Part II: Discriminative Margin Clustering

1
Part IIDiscriminative Margin Clustering

• Joint work with
• Rob Tibshirani, Dept of Statistics
• Patrick O. Brown, School of Medicine
• Stanford University

2
Gene Expression

• Micro-array technology
• Find expression values of all genes in a tissue
• Expression pattern of genes related to
  characteristics of tissue type
• Gene expression is combinatorial
• Many factors need to combine for expression of a
  gene
• Combinations of expressions lead to certain
  phenotypes
• Poorly understood

3
Feature Sets for Tumors

• Set of genes with higher expression in a cancer
  type compared to every normal tissue type in the
  body
• Combinatorial gene expression signature
• Potential use in diagnostics and drug treatments
• If these genes encode cell surface proteins
• can target them using antibodies
• Kills tumor cells
• Does not harm normal cells

4
Feature Set Definition
Convex combination of genes which gives maximum
separation in expression values
Constraint w1w2 1
w1xw2y
Expression value for Gene y
Tumor t
Margin m
Around 100 samples
Normal Set N
Expression Value for Gene x
5
Computing the Feature Set
Definition naturally extends to collections of
tumor samples
6
Example
Gene T N1 N2
g1 100 50 10
g2 100 10 50
w1g1w2g2 100 30 30
w1 0.5
w2 0.5
Margin 100 30 70
7
Contrast with Previous Work

• Previous work focused just on classifiers
• Separating tumor class from corresponding normal
  class
• Separating tumor from all other tumor tissues
• Linear and quadratic Support Vector Machines
• Brown et al. , Moler et al. , Ramaswamy et
  al. , Su et al., Grate et al.
• Problem Many cancers have poorly understood
  subtypes
• We focus on two combined aspects
• Classifiers separating tumor from all normal
  tissue classes
• Clustering tumors based on this paradigm of
  separation

8
Traditional Clustering

• Cluster tissues based on similarity of gene
  expression patterns
• Similar tissues have correlated gene expressions
• Eisen, et al. PNAS 1998
• Problem Genes driving the clustering
• Large classes of genes that are all regulated
  together
• Cell cycle and cell proliferation
  
• Protein biosynthesis and cell growth
• Respiration
• We need to weight these gene classes appropriately

9
Our Results

• Feature sets for tumor samples very small
• Picks only one from a correlated set of genes
• Genes with different functions expressed in
  different normal tissues
• Hierarchically cluster tumor samples
• Similarity metric for two tumor sets Combined
  Margin
• Tumor samples with similar feature sets group
  together
• Identify natural clusters of tumor samples
• Construct feature sets for each cluster
• Biological significance

10
Clustering Hardness

• Given
• Set of n tumors
• Margin M
• Find largest tumor subset with margin ? M
• Problem is n1-? hard to approximate
• Reduction from maximum clique problem

11
Clustering Algorithm
G
F
m2
m1
H
Gene y
E
Tumors
Margin m2
A
A
B
D
C
G
H
F
E
D
B
C
Margin m1
Normal
Gene x
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Cluster Boundaries

• Each node in tree labeled with combined margin of
  tumor samples in sub-tree
• Margin reduces as we move up the tree
• Chop tree at a chosen margin cut-off
• Sub-trees are the clusters
• Breast cancer samples group into three clusters
• ERBB2 (ERBB2 and GRB7)
• Luminal A type (ESR1, NAT1 and GATA3)
• Basal cell type(?) (Keratin, Fibrillin and
  Fibronectin)

13
Properties of Feature Sets

• Feature set for a tumor cluster
• Has at most 20 genes
• Most of the weight concentrated on a few genes

Tumor Cluster Genes Fraction of weight
ERBB2 Breast ERBB2 65
Luminal A Breast ESR1, NAT1, GATA3 55
Prostate sub-type AMACR 40
Ovarian sub-type MSLN, PAX8, COL1A2 65
14
Quality of Clustering

• Random partitioning of tumor samples
• Divide tumor samples randomly into training and
  test groups
• Cluster training group
• Find cluster with best feature set margin for
  test sample
• Label the sample with the tumor type for that
  cluster
• Classifies unknown tumor samples accurately
• At least 75 accuracy in categorizing test
  samples
• At least 90 accuracy for CNS, Breast, Kidney,
  Ovary and Prostate cancers

15
Discussion

• Small feature sets for a tumor class
• Based only on discriminating it versus normal
  tissues
• Property Also discriminates it from other tumor
  classes
• Highly expressed genes unique to the tumor class
• Biological validation of our method
• ERBB2 and ESR1 can be targeted by monoclonal
  antibodies
• Some of the most effective treatments for breast
  cancers
• AMACR is recently recognized prostate cancer
  marker
• Function not very well understood
• MSLN is a well studied ovarian cancer marker

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Expanding Feature Sets

• Consider weighted combinations which have close
  to optimal margin
• Let optimal margin M
• P(?) Polytope of feature sets with margin ? M
  - ?
• Find weight vector with min Euclidean norm in
  P(?)
• Intuition
• Manhattan norm of any weight vector 1
• Minimizing Euclidean norm spreads the weights
• Around 100 genes in feature set

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Genes in Larger Feature Sets

• Genes with similar expression patterns
• Example ERBB2 and GRB7
• Genes expressed across cancer types
• Not very strongly expressed
• Do not drive the clustering
• Example Proliferation and cell cycle related
  genes
• C20ORF1, CENPF, NUF2R, TOPK, L2DTL, KNSL1,
• Example Possible alterations to chromosome 22
• PRAME

18
Future Work

• Identify cell surface proteins in feature sets
• Possible use in chemotherapy and diagnostics
• Findings for Ovarian and Pancreatic cancers being
  tested in the laboratory
• Identify genes highly expressed across cancer
  types
• Examples TFAP2A, ADAM12 and LOX
• Biological significance?
• Succinct representations for biological
  functions
• Examples Cell cycle, respiration,
• Applications in clustering and modeling gene
  expression