Bio-medical Ontologies Maintenance and Change Management

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194 I.R. Godínez et al. 3.1.1 New Alpha-Beta Heteroassociative Memory Type Max LEARNING PHASE Let A = {0, 1} ,n,p ∈ Z + ,μ ∈{1, 2, ...p} ,i ∈{1, 2, ..., p} and j ∈{1, 2, ...n} and let x ∈ An and y ∈ Ap be an input and output vectors, respectively. The corresponding fundamental set is denoted by {(xμ , yμ ) | μ =1, 2, ..., p}. The fundamental set must be built according to the following rules. First, all the y vectors are built with the one-hot codification. Second, to each yμ vector corresponds one and only one xμ vector, this is, there is only one couple (xμ , yμ ) in the fundamental set. STEP 1: For each μ ∈ {1, 2, ...p}, from the couple (xμ , yμ ) build the matrix: [yμ ⊠ (xμ ) t ] mxn STEP 2: Apply the binary ∨ operator to the matrices obtained in step 1 to get the new alpha-beta heteroassociative memory type max V as follow: V = p� [yμ ⊠ (xμ ) t ]withtheij−th component given by: μ=1 vij = p� μ=1 α(y μ i ,xμ j ) RECALLING PHASE STEP 1: A pattern x ω is presented to V, the Δβ operation is done and the resulting vector is assigned to a vector called z ω : z ω = VΔβx ω The i−th component of the resulting column vector is: z ω i = n� j=1 β(vij,x ω j ) STEP 2: It is necessary to build the max sum vector s according to the definition 1, therefore the corresponding yω is given as: � 1ifsi = � y ω i = =1} . 0 otherwise sk AND z k∈θ ω i =1 where θ = {i|zω i Example 1. Let x1 ,x2 ,x3 ,x4 be the input patterns x 1 ⎛ ⎞ 1 ⎜ 0 ⎟ = ⎜ 1 ⎟ ⎝ 1 ⎠ 0 ,x2 ⎛ ⎞ 0 ⎜ 1 ⎟ = ⎜ 0 ⎟ ⎝ 0 ⎠ 0 ,x3 ⎛ ⎞ 1 ⎜ 0 ⎟ = ⎜ 0 ⎟ ⎝ 1 ⎠ 0 ,x4 ⎛ ⎞ 1 ⎜ 1 ⎟ = ⎜ 0 ⎟ ⎝ 1 ⎠ 1 (1)
Classifying Patterns in Bioinformatics Databases 195 and the corresponding output vectors y 1 ⎛ ⎞ 1 ⎜ = ⎜ 0 ⎟ ⎝ 0 ⎠ 0 ,y2 ⎛ ⎞ 0 ⎜ = ⎜ 1 ⎟ ⎝ 0 ⎠ 0 ,y3 ⎛ ⎞ 0 ⎜ = ⎜ 0 ⎟ ⎝ 1 ⎠ 0 ,y4 ⎛ ⎞ 0 ⎜ = ⎜ 0 ⎟ ⎝ 0 ⎠ 1 the output vectors are built with the one-hot codification, and to each output pattern corresponds one and only one input pattern, therefore the fundamental set is expressed as follow: �� x 1 ,y 1 � , � x 2 ,y 2� , � x 3 ,y 3� , � x 4 ,y 4�� Once we have the fundamental set, the learning phase of the new heteroassociative memories type Max is applied: STEP 1: ⎛ ⎞ 1 ⎜ 0 ⎟ ⎝ 0 ⎠ 0 ⊠ � 10110 � ⎛ ⎞ 12112 ⎜ = ⎜ 01001 ⎟ ⎝ 01001⎠ 01001 ⎛ ⎞ 0 ⎜ 1 ⎟ ⎝ 0 ⎠ 0 ⊠ � 01000 � ⎛ ⎞ 10111 ⎜ = ⎜ 21222 ⎟ ⎝ 10111⎠ 10111 ⎛ ⎞ 0 ⎜ 0 ⎟ ⎝ 1 ⎠ 0 ⊠ � 10010 � ⎛ ⎞ 01101 ⎜ = ⎜ 01101 ⎟ ⎝ 12212⎠ 01101 ⎛ ⎞ 0 ⎜ 0 ⎟ ⎝ 0 ⎠ 1 ⊠ � 11011 � ⎛ ⎞ 00100 ⎜ = ⎜ 00100 ⎟ ⎝ 00100⎠ 11211 STEP 2: The binary operator max � is applied to the matrix obtained before to build the matrix V ⎛ ⎞ 12112 ⎜ V = ⎜ 21222 ⎟ ⎝ 12212⎠ 11211 Once we have the V matrix, to recall x ϖ with ϖ ∈{1, 2, 3, ..., p} , particularly x 4 ,x 4 is presented to V:
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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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100 L. Stanescu, D. Dan Burdescu, a
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Page 147 and 148: Bio-medical Ontologies Maintenance
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Substructure Analysis of Metabolic
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entry compound relation subtype com
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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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296 M. Fernandez, M. Villasana, and
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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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