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Classifying Lymphoma Dataset Using Multi-class Support Vector Machines

INFS-795 Advanced Data Mining

Prof. Domeniconi

Presented by Hong Chai

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Agenda

(1) Lymphoma Dataset Description

(2) Data Preprocessing

- Formatting

- Dealing with Missing Values

- Gene Selections

(3) Multi-class SVM Classification - 1-against-all

- 1-against-1

(4) Tools

(5) References

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Lymphoma Dataset• Alizadeh et al.(2000), Distinct Types of Diffuse Large B-

cell Lymphoma Identified by Gene Expression Profiling• Publicly available at http://llmpp.nih.gov/lymphoma/• In microarray data,

Expression profiling of

genes are measured in

rows

Samples are columns

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Lymphoma Dataset• 96 samples of lymphocytes (instances)• 4026 human genes (features)• 9 classes of lymphoma:

DLBCL, GCB, NIL, ABB, RAT, TCL, FL, RBB, CLL

• Glimpse of data

DLCL-0042

DLCL-0031

DLCL-0036

CLL-60

CLL-68

FL-10 FL-11 GCB NIL-IgM

CLL-65

GENE2406X 0.75 0.12 0.28 0.58 0.37 -1.2 0.37 -0.6 0.37 0.12

GENE3689X 0.01 -0.4 -0.6 0.37 0.09 0.78 -0.8 2.45 -0.45 0.37

GENE3133X 1.43 -0.8 0.37 -0.5 0.37 1.15 0.37 -1.29 1.26 0.67

GENE1008X 0.05 0.64 0.37 0.12 0.63 0.35 0.12 0.37 -2.29 -0.8

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Lymphoma Dataset

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GoalTask: classification• Assign each patient sample to one of 9 categories, e.g. Diffuse

Large B-cell Lymphoma (DLBCL) or Chronic Lymphocytic Leukemia (CLL).

• Microarray data classification: an alternative to current malignancies classification that relies on morphological or clinical variables

Medical implications• Precise categorization of cancers; more relevant diagnosis • More accurate assignment of cases to high risk or low risk

categories• more targeted therapies • Improved predictability of outcome.

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Data Preprocessing

Missing Values Imputation• 3% of gene expression profiles data are missing• 1980 of the 4026 genes have missing values • 49.1% of genes (features) involved• Some of these genes may be highly informative for

classification• Need to deal with missing values before applying to

SVM

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Missing Value Approaches• Instance or feature deletion

- if dataset large enough & does not distort distribution• Replace with a randomly drawn observed value - proved to work well (http://globain/cse/psu.edu/courses/spring2003/3-norm-val.pdf)

• EM algorithm• Global mode or mean substitution

- will distort distribution• Local mode or mean substitution with KNN algorithm

(Prof. Domeniconi)

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Local Mean Imputation (KNN)1. Partition the data set D into two sets. • Let the first set, Dm, contain instances with missing value(s). • The other set, Dc, contains instances with complete values.

2. For each instance vector x Dm

• Divide the vector into observed and missing parts as x = [xo; xm]. • Calculate the distance between xo and every instance y Dc, using only those features that are observed in x. • From the K closest y’s (instances in Dc), calculate the mean of the feature for which x has missing value(s). Make substitution with this local mean.

(Note: for nominal features use mode. n/a in microarray data)

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Data Preprocessing

Feature Selection: Motivations

- Number of features large, instances small

- Reduce dimensionality to overcome overfitting

- A small number of discriminant “marker” genes

may characterize different cancer classes

Example: Guyon et al. identified 2 genes that yield zero leave-

one-out error in the leukemia dataset, 4 genes in the

colon cancer dataset that give 98% accuracy. (Guyon et al. Gene Selection for Cancer Classification using SVM, 2002)

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Feature Selection

Discriminant Score Ranking • Which gene is more informative in the 2-class

case:

+ - + -

Gene 1 Gene 2

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Separation Score

• Gene 1 more discriminant. Criteria:

- Large difference of μ+ and μ-

- Small variance within each class

• Score function

F(gj) = | (μj+ - μj-) / (σj+ + σj-) |

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Separation Score

• In multi-class cases, rank genes that are discriminant among multiple classes

C1 C2 Δ C3

• A gene may functionally relates to several cancer classes such as C1 and C2

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Separation Score• Proposing an adapted score function

For each gene j

Calculate μi in each class Ci

Sort μi in descending order

Find a cutoff point with largest diff(μi, μj)

μ+ μexp-cutoff-left

σ+ σexp-cutoff-left

μ- μexp-cutoff-right

σ- σexp-cutoff-right

F(gj) = | (μj+ - μj-) / (σj+ + σj-) |

Rank genes by F(gj)

Select top genes via threshold

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Separation Score

Disadvantage:

• Does not yield more compact gene sets; still abundant

• Does not consider mutual information between genes

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Feature Selection

Recursive Feature Elimination/SVM

1. In the linear SVM model on the full feature set

Sign (w•x + b)

w is a vector of weights for each feature, x is an input instance, and b a threshold.

If wi = 0, feature Xi does not influence classification and can be eliminated from the set of features.

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RFE/SVM

2. When w is computed for the full feature set, sort features according in descending order of weights. The lower half is eliminated.

3. A new linear SVM is built using the new set of features. Repeat the process until the set of predictors is non-divisible by two.

4. The best feature subset is chosen.

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Feature Selection

• PCA comment: not common in microarray data.

• Disadvantage: none of original inputs can be discarded

• We want to retain a minimum subset of informative genes to achieve best classification performance.

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Multi-class SVM

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Multi-class SVM Approaches

1-against-all • Each of the SVMs separates a single class from all

remaining classes (Cortes and Vapnik, 1995)

1-against-1• Pair-wise. k(k-1)/2, k Y SVMs are trained. Each SVM

separates a pair of classes (Fridman, 1996)

Performance similar in some experiments (Nakajima, 2000)

Time complexity similar: k evaluation in 1-all, k-1 in 1-1

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1 -against- All• Or “one-against-rest”, a tree algorithm• Decomposed to a collection of binary classifications• k decision functions, one for each class

(wk)T • x+bk, k Y

• The kth classifier constructs a hyperplane between class n and the k-1 other classes

Class of x = argmaxi{(wi)T • (x)+bi}

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1 -against- 1• k(k-1)/2 classifiers where each one is trained on data

from two classes• For training data from ith and jth classes, run binary

classification• Voting strategy: If

Sign(wij)T • x+bij)

says x is in class i, then add 1 to class i. Else to class j.

• Assign x to class with largest vote (Max wins)

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Kernels to Experiment

• Polynomial kernels

K(Xi, Xj)=(XiXj+1)^d

• Gaussian Kernels

K(Xi, Xj)=e^(-|| Xi - Xj ||/σ^2)

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SVM Tools - Weka

Data Preprocessing

• To ARFF format• Import file

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SVM Tools - Weka

Feature Selection using SVM

• Select Attribute • SVMAttributeEval

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SVM Tools - Weka Multi-class classifier

• Classify• Meta• MultiClassClassifier

(Handles multi-class

datasets with 2-class

classifiers)

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SVM Tools - Weka• Multi-class SVM

• Classify• Functions• SMO

(Weka’s SVM)

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SVM Tools - Weka• Multi-class SVM Options

• Method

1-against-1

1-against-all

• Kernel options

not found

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Multi-class SVM Tools

Other Tools include• SVMTorch (1-against-all)• LibSVM (1-against-1)• LightSVM

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References• Alizadeh et al. Distinct types of diffuse large B-cell lymphoma

identified by gene expression profiling, 1999• Cristianini, An Introduction to Support Vector Machines, 2000• Dor et al, Scoring Genes for Relevance, 2000• Franc and Hlavac, Multi-class Support Vector Machines• Furey et al. Support vector machine classification and validation of

cancer tissue samples using microarray expression data, 2000• Guyon et al. Gene Selection for Cancer Classification using Support

Vector Machines, 2002• Selikoff, The SVM-Tree Algorithm, A New Method for Handling Multi-

class SVM, 2003• Shipp et al. Diffuse Large B-cell lymphoma outcome prediction by

gene expression profiling and supervised machine learning, 2002• Weston, Multi-class Support Vector Machines, Technical Report,

1998