Class discovery in Gene Expression Data: Characterizing Splits by Support Vector Machines

Transcription

1 Class discovery in Gene Expression Data: Characterizing Splits by Support Vector Machines Florian Markowetz and Anja von Heydebreck Max-Planck-Institute for Molecular Genetics Computational Molecular Biology Berlin 26th Annual Conference of the Gesellschaft für Klassifikation GfKl 2002: Mannheim 1

2 Overview I II III IV Characterization of tumor types by gene expression profiles The SVM score ISIS: the algorithm Output of ISIS Florian Markowetz, Class Discovery in Gene Expression Data, GfKl 2002, Mannheim 2

3 Microarray Experiments Hybridization (red label) total mrna standard condition Target Probe Hybridization convert into numerical values total mrna (green label) gene 1 gene 2 gene 3 gene 4 gene 5 standard 14,243 5,323 10,300 1, ,232 experiment 12,154 27,152 1,407 3, ,993 interesting condition Florian Markowetz, Class Discovery in Gene Expression Data, GfKl 2002, Mannheim 3

4 Characterization of tumor types Between two different, but related tumor tissue types, often relatively few genes are clearly differentially expressed. Usual cluster algorithms are based on a global measure of similarity between samples, where (possibly conflicting) signals from different groups of genes are intermingled. Our approach: we try to find interesting bi partitions of the set of tissue samples and measure how well the two groups are separated by expression levels of a suitable small subset of genes. This gives a score for each partition. Florian Markowetz, Class Discovery in Gene Expression Data, GfKl 2002, Mannheim 4

5 The SVM score The SVM margin score S(B) of a bipartition B = {M, M} is the margin of a (linear) Support Vector Machine separating M from M. Samples in M Margin Separating Hyperplane Samples in M Florian Markowetz, Class Discovery in Gene Expression Data, GfKl 2002, Mannheim 5

6 Significance of the SVM score Comparison to 10,000 random partitions of the data: Dataset Class distance to SVM SVM margin local max. margin at local max. Leukemia AML 3 (59.1%) 1.6 (0%) 2.2 (0%) T-cell ALL 0 (0.5%) 2.6 (0%) 2.6 (0%) B-cell ALL 1 (13.3%) 1.9 (0%) 2.8 (0%) Lymphoma / CLL 2 (11.8%) 2.0 (0%) 2.8 (0%) leukemia FL 0 (0%) 2.4 (0%) 2.4 (0%) DLBCL-G 3 (24.3%) 1.7 (0%) 2.0 (6.2%) DLBCL-A 5 (49.5%) 1.7 (0%) 2.9 (0%) Melanoma cluster of 1 (8.8%) 1.2 (0%) 2.0 (10.2%) 19 samples Florian Markowetz, Class Discovery in Gene Expression Data, GfKl 2002, Mannheim 6

7 Input: Example data sets Dataset # samples # genes classes: # samples total used (total) Leukemia 72 4,000 AML: 25 Golub et al. (1999) (6,817) B-cell ALL: 38 T-cell ALL: 9 Lymphoma / 62 4,026 CLL: 11 leukemia (17,856) FL: 9 Alizadeh et al. (2000) DLBCL-G: 21 DLBCL-A: 21 Melanoma 31 3,613 cluster: 19 Bittner et al. (2000) (6,971) remaining: 12 Florian Markowetz, Class Discovery in Gene Expression Data, GfKl 2002, Mannheim 7

8 Step 1: Finding candidate partitions 1. Data matrix X = (x gj ) samples j = 1,..., n and genes g = 1,..., k. Florian Markowetz, Class Discovery in Gene Expression Data, GfKl 2002, Mannheim 8

9 Step 1: Finding candidate partitions 1. Data matrix X = (x gj ) samples j = 1,..., n and genes g = 1,..., k. 2. Compute average expression profiles of clusters of genes. = new data matrix Y = (y ij ) Florian Markowetz, Class Discovery in Gene Expression Data, GfKl 2002, Mannheim 8

10 Step 1: Finding candidate partitions 1. Data matrix X = (x gj ) samples j = 1,..., n and genes g = 1,..., k. 2. Compute average expression profiles of clusters of genes. = new data matrix Y = (y ij ) 3. For every gene cluster i and every sample j : the value y ij defines a bipartition given by the subsets M = {j y ij y ij } and M + = {j y ij > y ij }. Florian Markowetz, Class Discovery in Gene Expression Data, GfKl 2002, Mannheim 8

11 Step 1: Finding candidate partitions 1. Data matrix X = (x gj ) samples j = 1,..., n and genes g = 1,..., k. 2. Compute average expression profiles of clusters of genes. = new data matrix Y = (y ij ) 3. For every gene cluster i and every sample j : the value y ij defines a bipartition given by the subsets M = {j y ij y ij } and M + = {j y ij > y ij }. 4. Order splits by value of two-sample t-statistic 5. Choose highest scoring splits as candidates. Florian Markowetz, Class Discovery in Gene Expression Data, GfKl 2002, Mannheim 8

12 Step 2: Feature selection For each split B: select the 50 genes with highest absolute value of the two sample t statistic t g (B) t g (B) = µ gm µ g M (m 1)σgM 2 + ( m 1)σ2 g M m m(n 2) n, where m = M and m = n m. Florian Markowetz, Class Discovery in Gene Expression Data, GfKl 2002, Mannheim 9

13 Step 3: Local Search for Maxima Greedy Search: Start at B choose the neighboring split with the highest SVM score continue until a local maximum is reached Florian Markowetz, Class Discovery in Gene Expression Data, GfKl 2002, Mannheim 10

14 Output: Leukemia dataset S(J) AML T cell ALL B cell ALL Florian Markowetz, Class Discovery in Gene Expression Data, GfKl 2002, Mannheim 11

15 Output: Melanoma dataset S(J) clustered samples 12 other samples Florian Markowetz, Class Discovery in Gene Expression Data, GfKl 2002, Mannheim 12