for its members those of the n compound functions CF1-CFn which yield the r best
overall fit values (r<n).
-
The basic comparisons and analysis in conducting the above procedure is
indicated in the algorithm below:
-
For CF1: comp. D11 with Dgt1; D12 with Dgt2; D13 with Dgt3; ...; D1m
with Dgtm => STATISTICAL ANALYSIS => fit of CF1 with respect to descriptor
De = FITaf1(De);
-
For CF2: comp. D21 with Dgt1; D22 with Dgt2; D23 with Dgt3; ...; D2m
with Dgtm => STATISTICAL ANALYSIS => fit of CF2 with respect to descriptor
De
= FITaf2(De)
-
For CF3: comp. D31 with Dgt1; D32 with Dgt2; D33 with Dgt3; ...; D3m
with Dgtm => STATISTICAL ANALYSIS => fit of CF3 with respect to descriptor
De = FITaf3(De) ;
....
-
For CFn: comp. Dn1 with Dgt1; Dn2 with Dgt2; Dn3 with Dgt3; ...; Dnm
with Dgtm => STATISTICAL ANALYSIS => fit of CF3 with respect to descriptor
De = FITafn(De).
→New population P1 = set of r compound functions CF yielding the r best
fits FITaf(De).
-
The r compound functions CF(1)1 to CF(1)r of the new population P1 are
then processed in their symbolic object form according to the above-described tree
structure. The aim here is to generate from that population P1 a next generation
population P2 of compound functions. Advantageously, the system achieves 2 this
by using genetic programming techniques. These programming techniques model
aspects of biological regeneration or reproduction process naturally ocurring at
chromosone level, such as crossover and mutation. In this case, the analogue to a
chromosone is an elementary function EF in its symbolic representation.
-
Genetic programming is in itself well documented, but hitherto reserved
only to fields remote from electronic signal processing. Remarkably, it can be
implemented to a great advantage in the present field by virtue of the present
approach in which the compound functions question, whose primary purpose is to
operate on an electronic signal, are conveniently made exploitable, at critical phases
of their elaboration process, as symbolic objects. This "object" form, which
advantageosly uses the above-described tree structure, thereby becomes amenable to
genetic programming using standard knowledge of applied genetic programming.
Accordingly, detailed aspects involving normal knowledge of genetic programming
language and practice accessible to a person skilled in the art of genetic
programming shall not be detailed in the present description for reasons of
conciseness.
-
The concept of genetic programming applied to the present signal procesing
functions CF is illustrated in connection with two interesting aspects: crossover and
mutation. Each is implemented with adapted and specific rules and heuristics stored
in the heuristics database 14 and the rules database 15. Among the rules and
heuristics applied in the context of genetic programming are the formal and
boundary condition rules, and knowledge-based heuristics outlined above, and
adapted to circumstances. Overall, the rules and heuristics applied ensure that the
compound functions resulting from genetic programming operations are formally
acceptable, have a potential for exhibiting an improvement (in terms of fitness)
compared the functions from which they are generated, and remain within the
system's operating limits.
-
Crossover. Simply stated, crossover involves taking two compound
functions, say CF(1)p and AP(1)q, (for population P1) and creating from them a
new function CF(1)pq which contains a mixing of functions CF(1)p and AP(1)q, in
a manner analogous to two chromosomes combining to form a new chromosome.
-
An example of a new function CF(1)pq produced by crossover of functions
CF(1)p and AP(1)q is illustrated by figure 9 using the tree representation. In this
representation, the elementary functions are designated in their abbreviated form:
ep1-ep10 for compound function CF(1)p and eq1 to eq10 for compound function
CF(1)q.
-
Crossover is carried out by a crossover generator module 33 forming part of
the compound function construction program 25 stored in memory 24. The module
33 receives the two functions CF(1)p and CF(1)q as input and analyses their tree
structure using a set of stored crossover rules and heuristics. The analysis seeks to
determine, for each function, a suitable break point along a branch. The break point
divides the tree in question into a portion that is to be rejected and a portion that is
to be retained. In the example, it can be seen that for compound function CF(1)p,
the part of the tree structure comprising elementary functions ep7 to ep10 is
retained, and the part on the other side of the break point comprising elementary
functions ep1 to ep6 is rejected. Similarly for compound function CF(1)q, the part
of the tree structure comprising elementary functions eq1 to eq6 is retained, and the
part on the other side of the break point comprising elementary functions eq7 to
eq10 is rejected. The two retained portions of the respective trees are joined
together at their respective break points. This is carried out by attaching with a
straight branch the nodes of the respective retained parts lying adjacent the break
points. Thus, in the illustrated example, node eq6 is attached by a branch to node
ep7. The resultant crossover tree corresponding to compound function CF(1)pq is
then composed of elementary functions eq1-eq6, ep7-ep10.
-
More complex crossover operations can involve extracting at least one
section of a tree (not necessarily an end section) and inserting it within another tree
by producing one or several break points in the latter depending on where it is to be
accommodated.
-
The break points are determined in a guided ― or constrained ― random draw,
in which the guidance is provided by a set of crossover rules and heuristics.
-
A first such rule is of the formal type, and requires that two nodes
susceptible of being joined together must be formally compatible from the point of
view of types, as described above in the context of formal rules. To this end,
candidate break points for the random draw are considered in mutually indexed
pairs, each member of the pair being associated to a respective tree. The
corresponding nodes to be joined are identified in terms of which ones correspond
respectively to the operand and the operating function among the pair. Only those
pairs of break points satisfying the formal requirements are accepted as candidates.
-
Thus, in the illustrated example, the rules in question shall ensure that
despite the crossover resulting from a random draw, the operand type Toper(ep7) of
elementary function ep7 is the same as the output type Tout(eq6) of elementary
function eq6.
-
Another rule is of the boundary condition type and requires that the break
point should preferably be at the central portion of the tree, e.g. by using weighted
random draws, to ensure that the size of crossover-generated compound functions
shall be statistically similar in size over repeated generations.
-
Finally, knowledge-based heuristics are tested on crossover-generated
compound functions. The operators in the new compound function are tested one by
one starting from the break point. The knowledge-based heuristics provide a
probability for each new operator, regarding which the compound functions is
accepted or rejected at each step.
-
Mutation. Mutation involves taking one compound function CF(1)s and
forming a variant thereof CF'(1)s. The variant can be produced by modifying one or
a number of the parameters of CF(1)s, and/or by modifying the function's structure,
e.g. by adding, removing or changing one or several of its elementary functions, or
by any other modification.
-
An example of a new compound function CF'(1)s produced by mutation of a
function CF(1)s is illustrated by figure 10. In this representation, the initial
compound function CF(1)s has a tree structure formed of elementary functions es1
to es7 as shown.
-
This function is inputted to a mutation generator module 34 forming part of
compound function construction program 25. The mutation generator module 34
produces on that function one or several mutations on a guided - or constrained -
random basis.
-
In the illustrated example, the outputted mutated function CF'(1)s happens to
differ from the inputted function CF(1): i) at the level of the elementary function
es6, which is a lo pass filter operator whose parameter P'(es6) now specifies a cut-off
frequency of 450 Hz instead of 600 Hz in its original form P (es6), and ii) at
level of elementary function es1, which is simply being deleted.
-
The mutation process is governed by mutation rules and heuristics, which
include formal rules that likewise ensure that any changed function remains
formally correct, and boundary condition rules which govern the nature and number
of mutations allowed, etc.
-
The system can implement other genetic programming operations. For
instance, it can produce a cloning, which involves taking one compound function
CF(1)t and forming a variant thereof CF'(1)t. The variant has exactly the same
functional structure as the original function CF(1)s. Only the values of the fixed
parameters are modified. For instance, if the original compound function contains a
low-pass filter with a fixed cutoff frequency value of 500Hz, a clone would be the
same compound function with a different cutoff frequency value of 400Hz for
instance. A cloning parameter can control the extent of the variations of the values
(for example +/- 10%). Note that cloning is simply a special ― and restricted ― case
of mutation in the sense described above.
-
The genetic programming procedure comprising the above crossover and
mutation operations (and possibly other operations) are applied to the population P1
of functions over a given period or number of cycles. When the procedure is
terminated for the population, there results a new population P2 of compound
functions which are the genetic descendants of those from population P1.
-
The number of compound functions CF(2) forming the population P2 is
made to be the same as for population P, so as to accommodate for a selection of the
r best fitness functions of that population to produce its own succeeding population
of functions P3. In order to keep the population size constant, the cumulated
proportions of compound function generated randomly (R%), by mutation (M%), by
crossover (CO%), and cloning(C%), has to be so that R + M + CO + C = 100%.
This consideration applies to all succeeding generations so that their populations do
not dwindle in the course of eliminating the lowest fitness functions. Thus, the
creation of new population typically calls for a repetition of the random creation
procedure (described above for randomly creating the initial population P) to top up
the population, given that crossover operations tend reduce the population (if C <
CO).
-
The new population P2 is then treated in the same manner as the initial
population P, starting with a phase undergoing rewriting rules (the rules and
heuristics listed above have already applied explicitly or implicitly to that
population P2 in the course of the genetic programming (crossover and mutation)
operations.
-
Accordingly, the correlation, or fitness of each compound function CF(2) of
the new population is determined against the grounded truth descriptor values Dgt1
to Dgtm for the descriptor De. The procedure here is just as for obtaining
population P1, and the algorithm described above applies mutatis mutandis by
replacing P with P1, and P1 with P2.
-
The result gives a new set of the r best compound functions CF(2)1 to
CF(2)r for the descriptor De, forming the new population P2.
-
The above procedure is carried out iteratively over a given number of cycles,
each cycle producing a new population Pu from the previous population Pu-1 by
genetic programming and a selection of the best compound functions for the
population Pu.
-
Implementation of heuristics.
-
Further aspects of the heuristics used by the system are outlined below,
notably for function generation (producing the population P) and genetic
programming.
-
A heuristic can be represented as a function which has for argument
(operand):
- i) a current term: one or more functions or a tree section, corresponding to
the existing environment in terms of the composition of elementary functions EF -
for instance the elementary function combinations that have already been produced
during an ongoing function construction process;
- ii) a potential term: likewise one or more functions or a tree section, for
which the possibility of incorporation into the current term is to be considered by
the heuristic.
-
-
The heuristic function produces from the above argument a result in the form
of a value in a specified range, e.g. from 0 to 10, which expresses the
appropriateness or interest of constructing a function in which the potential term is
branched (according to the tree representation) to the current term, e.g. as its
argument.
-
The range of weighting coefficients (which are here expressed to one
decimal) expresses quantitatively the following:
weighting coefficient
0 | potential term forbidden from random draw |
1 | of very little interest |
... |
5 | of medium interest |
9 | extremely interesting |
10 | potential term imposed (i.e. must be selected). |
The heuristic function(s) can come into play in the following example:
current term = LPF(500Hz).FFT.S
potential term (to become the argument (operand) of the current term) =
FFT.DERIV.FFT.S
-
A heuristic shall determine the appropriateness of creating the branching
where the "S" of the current term becomes "FFT.DERIV.FFT.S".
-
In the above case, one example of an applicable heuristic function is the
one, which is here designated "HEURISTIC 245", that on the one hand favours the
presence of two FFTs (FFT.FFT.(...), and on the other hand discourages the
presence of three FFTs (FFT.FFT.FFT.(....). It is catalogued in the
heuristics
database 14 as:
- HEURISTIC245:
- statement of purpose: "interesting to have FFT of FFT, but not FFT of FFT
of FFT";
- form: HEURISTIC245(current term, potential term);
- potential term weighting coefficient attribution procedure:
- if type of current term is FFT,
- AND if current term does not contain other FFT type terms,
- AND if type of potential term is FFT,
- AND if potential term contains an FFT,
- THEN : potential term's weighting coefficient = 0.1 {indeed, the
complete function would then have three FFTs, and a low weighting
coefficient is therefore attributed}
- ELSE: potential term's weighting coefficient = 8.0.
- Procedures and statements of which the above is an example can be
adapted to all other heuristics of the database 14.
Another heuristic function designated HEURISTIC250 is as follows:
- HEURISTIC250:
- statement of purpose: "give preference to a filtering on raw signals".
- potential term applicable: Filter class {LPF, HPF, BPF..}
- form HEURISTIC250(current term, filter class)
- potential term weighting coefficient attribution procedure:
- if current term contains FFT, THEN: potential term's weighting
coefficient = 0 {filtering is meaningless if an FFT is carried out beforehand},
- if current term contains CORRELATION, THEN: potential term's
weighting coefficient = 3 {if a correlation is carried out beforehand, filtering
is of doubtful use, but could nevertheless return an interesting value},
- ELSE: potential term's weighting coefficient =7 {if the current term
does not contain signal modification operations such as FFT,
CORRELATION, it is generally useful to filter the signal to retain just some
of its spectral components}.
Other heuristics can be implemented to take in account a given
context, or an indication of the descriptor De for which the compound
function is constructed. These are referred to as "context sensitive
heuristics".An example of a context sensitive heuristic is as follows:
- Context sensitive heuristic CSHEURISTIC280
- statement of purpose: "to treat problems pertaining to a sung voice
(presence, extraction, ....), whereby it is useful to use frequencies of the
human voice e.g. from 200 Hz to 1500 Hz";
- context = analysis of voice
- potential term to which it is applicable: Filter(lowF, highF)
- current term to which it is applicable: any.
- potential term's weighting coefficient attribution procedure:
- if lowF (of signal) is close to 200 HZ, potential term's weighting
coefficient is correspondingly high (e.g. 9 for 200 Hz, 8 for 300 Hz, etc.);
- if highF (of signal) is close to 1500, potential term's weighting
coefficient is correspondingly high (e.g. 9 for 1500 Hz, 8 for 1400 Hz, etc.).
-
-
A further class of heuristics, known as "reference base sensitive
heuristics" takes into account the global nature of the signals in the learning
database 10. The latter is expressed by a quantity referred to as "global
reference indicator"
-
These heuristics therefore additionally have this global reference
indicator as their parameter. The latter can also be for instance a set of
descriptors taken out from that reference database.
-
They enable to select functions in dependence of the nature of the
reference signals.
-
An example a of reference base sensitive heuristic is as follows:
- HEURISTIC465;
- form HEURISTIC465 (current term, potential term, global reference
indicator):
- statement of purpose: "indicate that it is particularly useful to use
FFTs when the reference database signals overall have a complex spectrum".
- potential term's weighting coefficient attribution procedure:
- if current term does not contain other FFT type terms,
- AND if potential term is an FFT,
- AND if the reference database signals have (for the most part) a
complex spectrum, with spectral characteristics SC1, SC2, ..
-
-
THEN: potential term's weighting coefficient = 9.
Caching technique.
-
The iterative loops used by the system 2 involve a considerable amount of
processing, especially for the steps of extracting a value Dij of a compound function
CFi for a signal data Sj. In order to maximise the efficiency of that task, the system
advantageously uses the prior results cache 16 as a source of precalculated results
that save having to repeat calculations that have previously been performed.
-
The corresponding caching technique involves analysing a compound
function under execution in terms of its tree structure, and thus involves both the
symbolic, object representation of the function and its exploitation as an operator.
-
Figure 11 is an example illustrating how the caching technique is
implemented. At a time t1, the system 2 is required to calculate the expression
MAX*FFT*LPFILTER(F=600Hz)*(Si) (F=cut-off frequency) that appears at a
branch Brp of a given compound function CFu(Si).
-
Assuming that the prior results cache 24 is initially empty at that stage, the
main processor 22 proceeds in a stepwise manner on the successive elementary
functions. Thus, it calculates LPF(S), F=600Hz at a first step i) and stores the result
as R1, then calculates FFT*R1 at a second step ii) and stores the result as R2, and
finally calculates MAX*R2, which yields the value for the term of branch Br1.
-
The above intermediate and final values R1, R2 and R3 are sent to prior
results cache 24 together with an indication of the parts of branch Br1 that generated
them. Thus, the cache records that LPF(Si), F=600Hz = R1,
FFT*LPFILTER(F=600Hz)*(Si) = R2, and
MAX*FFT*LPFILTER(F=600Hz)*(Si) = R3 in a two-way correspondence table.
Note that results are stored in the cache 24 for an operation on a specific set of data
contained in the signal data Si. The set in question can correspond to a
predetermined time sequence of the associated audio file, for instance
corresponding to one sampling event.
-
At a later time t2, the main processor 22 is required to calculate the value of
a branch Brq belonging to another function CFv(S). In the example, the branch Brq
corresponds to the term AVE* FFT*LPFILTER(F=600Hz)*(Si).
-
The cache 24 now no longer being empty, the main processor 22 proceeds to
determine first whether at least one function of that branch has already been
calculated and stored in the cache 24. To this end, it performs a scan routine on
branch Brq by determining whether the first function to be calculated, i.e.
LPFILTER(F=600Hz)*(Si) is indexed in the cache 24. The answer being yes, it
determines whether the first and second functions together, i.e.
FFT*LPFILTER(F=600Hz)*(Si) are indexed in the cache. The answer being again
yes, it determines whether the first, second and third functions together, i.e.
AVE*FFT*LPFILTER(F=600Hz)*(Si) are indexed in the cache. The answer this
time being no, it is thereby informed that the most useful result in the cache is R2=
FFT*LPFILTER(F=600Hz)*(Si). Accordingly the main processor 22 rewrites the
contents of branch Brj as AVE(R2) and calculates that value. The result of that
calculation R4, indexed to the function AVE(R2), or equivalently to the term AVE*
FFT*LPFILTER(F=600Hz)*(Si), is sent to the cache 24 so that it need not be
calculated in whole at a later stage.
-
The cache 24 is thus enriched with new results every time a new function or
term is encountered and calculated. The caching technique becomes increasingly
useful cache contents grow in size, and contributes remarkably to the execution
speed of the system 2.
-
In practice, the number of entries in the prior results cache 24 can become
too large for an efficient use of allowable memory space and search. There is
therefore provided a monitoring algorithm which regularly checks the usefulness of
each result stored in the cache 24 according to a determined criterion and deletes
those found not to useful. In the example, the criterion for keeping a result Ri in the
in the cache 24 is a function which takes into account: i) the calculation time to
produce Ri, ii) the frequency of use of Ri, and iii) the size (in bytes) of Ri. The last
condition can be disregarded if available memory space is not an issue, or if it is
managed separately by the computer.
-
After a given number of cycles or a given execution time according to a
chose criterion, the system 2 produces as its user data output a descriptor extraction
(DE) function 4 (cf. figure 1). The latter is the member of the latest generation
population Pf of compound functions CF(f) that has been found to have the best fit
for the descriptor De. The user output can produce more than one member of that
population, for instance the b best fit functions CF(f), where b is an arbitrary
integer, or those compound functions that exhibit a fit better than a given threshold.
-
The criterion for ending the loop back to creating a new population of
functions is arbitrary, an ending criterion being for example one or a combination
of: i) execution time, ii) quality of results in terms of the functions' fitness, iii)
number of generations of functions (loops executed), etc.
-
Preferably, before an composite function is finally outputted as a DE
function for future exploitation, it is validated against signals of other music titles
taken from the validation database 18. As these signals are not used to influence the
construction of the DE functions 4, they serve as a neutral reference on which to
check their effectiveness. The checking procedure involves determining the degree
of fit between on the one hand a descriptor value obtained by making a DE function
operate on a signal Sv of the validation database and on the other the grounded truth
descriptor value associated to the music title of that signal Sv. An overall
correlation or validation value is generated by statistical analysis over a given
number of entries of the validation database 18. If the validation value is above an
acceptable threshold, the DE function 4 is validated and thus considered to be
exploitable. In the opposite case, the DE function is rejected and another DE
function is considered.
-
Figure 12 is a flowchart illustrating some steps performed by the system 2 of
figure 2 in the course of producing a descriptor extraction function DE 4, these
being:
- inputting user input data to constitute the learning database 10 (step S2),
whereby the database comprises the set of reference signals S1-Sm in association
with their global characteristic values Dgt1-Dgtm pre-attributed,
- preparing a population P1 of functions CF1-CFr each composed of at least
one elementary function (EF) (step S4),
- modifying functions of the current population using programmed means
22, 25 that handle their elementary functions as symbolic objects (step S6),
- operating each function of the population on at least one reference signal
using means 22, 27 that exploit the elementary functions as executable operators, to
obtain a calculated value for each compound function of the population in respect of
the reference signal (step S8),
- for each function of the population, determining the degree of matching
between its calculated value and the pre-attributed value Dgti for the signal from
which that value has been calculated (step S10),
- selecting functions of the population producing the best matches to form a
new population P2 of functions (step S12),
- if an ending criterion is not satisfied, returning to step S6, where the new
population becomes the current population (step S 14), and
- if an ending criterion is satisfied, outputting at least one function of the
current new population as a general function (4) of the user output (step S16).
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Heuristics and/or rules can be entered, edited, modified through the user
interface unit 26 e.g. by manual input (keyboard) or by download, thereby making
the system fully adaptive and configurable.
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Typically, the system generates several hundred compound functions over a
twelve-hour period. The learning database preferable comprises at least several
hundred titles, and preferably several thousand. The handling of such large
databases is simplified by the use of the above caching technique and heuristics.
Parallel processing, where a same function is calculated on several titles
simultaneously using respective processors over a network can also be envisaged.
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The size of the compound functions is typically of the order of ten
elementary functions.
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The system is remarkable in that it does not need to be informed of the
descriptor De for which it must a find a suitable DE function. In other words, all
that is necessary is to provide examples of just the descriptor values Dgti associated
to music titles Ti and their signal data Si. This makes the system 2 completely open
as regards descriptors, and amenable to generating suitable DE functions for
different descriptors without requiring any initial formal training or programming
specific to a given descriptor.
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In the embodiment, the system is connected to a network, such as Internet or
a LAN, in order to facilitate the acquisition of music titles through a download
centre 36. The networking also makes it possible to share and exchange elementary
functions, compound functions, heuristics, rules and DE functions found to be
interesting, as well as results data for the prior results cache 24, allowing parallel
processing, etc. In this way, an interactive community of searchers can be fostered
and allow the a rapid spread of new developments.
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The heuristics and/or rules can be entered / edited / parameterised through
the user interface unit 26; they can also be generated / adapted internally by the
system, e.g. by processing techniques based on analysing compound functions that
produce the best fits and determining common features thereof expressible as rules
and/or heuristics.
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Figure 12 is an example of different DE functions and their fitness produced
automatically by the system for evaluating the presence of voice in music title.
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Figure 13 is an example of different compositions of DE functions in terms
of elementary functions, and their fitness produced automatically by the system to
evaluate the global energy of music titles.
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The method and data implemented by the system can be presented as
executable code forming a software product stored on a computer-readable
recording medium, e.g. a CD-ROM or downloadable from a source, the code
executing all or part of operations presented.
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From the foregoing, it will be appreciated that the above-described system is
remarkable by virtue of many characteristics, inter alia :
- its genericity: the system is independent of a given descriptor, and is able
to infer an extractor (DE function) for arbitrary problems;
- its heuristics: the system contains many built-in heuristics that guide the
search, and reduce the search space. The originality here is that the system encodes
heuristics specific to signal processing, and provides a way to evaluate the fitness of
a given function by testing it against a real database of music titles;
- caching, which greatly reduces the workload on the main processor 22 and
accelerates calculation considerably;
- rewriting, which provides the groundwork for ensuring that functions shall
be calculated in their most rational form;
- implementation: the aim is calculate functions on an automated basis,
rather than manually. In the respect, the embodiment can be likened to an expert
system in artificial intelligence, where it substitutes the role of the human specialist
in signal processing. Extracting descriptors automatically from the digital
representation of an acoustic signal in accordance with the invention allows to
scale-up descriptor acquisition, and also ensures that the descriptors obtained are
objective.
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The remarkable aspects of the present automated system 2 can be
appreciated from considering how the task would have to be considered in a manual
approach. The starting point is the raw data signals as seen by the specialist in
signal processing. The latter tries out various processing functions according to a
empirical methodology in the expectation that some rule shall emerge for
correlating complex signal characteristics with that descriptor. In other words, the
approach is extremely heuristic in nature. It is also largely based on trial and error.
-
This task of manually finding a combination of signal processing functions
by signal processing experts is time-consuming and subject to many subjective
biases, errors, etc. In most cases it would be too impractical to be considered in a
real-life application.
System applications.
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1. Fully autonomous automatic descriptor extraction function
generating system.
-
In the embodiment described above, the programmed system 2 is able to
generate an exploitable DE function 4 from scratch using just the user data input
indicated with reference to figure 1.
-
The DE function typically takes on the form of executable code or
instructions comprehensible to a human or machine. The contents of the DE
function thereby allow processing on the audio data signal of any given music title
to extract its descriptor De, the latter being referenced to the function.
-
The process of extracting in this way the descriptor De of a music title can
be performed by an apparatus which is separate from the system. The apparatus in
question takes for input the DE function (or set of DE functions) produced by the
system 2 and audio files containing signals for which a descriptor has to be
generated. The output is then the descriptor value Dx of the descriptor De for the or
each corresponding music title Tx. The DE function (or set of DE functions)
produced by the system 2 is in this case considered as a product in its own right for
distribution either through a network, or through a recordable medium (CD,
memory card, etc.) in which it is stored.
2. Descriptor extraction
-
It will be noted that the system 2 already includes all the hardware and
software necessary to constitute an automated descriptor generating apparatus as
defined in the preceding section. In this case, the DE functions shown as user data
output of figure 1 are fed back to the system (or kept within system and stored).
The system can be switched to the descriptor extraction mode in which audio signal
data corresponding to a music file Tx to be analysed is supplied as an input and the
corresponding music descriptor value of Tx for the descriptor De is provided as the
output.
3. Authoring tool for producing descriptor extraction functions.
-
In a variant, the system is implemented more as an authoring tool. In this
implementation, the system allows the outputted DE functions to be modified by
external intervention, generally by a human operator. The rationale here is that in
some cases, while the functions produced automatically may not be strictly optimal,
they are nevertheless highly interesting as a starting basis for optimisation, or
"tweaking". The advantage in this case resides in that the human specialist has at
his disposal a descriptor extraction function firstly which is already proven to be
effective compared to a large number of other possible functions, indicating that it
possesses a sound structure, and secondly which is proven to be amenable to fast
and consistent execution. Note that the DE function outputted by the system 2 can
generally be modified by intervening in this case too either at the level of the basic
elementary function taken as a symbolic object, e.g. by substitution, removal, or
addition, or at the level of the internal parameterisation of a basic elementary
function, e.g. by changing a cut-off frequency value in the case of the low-pass
filtering elementary function.
4. Evaluation tool for externally produced descriptor extraction
functions.
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The aspect of the system 2 that analyses and evaluates compound functions
can be put at the disposal of external sources of candidate DE functions, so as to
help designers evaluluate their own descriptor extraction functions. The evaluation
can be used to provide an objective assessment of the "fitness" FIT of such a
candidate function with respect to the learning database 10 or validation database
18.
5. Function calculation tool for externally produced DE functions.
-
Similarly, the function calculation potential of the system 2, enhanced
notably by the above-described rewriting rules and the caching technique, can be
put at the disposal of outside users. The latter can then input a given complex signal
processing function (not necessarily in the context of descriptor extraction) and
receive a calculated value as an output.
Scope
-
While the invention has been described in the context of a system adapted to
process audio file signal data to produce descriptor extraction functions DE, it will
be apparent that the teachings of the invention are applicable to many other
applications where it is required to analyse low level characteristics of an electronic
data signal (digital or analogue) in view of extracting higher-level information
relating to its contents. For instance, the invention can be implemented for
obtaining descriptor extraction functions operative on video or image signal data,
the descriptors in this case being applicable to visual contents, such as indicating
whether a scene is set at night or daytime, the amount of action, etc. Other
applications are in the fields of automatic cataloguing of sound, scenes, objects,
animals, plants, etc. through high level descriptors.