Bio-medical Ontologies Maintenance and Change Management

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200 I.R. Godínez et al. y ω i = ⎧ ⎨ 1 I ⎩ ω i = p � k=0 0 otherwise Due to a matter of space we only show an example of the alpha-beta heteroassociative multimemory type max, the type min could be induced from this. Example 2. Let x 1 ,x 2 ,x 3 ,x 4 be the input patterns x 1 ⎛ ⎞ 1 ⎜ 0 ⎟ ⎜ = ⎜ 1 ⎟ ⎜ 1 ⎟ ,x ⎟ ⎝ 0 ⎠ 0 2 ⎛ ⎞ 0 ⎜ 1 ⎟ ⎜ = ⎜ 0 ⎟ ⎜ 0 ⎟ ,x ⎟ ⎝ 0 ⎠ 1 3 ⎛ ⎞ 1 ⎜ 0 ⎟ ⎜ = ⎜ 0 ⎟ ⎜ 1 ⎟ ,x ⎟ ⎝ 0 ⎠ 1 4 ⎛ ⎞ 1 ⎜ 1 ⎟ ⎜ = ⎜ 0 ⎟ ⎜ 1 ⎟ ⎝ 1 ⎠ 1 The output vectors are built with the One-Hot codification, and for each output pattern corresponds one and just one input pattern, therefore the fundamental set is expressed as follows: �� x 1 ,y 1 � , � x 2 ,y 2� , � x 3 ,y 3� , � x 4 ,y 4�� Each input pattern from the fundamental set must be divided into as many partitions as we choose, in this case in 3. Therefore, it is necessary to verify whether it is possible to divide the input pattern through the definition 6. n q 6 = =2∈ Z+ 3 Since 2 ∈ Z + , it is possible to divide each input pattern in 3 partitions of equals dimension. After that, the vector partition operator is applied, obtaining the new input patterns similar to this: ρ � x 1 , 3 � = �� 10 � , � 11 � , � 00 �� ρ � x 2 , 3 � = �� 01 � , � 00 � , � 01 �� ρ � x 3 , 3 � = �� 10 � , � 01 � , � 01 �� ρ � x 4 , 3 � = �� 11 � , � 01 � , � 11 �� then the new fundamental set is: �� x 11 ,y 1 � , � x 21 ,y 2� , � x 31 ,y 3� , � x 41 ,y 4� , � x 12 ,y 1� , � x 22 ,y 2� , � x 32 ,y 3� , � x 42 ,y 4 � , � x 13 ,y 1� , � x 23 ,y 2� , � x 33 ,y 3� , � x 43 ,y 4�� finally, from the new fundamental set, the q matrices V l are built: I ω k
Classifying Patterns in Bioinformatics Databases 201 V 1 ⎛ ⎞ 12 ⎜ = ⎜ 21 ⎟ ⎝ 12⎠ 11 , V2 ⎛ ⎞ 11 ⎜ = ⎜ 22 ⎟ ⎝ 21⎠ 21 , V3 ⎛ ⎞ 22 ⎜ = ⎜ 21 ⎟ ⎝ 21⎠ 11 Once we have the V l matrices, to recall x ω with ω ∈{1, 2, 3, ..., p} , particularly x 4 , the vector partition operator is applied to x 4 with q =3: ρ(x 4 , 3) = �� 11 � , � 01 � , � 11 �� then each one of the new vectors, x41 ,x42 ,x43 , are presented to its corresponding Vl matrix according to the new alpha-beta heteroassociative memory type Max algorithm. Therefore three new vectors, z41 ,z42 ,z43 ,areobtained. z 41 ⎛ ⎞ 0 ⎜ = ⎜ 0 ⎟ ⎝ 0 ⎠ 1 ,z42 ⎛ ⎞ 0 ⎜ = ⎜ 0 ⎟ ⎝ 1 ⎠ 1 ,z43 ⎛ ⎞ 0 ⎜ = ⎜ 0 ⎟ ⎝ 0 ⎠ 1 after that, from the three new resulting vectors the intermediate vector I4 is built I 4 ⎛ ⎞ 0 ⎜ = ⎜ 0 ⎟ ⎝ 1 ⎠ 3 finally, the expression 2 is applied in order to obtain the corresponding y4 vector: y 4 ⎛ ⎞ 0 ⎜ = ⎜ 0 ⎟ ⎝ 0 ⎠ 1 3.3 Proposed Classifier In this subsection we present the pattern classifier algorithm based on the alpha-beta heteroassociative multimemories that was mainly developed for bioinformatics applications. This new algorithm is known as Alpha-Beta MultiMemories Classifier (ABMMC). 3.3.1 ABMMC Algorithm LEARNING PHASE 1. The fundamental set is built taking k instances from each class; that is, the fundamental set is assumed to be balance with respect to each class. Thus, the first k instances belong to the first class, the next k instances belong to the second class, and so on.
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Amandeep S. Sidhu and Tharam S. Dil
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Amandeep S. Sidhu and Tharam S. Dil
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Preface The molecular biology commu
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Preface VII biomedical systems, and
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X Contents Mining Clinical, Immunol
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2 A.S. Sidhu, M. Bellgard, and T.S.
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Towards Bioinformatics Resourceomes
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2 The New Waves Towards Bioinformat
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2.4 Semantic Web Towards Bioinforma
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A Summary of Genomic Databases: Ove
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Appendix A Summary of Genomic Datab
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Protein Data Integration Problem Am
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Protein Data Integration Problem 57
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Fig. 3. Class Hierarchy of Protein
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72 L. Stanescu, D. Dan Burdescu, an
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Bio-medical Ontologies Maintenance
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Substructure Analysis of Metabolic
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Running Time 4500 4000 3500 3000 25
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6 Conclusion Substructure Analysis
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Completing the Total Wellbeing Puzz
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Genetic Algorithm in Ab Initio Prot
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Author Index Apiletti, Daniele 169
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Bio-medical Ontologies Maintenance and Change Management

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