EP1960916A1 - Method for stable and linear unsupervised classification upon the command on objects - Google Patents

Abstract

The invention relates to a method for carrying out a linear unsupervised classification which makes it possible to structure a database, which consists of objects and descriptors and is stable upon the command of objects. The inventive method comprises a stage for pre-converting qualitative, quantitative or textual data items into binary presence-absence data items and the following stages consisting in determining a structural threshold a<SUB>s </SUB>according to<SUB/>n<SUP>2</SUP> agreements between classifiable objects, wherein said structural threshold defines an optimisation criterion adapted to the data items, in using descriptors in the form of generators for structuring and building the partition or assembly of classes and in progressively merging a class generated by a descriptor and a partition (40, 41, 42) for an optimisation criterion by using a function f (C<SUB>ii</SUB>, C<SUB>i 'i</SUB>) = Min(C<SUB>ii</SUB>, C<SUB>i 'i </SUB>) for linearizing the sums of minimum functions.

Description

 METHOD OF CLASSIFICATION NOT SUPERVISED LINEAR AND STABLE ON THE ORDER OF OBJECTS

The invention relates to a method of unsupervised classification linear and stable on the order of objects.

It relates more generally to automatic classification techniques known as "clustering".

It is used in particular in the fields of "Data Mining" and

"Text Mining" for the discovery, without a priori, knowledge (or "knowledge discovery") in large databases. These data can be of structured type when it comes to behavioral or demographic data for example, or of unstructured type when it comes to textual data.

Starting from a database consisting of a set (or population) of n objects described by a set of m descriptors (or variables), the automatic classification consists in structuring these objects in the form of very homogeneous classes (or groups). This homogeneity reflects the fact that two objects of the same class must be more similar (or similar) to each other than two objects belonging to two distinct classes. The constitution of these classes will make it easy to detect groups of objects with similar profiles or themes depending on whether they are structured or unstructured data.

This problem is highly combinatorial to be solved by an exact method. For this purpose, less expensive heuristics in terms of processing times and machine resources have been developed to find approximate solutions.

Some of these heuristics propose solutions by arbitrarily fixing the number of classes, while others propose a hierarchy of partitions with variable number of classes. For example, the following heuristics can be cited:

® "mobile centers" type methods such as "k-means", dynamic clouds ...

• Hierarchical classification methods (ascending or descending) • The "first representative" or "first leader" methods.

Examples for different unsupervised classification methods are given in the following references: 1) Saporta G. (1990),

Probability, Data Analysis and Statistics, Technip; 2) Lebart et al (1995),

Multidimensional exploratory statistics, Dunod; 3) Hartigan, J. (1975),

Clustering Algorithm, John Wiley and Sons, New York, NY, US.

The "mobile centers" and hierarchical classification methods arbitrarily set a number of classes. As for "first leader" methods, they require the setting of a similarity threshold and are dependent on the order in which the objects are taken into account. Indeed, they can lead to completely different results depending on the order in which the objects are stored. Nevertheless, they allow to process, in reasonable times, large amounts of data. However, to obtain these performances, these methods require the fixing of a maximum number of classes very small compared to the number of objects.

Among the major problems encountered, to answer the problem of the automatic classification, we can mention:

• the determination of the number of classes underlying the population in question,

The performances in treatment time according to the volumetrics to be treated and in terms of the quality of the homogeneity of the classes obtained,

• the power of interpretation of the results obtained; definition of statistical indicators for the measurement of the homogeneity of the classes as well as the discriminating power of the descriptors participating in the formation of these classes.

The idea of the present invention relies in particular on the theory of relational analysis. As a reminder, this theory, as described in one of the following references: 1) P. Michaud and JF Marcotorchino, "Optimization Models in Relational Data Analysis", Mathematics and Human Sciences, No. 67, 1979, p7-38; 2; JF Marcotorchino and P Michaud, "Aggregation of similarities in automatic classification", Journal of Applied Statistics, Vol 30, n ° 2, 1981, makes it possible to answer the problems of determining the number of classes and the interpretation of the result obtained. However, the underlying theoretical model is extremely expensive in terms of machine resources as soon as the number of objects is greater than 100. The invention uses a heuristic of this theory which makes it possible to very finely approximate the theoretical result on large numbers of objects. data base.

The invention relates to a linear unsupervised classification method for structuring a database of objects and descriptors, which is stable on the order of the objects comprising a preliminary step of transforming qualitative, quantitative or textual data into data. binary presence-absence characterized in that it comprises at least the following steps: a) determining a structural threshold _s function of the n ² agreements between the objects to be classified, the structural threshold defining an optimization criterion adapted to the data, b) use the descriptors as generators of structuring and construction of a partition P or set of classes, c) gradually merge a class generated by a descriptor and a partition (40, 41, 42), d) for a criterion of optimization involving a function f (C _n , C _ιV ) = Min (C _π , C _ιY ) linearize sums of functions Minimums.

The method may comprise a step where the classes of the partition are grouped together.

The merging step c) comprises, for example, a step in which the best operation (in the sense of the optimization of the criterion) of the following 4 is determined from two classes in intersection:

• "Breakage" of the first class and formation of two classes; • "Breakage" of the second class and formation of two classes;

• "Breakage" of the two classes to form three classes;

• Meeting of the two classes in intersection to form a single class.

The grouping of the classes of a partition is, for example, carried out on several hierarchical levels and comprises the following steps: • reduce the value of the structural threshold at each level so that weakly negative contributions can become positive,

® maximize links between built classes where links are determined using the contribution of a pair of objects Link (C _q , C _q ,) = Σ Σ Contrib ,,, = Σ Σ C _n , - α'x / _(C;, C ₁ ,,,) içCqi'≡Cq 'l≡Cqi'≡Cq' with α Ia new value of a

® group two classes with a positive link, and repeat this process on all levels.

The invention also relates to a linear unsupervised classification device for structuring a database composed of objects and descriptors, which is stable on the order of the objects comprising a preliminary step of transforming qualitative, quantitative or textual data into binary presence-absence data characterized in that it comprises at least the following elements: a computer comprising a memory, a database and a processor adapted to implement the steps of the method having one of the characteristics previously stated.

The invention notably has the following advantages:

• the ability to automatically detect the number of classes during the ranking,

• the ability to process large amounts of data in reasonable time,

® independence from the order of the objects of the base. It is naturally stable with respect to the order of treatment of objects, • the method makes it possible to define and calculate very quickly (linear complexity) indicators measuring the quality of the results obtained,

• the process is stable with respect to the duplication of objects. In other words, if we multiply the base several times, we find the same initial solution with the duplicated objects within the same class.

Other features and advantages of the present invention will appear better on reading the description below and appended figures which represent: FIG. 1, a diagram corresponding to a generic system of a system supporting the method according to the invention,

FIG. 2, a block diagram describing the general operation of the processing chain of the field of data mining applied to a body of documents or to a digital database,

FIG. 3, a block diagram which shows the steps of the preprocessing phase which is carried out before the automatic classification process,

FIG. 4, a block diagram which represents the scheduling of the steps constituting the method of this invention,

FIG. 5, a block diagram which details the various operations performed during the processing 41 of FIG. 4,

• Figure 6, the basic operation of determining the optimal local partition (in one, two, or three classes) from two classes in intersection,

FIG. 7, the quantities evaluated during the basic operation described in FIG.

• Figure 8, a block diagram that shows the steps of the class hierarchical aggregation process.

FIG. 1 illustrates, without limitation, an example of application of the method according to the invention, making it possible to automatically generate various actions to be performed from the classification result.

The system on which the process operates comprises, for example, a computer 1 comprising a memory 2, a processor 3 associated with the classification process 5. The computer 1 is linked to a database 4. The classification result is presented for example, in the form of a set of classes stored in a suitable device 6. The device 6 is, for example, in connection with a server 7 sending e-mail for example. The server is provided with appropriate processing means known to those skilled in the art for processing the received class information and triggering mechanisms for sending messages to the persons of the classes concerned.

Any device for driving and / or driving actions according to the results of the classification may be used. The description which follows is given for illustrative purposes in a general context of instructions executable in a computer program, such as program modules executed by a computer or any other computer.

The invention can be implemented on any type of computer, electronic organizer, etc.

In Figure 2, the starting point can be either any database (set of individuals described by a set of numeric variables), or any body of documents. These two types of data are represented by the rounded blocks 20 and 25, respectively. In the case of digital data, there may be an optional pre-processing phase 21 which consists of conventional statistical processing such as centering or data reduction or else transformations ... etc. These pre-treatments lead to the data table 22. It is this table that constitutes the source of the information analysis treatments. With regard to a body of documents, during a pre-processing phase 26 each text is transformed into a vector whose dimensions correspond to descriptors obtained by a linguistic process which can be morpho-syntactic analysis, extraction of concepts, extraction of co-occurrences ..., linguistic and semantic processing etc. . We then obtain a presence-absence (binary) or frequency matrix 27 which constitutes the source of the processing represented by block 23.

Block 23 corresponds in particular to the data processing and analysis phase. These treatments can be of several types (supervised classification, unsupervised classification, statistical notation or "scoring", regression ...). In the context of the invention, it is unsupervised classification of data also known as automatic classification or "clustering" (Anglo-Saxon term). The invention particularly relates to an unsupervised classification method, the result of which is, for example, a hierarchy of partitions of the objects 24 or documents 28 according to the initial data type.

The input data of FIG. 3 are in the form of a table T, 22 or 27, respectively denoting the cases of numerical data and the case of corpora of documents, crossing the set /, consisting of n objects O ₁ , O _j , ..., O _n (individuals or documents), and the set V consisting of m variables (or descriptors), V ¹ , V ² , ..., V "measured on /. I = {θ _v O ₂ , ..., O _n ) v = {v \ v ² , ..., vή

Table T has the general term t _lk which represents the value taken by the variable V ^k on the object O ₁ and is in the following form:

The general term t _ιk , input data, represents:

• the modality of the variable k taken by the object i in the case of a qualitative variable, • the value of the variable k taken by the object i if it is a quantitative variable, ® the presence or the absence of the lexical unit k in the document /, if it is textual data.

In the case of qualitative and quantitative data, the method applies on this table re-coding treatments described below, for example the discretization of quantitative variables or the recoding of qualitative variables into presence / absence descriptors. The qualitative and quantitative variables are transformed into binary variables which will constitute a table K of presence-absence.

In the case of qualitative variables, the transformation consists, for example, in a re-coding of the modalities into presence-absence descriptor vectors.

For quantitative variables, these are discretizations that consist of transforming quantitative variables into qualitative variables where each modality corresponds to an interval. For example, the quantitative variable "size" expressed in cm and measured on a set of individuals. suppose that in the population considered, the size of the individuals constituting it is between 140 cm and 210 cm, a possible discretization would be to cut the variable in three following intervals [140,160 [; [160.180 [; [180.210]. These three intervals then correspond respectively to the three following modalities: small, medium and large. Therefore, an individual who has the size 175 cm for example, will after discretization the average modality.

Table K, 31, of general term k obtained after these transformations will be of the following form:

Its general term k _I} can have two meanings depending on whether it is initially qualitative variables or quantitative variables:

In the case of a qualitative variable, k _υ has the following definition:

_ [1 if object i has the modality j

77 i

J [0 otherwise In the case of a quantitative variable, k _is the following definition: i fl if the object belongs to the segment j K j - \

J [0 otherwise

In the case of textual data, there is no recoding step since at the end of the pre-processing step, 26, we already obtain a presence-absence binary array K whose general term k _is for meaning: 1 if the document has the lexical unit i j 0 otherwise Each variable in Table T, whether qualitative or quantitative, will generate several presence-absence descriptor vectors. Indeed, the tables T and K are of different dimensions.

Consider the variable "CSP" (Socio-Professional Category) and suppose that we are in the presence of four individuals (11, 12, 13, 14). Suppose that the possible modalities of the variable CSP are: manager, worker, liberal profession. Suppose, moreover, that these four individuals have the following modalities:

After recoding the modalities of the qualitative variable CSP, we obtain the following result:

Each category of the variable considered therefore becomes a presence-absence descriptor. Therefore, the table of transformed data K will be of dimensions {nxp) with p> m where m is the number of variable of set V.

From Table K, 31, statistical calculations are carried out, 32 (means, standard deviations, discrimination coefficients, etc.), which in particular make it possible, on the one hand, to parameterize the filtering of the descriptors, 33 (elimination of the descriptors not discriminating), on the other hand, to calculate an indicator called structural threshold, 34, which makes it possible to dispense with any parameterization of the classification process (non-fixation neither of a number of classes nor of a maximum number of classes ). The indicator is detailed later.

Filtering eliminates unclear descriptors. The elimination of the descriptors will be different according to the type of the latter. In the case of numerical data is based on an indicator of relevance of the descriptor.

In the case of documents, we use the frequency of occurrence of a descriptor throughout the body or any other indicator of discrimination measurement such as entropy ... and eliminates those which are, a priori, little discriminating. At the end of the filtering step, there is a new reduced bitmap, 35, which contains a small number of columns. It is this new table which serves as input data to the automatic classification process described by block 36 and detailed in FIGS. 4 and 5.

Structural threshold and criterion adapted to the data

The method according to the invention uses a structural or indicator threshold which has the particular function of defining an optimization criterion adapted to the data.

To better understand its role, we recall the theory of relational analysis that is based on maximizing the following simplified Condorcet criterion:

W ⁼ Σ, Σ = 1; = 1 I ^C, -i ^χ / ^(C ,, ^C,,) k. ' where C, represents the degree of resemblance between the two objects i and i. For example ;

and O ₁ represents the profile of the object O ₁ given by the i- ^th row of Table K:

0 ₁ = {k, ₁ , k _ι2 , -, k, _J , -, k _ψ ) and where f (C _π , C _iγ ) is a function of the maximal proper agreements of the individuals / ^' and i' For example: / (C _B , C _IV ) = | (C _B + C _IV )

f {C _u , C _ιV ) = Mm (C ₁₁ ^ ₁ ,,) etc ...

X _n , is also given by: ¹

Y _ 11 if objects i and i are in the same class ^zz 0 otherwise

The method according to the invention is of linear complexity insofar as the formulas of the type ΣΣC _n , and ^^ / (C 1, C _jV ) are computable

II 'II' linearly. The functions previously exemplified are all linearizable. Indeed, the similarity measure C _n used is a scalar product having known linearity properties, the function f (C _n , C _lY ) = - (C 1 + C, _V ) is linear, however, the function

f (C ₁₁ , C _n ) = Mm (C _n , C ,,,,) is not linear. However, one can linearize the calculations of the type ΣΣMin (C _n , C _lV ). i / '

The invention for illustrative purposes describes the particular case f (C _n , C _ιV ) - Min (C _n , C _lY ) particularly suitable for bases containing a large number of missing data and the procedures that make it possible to calculate with a linear complexity the Calculations of the type ΣΣMin (C _n , C _lV ).

The method according to the invention implements, for example, the following criterion:

C ^β ") = ΣΣ [C, -a χf (C _π , C _ή ,)] X _n ,

= 1 / '= 1

ΣΣContrib _u , X ,, ι = l ι '= ï

where a is a threshold and the quantity Contrib _n , the unit contribution of the two objects i and / 'to criterion C (JQ.

According to the invention, the structural threshold parameter a _s is calculated automatically. It is an indicator that is a function of the n ² agreements between the objects to be classified: We can give as an example, its formulation when it represents the ratio between the arithmetic average of the agreements between all the objects on the arithmetical average of their maximal chords. :

This formula is linearizable when one places oneself in the same conditions as those mentioned above. The criterion C ^a * (X) used in the invention consists, for example, in comparing the agreements between any two objects with the product of the threshold a _s by their maximum agreement (which represents a percentage of the maximum agreement).

Thus, two objects will be a priori in the same class as long as their similarity is greater than or equal to the calculated maximum agreement percentage (positive contribution).

Automatic classification method of the invention

The method of classification 36 is described in detail in FIG. 4. The starting point is the array of binary data whose descriptors have been filtered.

The first step of the classification process of sorting the descriptors, 40, is based on a measure of the contribution to the criterion of each descriptor (quality of a descriptor). For example, descriptors are used as "generators" for structuring the population of the objects to be classified. A descriptor is represented by a column vector of 1 and 0 (presence-absence). We associate with this descriptor a class which is composed of the objects whose value taken is 1. We can then calculate for each class of objects C _q its contribution measure Contrib (C _q ) to the global criterion:

Contrib (C _q ) = Σ Σ Contrd ,,, = Σ Σ C _n , - ax Σ Σ / (C ,,, C _n ,) [1] leCqi'eCq leCqi'eCq l≡Cqi'eCq The evaluation of the contribution of a class is of polynomial complexity. In fact, suppose that all the objects constitute a single class, it would then be necessary to calculate n ¹ unitary contributions in order to determine the value of the criterion.

In the case where C _n , is a dot product, the first part of the formula on the right,, is simplified as follows:

where R ^q = (r ⁹ , r ^{9 '} , • • • • •, r _p ^q ) is called a representative of the class C _q whose terms are given by the sum in column of each modality of the table K for the objects of the class: r? = Σk ,,.

I ^ Cq Each value r? , j = \, ..., p, represents the number of objects of the class C _q which has the modality /.

In the case where f (C _n , C _lV ) = MIn (C _n , C _ιV ), the second part of the formula on the right of equation [1] is equal to T ^ Mm (C ₁₁ , C _IV ). We give below the leCqi'eCq procedure allowing to compute with a linear complexity this quantity.

_***** ***** _{**************} ***** _********* ***** _* * _{***** *************************}

MinCC procedure (Class C)

Requires: CαrdC> 0

Requires: Sorted list of individuals for class C Integer: result - 0

Integer: j = next element of C

Integer: i = 0

As long as the class C is not traveled Make result = result + [(CardC -i) x2 -l] x C _M j = next element of C i = i + l

End as long as

_{************************************************** *********************************************} Thus, for each descriptor q, the value of the contribution of the class generated by the latter or a measure of the quality of the descriptor with respect to the criterion. This is followed by sorting, for example, in descending order of these contributions in order to obtain an order of taking into account the descriptors. The choice of this order has very little influence on the quality of the result (there may be some local differences). However, taking the classes generated by the descriptors of better contributions first, makes it possible to have a stable solution more quickly and thus to accelerate the process of calculating the best partition 41 resulting from the intersection between the current partition and that generated by a descriptor.

This process 41 consists in particular of "fusing" progressively 42, a class generated by a descriptor 40, and a current partition (composed of several classes). This "merge" operation consists in determining from two classes in intersection the best operation (in the sense of the criterion) among the following 4:

• "Breakage" of the first class and formation of two classes; ® "Breakage" of the second class and formation of two classes;

• "Breakage" of the two classes to form three classes;

® Meeting the two classes in intersection to form a single class. These operations are illustrated in FIG. 6 and the calculations making it possible to decide on the best operation in FIG. 7.

This process amounts to building step by step a partition which optimizes locally and progressively the global criterion.

Once all the descriptors are used, we consider the resulting partition P ₀ as a first finalized partition of the objects 43.

During the "merge" phase (40, 41, 42) of classes, we try to "merge" only classes that have intersections. The purpose of the processing 44 is to merge, that is to say to bring together classes that have no intersection if this operation makes it possible to optimize the criterion (class fusion test of the partition obtained between them) . This leads to a modified partition 45, or level 1 partition, which constitutes the final partition of the classification process.

This partition 45 constitutes the input of the class aggregation process, 46, which is described in FIG. FIG. 5 represents an example of a functional diagram of the treatment

41. The latter consists in particular of "merging" a new class generated by a descriptor X denoted C _x , 50, with the current partition P consisting of K classes 51. The process is as follows: • Calculation of the intersections between the classes of the partition P and the class C _x ,

52, • Sort of the set A of the classes C _y of the partition P in intersection with the class C _x in descending order of the cardinal of their intersection, 53, for example, • For each class C _y , 55, of set A, merge the two classes

C _v and C _x , 54.

We cross all the intersections between C _x and P and once all the classes C of A have been merged with C _x , 55, we obtain a new partition of the objects which improves the global criterion and which then becomes the new current partition 51 The next step is to move to a new descriptor, 42, and repeat this process until all descriptors have been traversed.

The cardinal of the elements of the set of intersections of a class C _x with the classes of a partition P, 52, can be obtained linearly in the manner described hereinafter.

Class C _{x is considered} as the class whose intersection with a partition P is to be evaluated. In this class, we associate a sorted list, for example, in ascending order of the indices of the objects it contains. Indeed each object is identified by a unique integer which is its index. To sort the objects, one uses for example a linear sorting (for example the sorting by base whose reference is the following one: Cormen et al (2002), Introduction to the algorithmic, Dunod) since one knows the upper bound of values to sort. For the operation of calculating the cardinal of the intersections, we use a vector A of dimension n for which each dimension i represents the index of the class where the individual O ₁ is stored.

Example of calculation of intersection cardinals:

If we take a population of 6 objects O ₁₁ O ₇ , - - -, O ₆ and a current partition of these objects P, 51, consisting of three classes

The vector A is equal to:

Thus if we "merge" the existing partition with a class C _x = [O ₂ , 0 ₃ , 0 ₄ , 0 ₆ ] 50, we are able to quickly find the cardinal of the intersection set of the class C _x with the classes of the existing partition, in this case

Cαrd (lnter (C _x C _x )) = 1, Cαrd (lnter {C ₂ C _x )) = 3 and Cαrd (lnter (C _χ C _x )) = 0. The number of operations performed when calculating intersections 52 is equal to the number of objects in the class C _x to merge with the partition P. Indeed, we look for each object of the new class if it belongs to a class of the partition P, if yes we increment the intersection counter of this class.

If there are several intersections between a class C _x and a partition P, we calculate as indicated above, the cardinal of the different intersections between C _x and the different classes C _y of the partition P in order to have a take order into account.

From the intersection of C _x and a class C _y of partition P, we evaluate what is the best configuration among those present in FIG. 6. For this, the quantities identified in FIG. FIGS. 6 and 7 therefore explain an example of basic operations of the invention represented by the processing 54. The process of "merging" two classes is, for example, the following.

Let R ^x and R ^{y be} the vectors representing classes C _x and C _y , let the vectors R ^a , R ^b and R ^{c be} defined by:

R "= R ^y -R ^c R ^b = R ^X -R ^C where C _c -C _x is the class defined by the intersection of C _x and C (the objects in both the class C _x and in C _y ) and R ^{c is} its representative. R "therefore represents the objects which are only in C _y and R ^b those which are only in C _x .

At will define respectively CardA, CardB and CardC as the cardinals of the classes represented by R ", R ^b and R ^c .

The two lists of objects contained in the classes C _y and C _x are sorted in ascending order of their index. We can therefore apply the following standard procedure to quickly calculate the three vectors:

_{************************************************** ****************************************} Vector Calculation Procedure (Class C _x , Class C _y )

R ^α = R ^y

R ^b = R ^X

R ^c = 0

CαrdA = CαrdB = CαrdC = 0

L ₁ = list of objects of C _y e = head of the list L _x L ₂ = list of objects of C _x / = head of the list L ₂

As long as the list L ₁ is not traversed Make As long as the list L ₂ is not traversed Do If e = f Make R ^e = Ô. R "= R ^a - R ^e R ^b = R ^b - R ^e

R ^c = R ^C + R ^e e = head of the list L ₁ f = head of the list L ₂ cardC = cardC + 1 Else If e </ Do e = head of the list L ₁ cardA = cardA + 1 Else

/ = head of the list L ₂ cardB = cardB + 1

End If End As long as

End as long as

_{************************************************** *********************************************} From these three vectors, it is possible to choose the best solution from the following four, the latter being represented on an example in Figure 6:

© "break" the class C _y to form the two following classes: C _y - C _x and

C _x ® "break" the class C _x to form the two following classes: C _x - C ₁ , and

® "break" the class C _x and "break" the class C _y to form the following three classes: C _x - C _y , C _y - C _x and C _y n C _x • merge the two classes to form a single class . C u C _(choosing the best of the four solutions is based, for example, on the assessment of "links" between different 3 subclasses highlighted below above. The general calculation of the "link" between two classes C _q and C _q , is given by the following formula:

Link (C _q , C ₉ ) = Σ ΣContrib ,,, = Σ Σ (C ₁₁ , - ax / (C ₁ ,, C, _v ))

^<sC / ^eC V ^{! eC} / ^eC V

When the measure of similarity is a scalar product, and when f (C _1n C ₁ ,,,) - Min (C _π , C _lY ), one can as before, linearize the computation of the link between two distinct classes. The method uses for this the properties of linearity of the dot product, which gives the following simplification:

Link (C _q , C,) = <R ", R ^{9 '} > -ax Σ Σ Mm (C ₁₁ , C ₁ ,,,) l≡Cqi'≡Cq'

One can also use the following procedure which makes it possible to evaluate with a linear complexity the quantity Σ Σ _j Min (C ₁₁ , C ₁ , ₁ ,): leCqi'εCq '************* ************************************************** ********************************

MinCC procedure (Class C, Class C)

Requires: CαrdC> 0

Requires: CαrdC '> 0 Requires: Sorted list of individuals for classes C and C

Whole: result - 0

Integer: nb _lines = CardC

Integer: nb _cols = CardC

Integer: j = next element of C Integer: f = next element of C

As long as class C is not covered and class C is not covered Do

If j <f result - result + nb_ collars x C j = next element of C nb __ rows - nb_ rows - 1 Otherwise

If I do result = result + nb lig CJnes x CJ .J, f = next element of C nb ___ necks -nb _ necks - 1 Otherwise result - result + (nb _ necks + nb__ rows - 1) x C _ff j = next element of C f = next element of C nb _ lines = nb _ lines - 1 nb _ necks -nb _ necks - 1 End If

End if

End as long as

_{************************************************** ****************************************}

In the context of the intersection between two classes, the method evaluates the following three quantities which are represented on an example in Figure 7:

Lie _n = (C _y -C _c , C _x -C _c ) = <R ^a , R ^b > -ax Σ Σ / (C _U , C ,,) i≡CyiΛieCc eCxnj'ïCc

Link Link ₂ = (C _y C _C CJ = <R ", R ^C> -ax Σ Σf (C ,,, C _lY) ifΞCymeCc ECC

Link ₃ = Link (C _x -C _c , C _c ) = <R ^b , R ^c > -ax Σ Σ / (C _n , C ₁ ,,) leCxmeCc eCc

Thus, to locally maximize the global criterion:

• If Link, + Link ₂ + Link ₃ is the largest, choose solution 4 (merge of the two classes);

• If Link ₂ is the largest, choose solution 2 ("breaking" of C _x );

• If Link ₃ is the largest, choose solution 1 ("breaking" of C ₁ ); Si If 0 is the largest, that is to say that Link _} + Link ₂ + Link ₃ <0, Link, <0 and Link ₃ <0, then choose solution 3 ("breaks" of C _x and C _v ) . Once the class C _x , 50, is merged with the first class C, we continue the processing with the other classes of the partition P in intersection with the class C _x , 55 ,. For this, the class C _x will be transformed into class C _x : @ If the solution 1 is chosen, C _x , = C _x

• If solution 2 is chosen, C _x , = C _x ~ C _y

• If solution 3 is chosen, C _x , = C _x - C _v

• If solution 4 is chosen, C _x , = C _x vj C _y

In any case, the new class C _x , contains the objects that can belong to the other classes of the partition P since we know, in advance, that no object of the class C _y can belong to another class of the score P.

How to remove objects to a class

To remove a set of objects Δ from a class, it suffices to remove Δ from the list of objects of the class and to subtract the representative R ^Δ from the representative of said class. For example, during the operation C _x = C _X - C _V , R ^A is equal to R ^c .

Indeed, we subtract from the class C _x , the objects in intersection represented by the representative R ^c . Thus R ^{x '} = R ^X - R ^c .

In this way, the "breaking" operations do not require a large calculation time because the quantity subtracted from the class representative is always equal to the vector R ^c which is already calculated. On the other hand, removing objects from the list is a simple, linear operation.

Reunion procedure of two classes In this procedure, we know the representative of the intersection of C ₁ and C ₂ (defined by R ^c above) and the cardinal of the intersection (defined by CαrdC above). We thus seek to create the class C ₁ u C ₂ , without performing a complete linear sorting. _{************************************************** *********************************************}

Meeting Procedure (Class C ₁ , Class C ₂ , Inter Representative, Whole

Cαrdlnter)

Temporary vector size (CαrdC, + CαrdC ₂ - Cαrdlnter) Integer position = 0

L _x = list of objects of C ₁ e = head of the list L _x L ₂ = list of objects of C ₂ / = head of the list L ₂ As long as the list L ₁ is not covered Do

As long as the list L ₂ is not traversed Do If e = f Make el = ee = head of the list L _x / = head of the list L ₂

Otherwise If e </ Do el = ee = head of the list L ₁ El = ff = head of the list L ₂ End If

Temporary [position] = el Position = position + 1 End As long as

End As Temporary Copy In The Object List

Representative = Representative (C ₁ ) + Representative (C ₀ ) - Inter ********** _{*************} ************ ******* _*** ** _* *********** _************ ********** _{**** ***} ******* Consolidate Procedure (Partition P) 44

Let K be the number of classes of the partition P

For each class C _q of the partition P, one calculates Contrib (C _q )

Let C _{x be} the class with the strongest contribution We calculate the vector S of κ - \ values defined by:

S = (s _v s ₂ , ..., s _k _,) and where

[LUm (C _x , C,) ά l <x

^S '[Link (C _x , C _{1 + 1} ) if I> x

For all the positive link values of S, we will merge the corresponding classes. All of these classes will be marked as affected and can not be merged later. Iterates the process with the whole

K 'unmarked classes.

Hierarchical aggregation method of the classes of the invention In FIG. 8, an example of an architecture of the hierarchical aggregation method of the classes in meta-classes is represented.

This method consists, in particular, in grouping on several levels (the number of levels is to be set by the user) classes between them. The optimization of the global criterion passes, for example, by maximizing the links between the classes formed. In other words, the classes obtained must ultimately have negative links. Now, the calculation of the links is based on the definition of the contribution Contrit _^ , of a pair (i, f) of objects. The definition of the contribution of a pair of objects is described below when the function / is the function Minimum: Contrib _u , = C ₁₁ , - α x MIn (C _n , C ,,,,) The process of class aggregation, proposed by the invention, then consists in decreasing at each level the value of the structural threshold 80, so that the weakly negative contributions can become positive. In this way, the link between two classes can become positive which makes it possible to group them 81, and to highlight relations between the classes of a partition. This process is repeated as many times as there are levels 82. We then obtain a set of nested partitions 83, which makes it possible to detect hierarchical and conceptual relationships (on several levels) between the classes considered initially in the score 45. The invention, by this principle, thus makes it possible to make the discovery of knowledge. The hierarchical aggregation procedure for classes from a level j to a level y + 1 is similar to the grouping procedure described above.

Calculations allowing the evaluation of the quality of the classification results of the invention The theoretical formulas of the indices of measurement of the quality of the solution obtained, expressed as a percentage, are given here. The closer the index is to 100%, the better the quality of the studied solution (partition, class or individual qualities).

We first introduce some notations:

The agreement between two classes: A _cσ - ^] TC ₁₁ ,

The maximum agreement between two classes: AM _cc , = Σ Σf (C ₁₁₁ C ₁ .,.) ΙeC eC

The disagreement between two classes: A ^ _r C _r C - ~ A ^{Λ ± 1V} M _r C _r C - A ^Λ _r C _r C

The final quality of the score obtained is given by:

ΣA _cc + Σ Σ _cc ΣAc -Σ ΣA _{cσ +} Σ VΣA ΛMλ / t C, C

C = I C = I C '≠ C _ C = I C = I C' ≠ C C = I C ≠ C

Q =

ΣΣ ^ cc ΣΣAMcc

Where C is the number of classes of the partition.

The quality of a class C is given by:

A _cc + 2x Σ _cc A _Cc -2x ΣA _cc + 2x ΣAM _t CC C '≠ C _ C' ≠ CC ≠ C

Q _c C = NbCl NbCl

AM _cC + 2 x ^ AM _cσ AM _cc + 2 ^ γ _j At 4M λyf

C _c C

C '≠ C C' ≠ C The quality of an object i belonging to a class C is given by:

Σ ^C '' + ΣQ. ΣC, -ΣC _π , + Σ / (C _B , C ,,) p. _ i'eC eCt _ eC (VC ι ^ C_

Σf (C _u , C _{ι V} ) Σ / (C _B , C, _V )

, '= 1,' = 1 where C _n , = f (C _u , C _lY ) - C _n , is the disagreement between the individual i and the individual i '.

The sums on the terms A _cσ are linearized when the similarities C _n , are scalar products thanks to the properties of linearity of these last ones. Examples of procedures for calculating linearly the following quantities occurring in the different quality formulas are given below.

/ (C 1, C _IV ) = M "(C 1, C, _v ):

C _lY )

• ΣMin (C ,,, C _ιY ) t'sC We note respectively these quantities SS'MinCC, S'MinC and MiniC:

_{************************************************** *********************************************}

SS'MinCC procedure (Class C, Class C)

Need ; K> 0 Integer: result = 0

For z = l up to n in increments of 1 Do result = result + ((n - i + V) x 2 - 1) x C _n End For

_{************************************************** ********************************************* ************************************************** ************************}

S'MinCC procedure (Class C, Class C)

Requires: CαrdC> 0 Requires: K> 0

Need ; Sorted list of individuals for C classes Integer: result - 0 Integer: nb _lines = CardC Integer: nb _cols = n Integer: j = next element of C

Integer: i = 1

As long as the class i ≤ n and C is not traversed Do If / = j make a result - result + (nb _ cols + nb_ rows - 1) x C _n nb _ rows = nb _ rows - 1 nb _ cols = nb _cols - 1 i = i + lj = next element of C If result = result + nb_ rows x C ₁₇

/ = / + 1 nb _cols = nb _cols - 1

End If End as long as

_{************************************************** *********************************************}

_{************************************************** ****************************}

MiniC procedure (Class C)

Requires: CαrdC> 0 Requires: Sorted list of individuals for class C

Integer: result = 0 Integer: nb_cols = CardC Integer: j = next element of C

As long as the class C is not traversed and nb _cols ≤ j Do If z = / Make result = result + nb _ cols x C _n Otherwise result = result + C j - next element of C nb _cols = nb _cols - \

End if

End as long as

_{************************************************** *********************************************}

Claims

1 - Linear unsupervised classification method for structuring a database composed of objects and descriptors, which is stable on the order of the objects comprising a preliminary step of transforming the qualitative, quantitative or textual data into presence binary data -absence characterized in that it comprises at least the following steps:

• determining a threshold _s structural function of ri ² agreements between the objects to be classified, the structural threshold defining an optimization criterion adapted to the data,

• use the descriptors as generators for structuring and building a partition or set of classes,

• gradually merge a class generated by a descriptor and a partition (40, 41, 42), • for an optimization criterion involving a function f (C _u , C _ιY ) = Min (C _u , C _ιr ) linearize sums of functions Minimums.

2 - Method according to claim 1, characterized in that it comprises a step where one groups the classes of the partition between them.

3 - Process according to claim 1, characterized in that the melting step comprises a step wherein is determined from two classes in intersection the best operation (in the sense of the optimization of the criterion) among the following 4:

• "Breakage" of the first class and formation of two classes; • "Breakage" of the second class and formation of two classes;

• "Breakage" of the two classes to form three classes;

• Meeting of the two classes in intersection to form a single class.

4 - Classification method according to claim 2, characterized in that the grouping of the classes of a partition is performed on several hierarchical levels and comprises the following steps:

• decrease at each level the value of the structural threshold (70) so that the weakly negative contributions can become positive, • Maximize links between built classes where links are determined using the contribution of a pair of objects

Link (C _q , C _q ,) = Σ ΣContrib _u , = Σ ΣC _U , -a'xf (C _u , C _ιV ) i≡Cqi'≡Cq 'i≡Cqi'≡Cq' with a ' new value of a

• group (71) two classes whose link is positive, and reiterate this process on all levels.

5 - Device allowing linear unsupervised classification for structuring a database composed of objects and descriptors, which is stable on the order of the objects comprising a preliminary step of transforming the qualitative, quantitative or textual data into binary data of presence-absence, characterized in that it comprises at least the following elements: a computer (1) comprising a memory (2), a database (4) and a processor (3) adapted to implement the steps of process according to one of claims 1 to 4.

6 - Device according to claim 2, characterized in that it comprises a means (7) for conducting actions according to the results of the classification.