A new hybrid fusion method for diagnostic systems

Transcription

1 A new hybrid fusion method for diagnostic systems Zemirline A. ITI Department ENST Bretagne Brest, France LATIM, INSERM-U650 Lecornu L. ITI Department ENST Bretagne Brest, France LATIM, INSERM-U650 Solaiman B. ITI Department ENST Bretagne Brest, France LATIM, INSERM-U650 Abstract In this work, we present a new fusion method which uses fuzzy subsets. This method is applied to the bases of diagnostic systems. It aims at combining all the bases into only one base and then caring for the characteristics of this base. This method is characterized by a hybrid fusion, which combines data fusion with primitive fusion. Primitive fusion relies on a measure of distortion between various bases. This measure of distortion is integrated into the diagnostic system in order to improve its performance. It is defined such as degrees of confidence associated to each base parameter. The degrees of confidence are then integrated into the methods for calculating similarity and also into the case evaluation and classification which is all that is used by a diagnostic system. Keywords: Diagnostic Systems, Medical Applications, Decision Support Systems, Information Retrieval, Information Fusion, Data Fusion, Data Mining, Fuzzy Methods. 1 Introduction These days, several institutions and organizations combine data of the same type coming from different sources and/or produced at different instants. This situation is faced, in particular, by medical complexes, where they have to store a new set of data each year. On the one hand, the data has to be exploited to extract new information and, on the other hand, it has to be amalgamated with its older versions. The type of fusion that we propose in this study is a hybrid fusion combining two types of fusion: data fusion and primitive fusion. This hybrid fusion consists of grouping several sources of case bases to obtain only one case base which is associated with a knowledge base. This knowledge base describes the degree of confidence of the parameters in this new base. There are two types of data fusion [8,9]: record linkage and grafting. Record linkage is used when the same static unit is required in two different data sources. Grafting is used when the fusion of the two sources is based on the creation of a synthetic unit. The objective of these techniques is to have a single base to which the methods of data mining and knowledge discovery process could be applied. In this work, we have the case bases coming from different sources but which are harmonized, i.e. the bases have a significant number of parameters in common. The objective of our fusion is not limited only to enriching the training base by increasing the number of cases, but it also allows the diagnostic system or casebase reasoning system to have more precise and more relevant results for the recognition of

2 certain classes. This is possible by taking into account the primitive classification according to its importance in the description of the new case base and those data which were amalgamated, to integrate them into methods such as the measure of case similarity and degree of membership. Our method of fusion can be considered as a hybrid method because it relies on knowledge fusion and base fusion. The feature which distinguishes it from the other fusion methods is that the elements of the bases are not subject to modification. In this work, we have tackled the regularly confronted problem of integrating the new case bases into a diagnostic system. As an example, we take a diagnostic system which applies to medical bases. These medical bases are of the same type and they contain descriptions of endoscopic lesions. However, each one of these bases has its own features while describing the lesions. This article is organized in the following way: in the second section, we describe the diagnostic system to which our method of fusion is applied and the clinical context on which our system is based. In section tree, we describe the fusion method. In the fourth section, we analyze the results obtained through our method. We finish finally with a conclusion. 2 Diagnostic system of endoscopic lesions Our diagnostic system of endoscopic lesions provides the type of lesion corresponding to a case and presents the most similar cases. Our system is based on a case base and knowledge bases deduced from the case base. From all the bases, we find 206 parameters and 89 types of lesions. The knowledge base Two types of knowledge bases are defined: internal knowledge bases and external knowledge bases. Our approach involves of directing fusion according to our objectives. This obliges us to develop the knowledge base for each base. This knowledge base contains information describing the importance of parameters in the definition of different classes which should be recognized by our diagnostic system. It is called an external knowledge base because it is not used by the system for its internal functioning like case evaluation and the measure of case similarity. It is presented in a particular form in order to facilitate the comparison with other knowledge bases coming from other systems. Thereafter, the external knowledge bases of various systems are amalgamated to give a new knowledge base: the confidence knowledge base. This base results from the measure of disparity between the various external knowledge bases. This base is constituted by attributing a degree of confidence to each parameter. Then, the diagnostic system combines the information from this knowledge base with the information extracted from the internal knowledge base. This procedure is represented in Figure 1. The case base The case base that we use in this study comes from a system of endoscopic image analyses [2]. It is an assistance system for decision-making in the diagnosis of endoscopic lesions. These lesions are described from endoscopic image via symbolic terms which are defined by the minimal standard terminology of the SEGE (European Company of Gastro- Enterology). A case in a base represents a description (a set of parameters) of an endoscopic lesion. Figure 1: Hybrid fusion integrated in a diagnostic system (a) The internal knowledge base: This is a knowledge base designed from the case base; no data or external information at the base is introduced for the definition of this knowledge base. The diagnostic systems relies

3 on the internal knowledge base for the classification of the cases and the measure of similarity between two cases. This knowledge base is composed of functions of membership for each class. A function of membership is built from the frequencies of appearance of a set of parameters in a set of cases, where the latter all belong to the same class. A histogram of the frequencies of the parameters of the set of these cases is produced and then this histogram is normalized by the maximum frequency: Ω : is the set of parameters which appears in the case base. f Ai : is the frequency of appearance of parameter I in the set of cases which belong to class A (with lesion A). e i : is a set of parameters which is included in Ω and corresponds to the description of the i-th case of the case base. n i : is the number of parameters of e i. µ A : is the membership function of class A which is defined as: µ A f Ai = f Ai /max f Aj j Using this membership function, we can calculate the degree of membership of a case to a given type of lesion, by using the compromise operator such as the geometric mean: degree A e i = n i j e i µ A f Aj The reason for using the geometric mean is that it is one of the combination methods which takes a zero value if one of the elements of combination is equal to zero. However, we consider that a case does not belong to a class if it has a parameter having a degree of membership equal to zero. These functions of membership are used to measure the similarity between two cases. The measure of similarity is composed of diagnostic systems which use case base reasoning. The method sim A is a variation of the standard cosine method [4], which is a frequently used method to compute the similarity between cases which are composed of textual attributes. sim A e i,e j = k e i,k e j µ A f Ak µ A f Ak k e i The methods presented below apply to diagnostic systems which do not take into account the singularities of the amalgamated bases. Next we will present new methods of the same type but which integrate the features of the amalgamated bases into their calculation. (b) The external knowledge base: This knowledge base is designed to be a fusion interface. This interface is able to compare the bases in order to measure the distortions between them. Our work involves attributing a linguistic value of uncertainty to each parameter to define their importance in the characterization of different classes without using numerical values such as their frequencies of appearance in various classes. The motivation to use linguistic values instead of numerical values is the same as that introduced by Zadeh [7]. The linguistic characterization is, in general, less specific than the numerical one and is more significant. The linguistic variable is characterized by a quintuple [7]: (x, T(x), U, G, M) x is the frequency and is the name of the linguistic variable for our study. T(x) is of the set of terms associated with the linguistic value. For our case, it is the following set {Never, Exceptional, Rare, Usual, Frequent, Very Frequent, Always}. U is a universe of discourse which for our case is U = U= [f min, f max ] (f min : corresponds to the minimum frequency of appearance of a description parameter of a class; f max : corresponds to the maximum frequency).

4 The terms of T(x) are characterized by fuzzy subsets defined by following functions of membership: K: the set of centroids of fuzzy subsets obtained by the algorithm of fuzzy c- means (FCM) [ 10 ], k={ f min,..., k i 1, k i,k i1,..., f max } µ iα : corresponds to the function of membership in linguistic term for the class i. This function has the frequency of appearance f as its argument. µ i f ={ 1 f k i /k i k i 1 si f k i 0 else An example of the functions of membership of the set T(x) is presented in Figure 1. Figure 2: Linguistic values of the variable frequency. 3 Fusion Method [1] : We can distinguish two types of fusion Fusion of data of the same type coming from different sources. Fusion of primitives combining characteristics extracted from various bases. Decision fusion combines the results of different decision systems in order to deduce a final decision. Three approaches to decision fusion can be deduced: decision fusion by majority vote, decision fusion based on rules and decision fusion based on the reliability of the decisions. Our fusion method involves comparing the importance of a parameter in the characterization of a class (a type of lesion) in different bases to be amalgamated. We first define an external knowledge base where the parameters (frequencies) are grouped according to their importance in the representation of a class. Then we reach a stage where we compare these knowledge bases coming from different sources to estimate their divergence. Before passing on to the presentation of fusion method, we illustrate an example of divergence. We take a parameter which is contained in a source A. It has a high frequency of appearance in the representation of a given class which is expressed by a strong degree of membership of the 'very-frequent' subset for this class. In a source B, the same parameter has a very low frequency of appearance in the representation of the same previously mentioned class which is expressed by a strong degree of membership of the 'exceptional' subset for this class. In this example, one notes a great disparity in the consideration of a parameter in the definition of the same class of two distinct sources. This term can be regarded as ambiguous for defining this class and can result in: Not taking this parameter into account to define this class during the training process applied to the base resulting from fusion. Not taking the ambiguity into account giving this parameter the same degree of confidence as others which do not have ambiguities in the class definition. We propose a global measurement operator of conflict between p+1 sources. This operator applies to the p knowledge bases deduced from p sources and to another knowledge base which is deduced from the coupling of the aforementioned p bases. This knowledge base is called F for simplification. Our operator functions in the following way: for a parameter t and a class c, it recovers the uncertainty term from F of which the parameter t has the greatest degree of membership for the class c. The linguistic term is taken as a reference mark for the calculation of disparity between p knowledge bases. Then for each p base, the operator calculates the degree of membership of the linguistic parameter t in and in other linguistic terms

5 which are the direct neighbors of for the class c and we recover the highest degree of membership of one of these linguistic terms for example, the usual linguistic terms for direct neighbors are 'rare' and 'frequent'. Thereafter, we keep the lowest value of the degrees of membership obtained from p bases. Here the goal is to find a base in the p bases which gives the level of representation of the parameter t for the class c that is the farthest from the average of the p bases. Then we deduce the degree of reliability (degree of confidence) of a parameter after the fusion of p bases. The whole above mentioned procedure is followed by the measurement of conflict between p sources (p bases). This measurement is inspired by the method proposed by Dubois and Prade [6]. In this work, a conflict is defined as the distance that separates the classification of a parameter between the new base (base resulting from fusion) and the p bases (bases which were amalgamated). We propose a global measurement operator for the conflict between p sources (p knowledge bases defined previously) of a class c. This operator relies on T-conorm U: µ ikl : represents the function of membership in the linguistic term k for lesion i of the knowledge base l. F: represents the knowledge base deduced from the coupling of p bases. f itl : corresponds to the frequency of appearance of parameter t in base l for class i (lesion i). h iα : conflict measurement operator concordance i : interpreted as the minimum degree of consensus of n knowledge bases on the membership of a parameter for class i (lesion i). Selection of the linguistic term µ F i f F it = max µ F ij f F it j =1...p such that: We recover the lowest one among the degrees of membership obtained from the p knowledge bases: h k i t= min U µ i 1 f k it, µ k i f it k =1...n concordance i t=1 h i t k k, µ i 1 We define a function of measurement of confidence by taking the degree of concordance of a parameter as an argument: µ conf ( x ) = where is a constant. 1 si x [0.5, 1] ε x si x [0, 0.5[ This function of membership of confidence considers that a measurement of concordance is completely reliable if the degree of concordance remains within 0.5 and 1, i.e. a descriptive parameter is relaible if these frequencies of appearance in the various bases belong to the same class having the greatest degree of membership for the knowledge base F or a class close to it. Owing to our fusion method we are able to calculate the degree of confidence of each descriptive parameter for a given type of lesion enabling us to add it into the calculation of the degree of membership. By integrating the index of confidence into the methods of calculation of similarities or the method of degree of membership measurement, we are able to refine the results by giving more weight to the parameters that have high degree of confidence. The integration of the index of confidence into the calculation of the degree of membership makes it possible to take into account certain parameters whose index of confidence is higher than a certain value: ε: a constant such that ε [ 0,1[ conf A t=µ conf concordance A t degree A e i = 2n i j =0,conf A j ε conf a j µ F A f F Aj The integration of the index of confidence into the calculation of the similarity f k it

6 between cases allows us to take into account only the parameters higher than the constant ε: sim A e i,e j = 4 Results k e i,k e j,conf A i µ F A f F Ak µ F A f Ak k e i,conf A i F Figure 3 gives the results of three types of fusion methods applied to a diagnostic system: Data fusion method: It is a very simple grouping of data from distinct sources. Decision fusion Method: This method combines the results of the diagnostic system applied to various sources and takes the result having the greatest reliability. Hybrid method: This is our method applied to a diagnostic system which takes into account the degree of confidence calculated through our fusion method. Figure 3: Results of good estimates of various case bases. The test that we carried out to assess the diagnostic systems, which are based on various fusion methods, consists of amalgamating 1000 cases at the starting base at each stage. Our method is the one which presents the best estimates. We note that at the beginning, the three methods present almost the same estimates but right from the first fusion, the difference between the estimates increases; in fact all estimation rates incrise but it is our method that gives the greatest good estimation rate. The progression of the good estimation rate slows down but it is still our method that presents the greatest progression coefficient. Our fusion method makes it possible to certain extent to measure the distortion between different bases of the same type before they are amalgamated. It can be a selection tool for the bases that can be amalgamated between them, for example, if one finds oneself with several different databases of the same type but coming from different sources and one wants to reduce the number of these bases, one has to group the bases by taking the degree of distortion as criterion for each group. The degree of distortion must be the least so that the groups could be amalgamated. 5 Conclusion : We have presented a new method for fusion which makes it possible to merge a set of case bases. There case bases come from different sources. Our method is based on the determination of a degree of confidence of different parameters which constitute the case base. This degree of confidence of parameters is used to evaluate the base resulting from the fusion of other bases. We have presented experimental results, showing that the proposed method always outperforms the decision fusion method and the data fusion method. The performance gap increases with the problem size. Our method promises performance and is not limited only to enriching the training base by increasing the number of cases. We have also shown that our method allows the diagnostic and Case-Based Reasoning system to have more precision and more relevant results to recognize classes. This is possible by taking into account the primitive classification according to their importance in the description of the new case base and those which were grouped, to integrate them into methods such as the measure of case similarity and degree of membership. Our method is interesting as it presents the possibility of its application to any case base. It is adapted to any domain, unlike the other methods. Our hybrid method can also be used to highlight the parameters whose degree of importance for a base has evolved over a given

7 period. A commercial area of application could rapidly assess the effectiveness of marketing by applying our fusion method to pre and post marketing bases. References [1] D. Hall and J. Llinas. Handbook of Multisensor Data Fusion. CRC Press (2001). [2] C. Le Guillou, J-M. Cauvin, B. Solaiman, M. Robaszkiewicz, and C. Roux. Upper Digestive Endoscopic Scene Analyzer. 23 rd Conference of the IEEE Engineering in Medecine and Biology Society, [3] S. Chauvin. Evaluation des théories de la décision appliquées à la fusion de capteurs en image satellitaire, Thèse de Doctorat d'université, Nantes, [4] G. Salton and M. J. McGill. The SMART and SIRE Experimental Retrieval Systems. McGraw-Hill, New York, [6] D. Dubois and H. Prade. Combination of Information in the framework of Possibility Theory. In Data Fusion in Robotic and Machine Intelligence. M. Abidi and al. eds. Academic Press, [7] L. A. Zadeh. The concept of linguistic variable and its application to approximate reasoning-ii. Information Sciences, 8, 1975, [8] G. Saporta. Data fusion and data grafting,computational Statistics and Data. Analysis, 38 (4), , 2002 [9] Rapport de méthodes Fusion de données Etude de faisabilité. OFS Neuchâtel 2004, [10] J. C. Bezdek. Pattern Recognition with Fuzzy Objective Function Algoritms, Plenum Press, New York, 1981