Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data
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Transcript of Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data
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Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data
Presented by: Tun-Hsiang Yang
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purpose of this paper
Compare the performance of different discrimination methods
Nearest Neighbor classifier Linear discriminant analysis Classification tree Machine learning approaches: bagging, boosting
Investigate the use of prediction votes to assess the confidence of each prediction
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Statistical problems:
The identification of new/unknown tumor classes using gene expression profiles
Clustering analysis/unsupervised learning
The classification of malignancies into known classes
Discriminant analysis/supervised learning
The identification of marker genes that identified different tumor classes
Variable (Gene) selection
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Datasets
Gene expression data on p genes for n mRNA samples:
n x p matrix X={x ij},
where x ij denotes the expression level of gene (variable) j in ith mRNA sample(observation)
Response: k-dimensional vector Y={yi},
where yi denotes the class of observation i
Lymphoma dataset (p=4682, n=81,k=3) Leukemia dataset (p=3571, n=72, k=3 or 2) NCI 60 dataset (p=5244, n=61, k=8)
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Data preprocessing
Imputation of missing data (KNN)
Standardization of data (Euclidean distance)
preliminary gene selection
Lymphoma dataset (p=4682 p=50, n=81,k=3) Leukemia dataset (p=3571p=40, n=72, k=3) NCI 60 dataset (p=5244p=30, n=61, k=8)
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Visual presentation of Leukemia dataset
Correlation matrix (72x72) ordered by class Black: 0 correlation / Red: positive correlation / Green: negative correlation
P=3571 p=40
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Prediction Methods
Supervised Learning Methods
Machine learning approaches
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Supervised Learning Methods Nearest Neighbor classifier(NN)
Fisher Linear Discriminant Analysis (LDA)
Weighted Gene Voting
Classification trees (CART)
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Nearest Neighbor
The k-NN rule
Find the k closest observations in the learning set
Predict the class for each element in the test dataset by majority vote
K is chosen by minimizing cross-validation error rate
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Linear Discirminantion Analysis
FLDA consists of
finding linear functions a’x of the gene expression levels x=(x1, …,xp) with large ratio of between groups to within groups sum of squares
Predicting the class of an observation by the class whose mean vector is closest to the discrimination
variables
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Maximum likelihood discriminant rules
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•Predicts the class of an observation x as C(x)=argmaxkpr(x|y=k)
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Weighted Gene Voting
An observation x=(x1,…xp) is classified as 1 iff
Prediction strength as the margin of victory(p9)
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Classification tree
Constructed by repeated splits of subsets (nodes)
Each terminal subset is assigned a class label
The size of the tree is determined by minimizing the cross validation error rate
Three aspects to tree construction
the selection of the splits
the stopping criteria
the assignment of each terminal node to a class
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Aggregated Predictors
There are several ways to generate perturbed learning set:
Bagging
Boosting
Convex Pseudo data (CPD))),((maxarg kLxCIw b
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Bagging
Predictors are built for each sub-sample and aggregated by
Majority voting with equal wb=1
Non-parametric bootstrap: drawing at random with replacement to form a
perturbed learning sets of the same size as the original learning set
By product: out of bag observations can be used to estimate misclassification rates of bagged predictors
A prediction for each observation (xi, yi) is obtained by aggregating the classifiers in which (xi,yi) is out-of-bag
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Bagging (cont.)
Parametric bootstrap:
Perturbed learning sets are generated according to a mixture of MVN distributions
For each class k, the class sample mean and covariance matrix were taken as the estimates of distribution parameters
Make sure at least one observation sampled from each class
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BoostingThe bth step of the boosting algorithm
Get another learning set Lb of the same size nL
Build a classifier based on Lb
Run the learning set L let di=1 if the ith case is classified incorrectly
di=0 otherwise
Define b=Pidi and Bbdi=(1- b)/ b
Update by pi=piBbdi/ piBb
di
Re-sampling probabilities are reset to equal if b>=1/2 or b=0
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Prediction votes
For aggregated classifiers, prediction votes assessing the strength of
a prediction may be defined for each observation
The prediction vote (PV) for an observation x
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Study Design
Randomly divide the dataset into a learning and test set (2:1 scheme)
For each of N=150 runs: Select a subset of p genes from the learning set
with the largest BSS/WSS Build the different predictors using the learning
sets with p genes Apply the predictors to the observations in the test
set to obtain test set error rates
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Results
Test set error rates: apply classifier build based on learning set to test set. Summarized by box-plot over runs
Observation-wise error rates: for each observation, record the proportion of times it was classified incorrectly. Summarized by means of survival plots
Variable selection: compare the effect of increasing or decreasing number of genes (variables)
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Leukemia data, two classes
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Leukemia data, three classes
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Lymphoma data
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Conclusions In the main comparison, NN and DLDA had the smallest error
rates, while FLDA had the highest error rates
Aggregation improved the performance of CART classifiers, the largest gains being with boosting and bagging with CPD
For the lymphoma and leukemia datasets, increasing the number of variables to p=200 did not affect much the performance of the various classifiers. There was an improvement for the NCI 60 dataset.
A more carefully selection of a small number of genes (p=10) improved the performance of FLDA dramatically