lecture22_slides

lecture22_slides - Overview of today Today: Review of...

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Overview of today Today: Review of clustering - More on clustering: - K-means clustering - Validating clusters
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Introduction to clustering What is clustering? Process of grouping a set of objects (e.g. tumor samples or genes) into classes of similar objects Why cluster? Find natural structure in the data, not just differences that correspond with things we know about (e.g. differential expression)
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Example: Clustering samples (or conditions) Samples Garber, Troyanskaya et al. Diversity of gene expression in adenocarcinoma of the lung. PNAS 2001, 98(24):13784-9. Tumors with similar signatures may respond to the same treatment!
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Example: clustering genes Genomic expression programs in the response of yeast cells to environmental changes. Mol Biol Cell. 2000 Dec;11(12):4241- 57. Gasch AP, Spellman PT, Kao CM, Carmel-Harel O, Eisen MB, Storz G, Botstein D, Brown PO. Genes with similar profiles may perform similar functions!
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Example: clustering genes Gene expression Environmental conditions
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How do we define a clustering method? • We need to define what we mean by similarity? When are two genes’ profiles similar? • We need to define an algorithm (i.e. a recipe) for grouping “similar” objects
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How do we define similarity? • Clustering requires us to define what we mean by similarity (Example: what do you mean when you say two genes have “similar” profiles?) x y Time/Environment Gene expression Possible metrics Euclidean distance Pearson correlation Which metric you pick depends on what kind of similarity you hope to find.
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Measuring similarity of profiles: Euclidean distance • Euclidean Distance N n n n y x y x d 1 2 ) ( ) , ( N x x x 1 N y y y 1 x y Time/Environment Gene expression
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Euclidean distance: example • Euclidean Distance: Absolute difference a b 5 . 0 2 . 0 a c 5875 . 1 ) , ( c a d 8025 . 2 ) , ( b a d 2211 . 3 ) , ( c b d
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Measuring similarity of profiles: Pearson correlation • Pearson Correlation N x x x 1 Two profiles (vectors) and ] ) ( ][ ) ( [ ) )( ( ) , ( 1 2 1 2 1 N i y i N i x i N i y i x i pearson m y m x m y m x y x C N y y y 1 x y x y +1 Pearson Correlation – 1 N n n x x N m 1 1 N n n y y N m 1 1
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• Pearson Correlation captures similarity in the
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This note was uploaded on 10/21/2011 for the course CSCI 3003 taught by Professor Staff during the Spring '08 term at Minnesota.

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lecture22_slides - Overview of today Today: Review of...

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