Classifica4on Binary classifica,on Given a set of examples ( x i , - - PDF document

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CSCI1950‐Z Computa4onal Methods for Biology Lecture 17

Ben Raphael April 6, 2009

hJp://cs.brown.edu/courses/csci1950‐z/

Classifica4on

Binary classifica,on Given a set of examples (xi, yi), where yi = +‐ 1, from unknown distribu4on D. Design func4on f: Rn  {‐1,+1} that op+mally assigns addi4onal samples xi to

• ne of two classes.

Supervised learning (xi, yi) training data xi(j): feature. Rn: feature space.

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Classifica4on in 2D Hard vs. So\ Op4on

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Decision Surfaces

Linear Nonlinear

Embedding in Higher Dimension

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Cancer Classifica4on

(ben‐Dor et al. JCB 2000)

• Colon cancer (Alon et al. (1999))

– 62 samples. 6000 measured genes. 2000 selected.

• Ovary (Schummer et al. (1999))

– 15 cancerous, 13 normal, 4 other 4ssues. 100,000 cDNA clones

• Leukemia (Golub et al. (1999))

– 25 AML. 47 ALL. 7,129 genes measured genes.

Cancer Classifica4on Results

(ben‐Dor et al. JCB 2000)

Clustering method Select similarity threshold (CAST or hierarchical) to maximize compa+bility with sample labeling. Linear kernel K(x, y) = x . y Quadra4c kernel K(x, y) = (x . y + 1)2 Less than margin

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Results

Colon cancer data