Sample classification using the GA/KNN algorithm with varying ...

Sample classification using the GA/KNN algorithm with varying values
of the p parameter
By
E. Prabhu Raman
George Mason University
Abstract : The GA/KNN method developed by Leping Li 1 has been tested and is
proved to classify ALL/AML samples efficiently. This study explores the results obtained
after modifying the KNN method used in the GA/KNN method by varying the
minkowski’s p-parameter. The GA/KNN method did not efficiently classify the test
samples in the runs performed. Out of 34 test samples, around 12 - 14 samples were
misclassified in each run. It was observed that an odd numbered p parameter (3,5,7) gave
the same classification result, it classified all of the samples as ALL. It were only the
even numbered parameters(2,4,6) which could classify some of the AML samples
correctly in the test data.
Introduction : With the invention of microarray technology, it is possible to measure
the expression of thousands of genes at a time. A microarray image gives a snapshot of
the activity of each gene of a cell at the time of mRNA extraction.
Hence, we can develop expression signatures for cells by which we can identify an
unknown type of cell. This approach is thus applied to identify tumor samples. Firstly,
using a training set, a signature is constructed. Then, using that signature samples are
classified into different classes.
This study deals with leukemia data (Golub et al, 1999 3 ). There are 72 samples
comprising of classes Acute lymphoblastic leukemia(ALL) and Acute myeloid
leukemia(AML). Subclasses exist within these two classes.
The GA/KNN algorithm employs constructing subsets(the user specifies the size) of
genes. The Genetic Algorithm is used to choose relatively few discriminative subsets of
genes 1 . The KNN is used to decide whether a subset is discriminative or not. For a
detailed description, please refer to Li et al. 1
The p parameter comes in the distance formula which comes in the KNN calculation. The
distance is calculated between n dimensional data points(samples), n being equal to the
number of genes. If S1,S2,….Sm are the m samples. And g1k,g2k,….gnk are the n
expression values of the n genes of sample Sk. Then using a p parameter of value 2, we
would calculate distance between any two samples Sj and Sk as :
D = [ (g1k – g1j) 2 +…….+(gnk – gnj) 2 ] 1/2

Similarly if the p parameter equals 5, then the formula will be as follows:
Methods :
D = [ (g1k – g1j) 5 +…….+(gnk – gnj) 5 ] 1/5
Data: Golub data was obtained from BINF 733 website .The data was filtered and
transformed to log scale as shown below (taken from Li et al. 1 ).
The filtering was done by excluding genes whose expression levels were below 50 in
more than 57 out of the 72 samples. 5455 genes were left after the filtering which were
transformed to the log scale. The data set was tailored to act as an input for the GA/KNN
algorithm.
Usage of GA/KNN algorithm:
The GA/KNN source code was kindly provided by Dr. Leping Li .First, it was run on the
dataset without any modification. In that case the p parameter was equal to 2. Then the
code was modified by changing the distance calculation used while calculating the Knearest
neighbors. Then the modified source code was run for p parameter values 3, 4 ,5,
6 and 7. Higher p values increased the run time of the program and the program did not
successfully execute because of limited computing resources.
The program was run several times on unix server(mason.gmu.edu) to find out the
optimal parameters, taking into account the run time. The following parameters were
found best suited for the golub data set:
Chromosome length : 10 (higher values did not change the output)
Number of near optimal solutions : 5000(higher values did not change the output)
Termination fitness cutoff : 36
K( in KNN) 3
Number of training samples 38
Number of test samples 34
For a Detailed description of each of these parameters please refer to Li et al 1 .
The results from the algorithm were analyzed and the number of wrong classifications
were counted for each run(for each value of p parameter). Each run of the program
yielded a Gene ranking. 50 Top ranked genes were taken in each case and the dataset was
cut short from 5455 genes across 72 samples to 50 genes across 72 samples. This data
was now plotted in its first two principal components using MATLAB.

Results :
The GA/KNN did not work perfectly well in this study for the golub data. 12 – 14
samples out of 34 were misclassified in each run.
p ALL misclassifications AML misclassifications Total misclassifications
2 6 7 13 out of 34
3 0 14 14 out of 34
4 5 7 12 out of 34
5 0 14 14 out of 34
6 7 7 14 out of 34
7 0 14 14 out of 34
For the p parameter value 3, 5, 7 the results are alike. Similarly we can see similarity
between the results with even numbered p parameter. The striking feature is that that odd
numbered p values fail to classify AML samples totally. The p parameter 4 seems to be
the best choice for the dataset as it classifies 22 samples out of 34 correctly. There is not
much difference between the outputs of even numbered p-values. Please Refer to the next
page for explanations of the PCA graphs shown below.
p = 2

p = 3
p = 4

p = 5
p = 6

p = 7
The PCA of even numbered p parameter (except p = 6) runs seem to distinguish ALL and
AML better. ALL is concentrated towards one end and the AML samples towards
another. But in the odd numbered p value runs, The ALL samples are at the centre and
are not so well separated and hence do not distinguish so well. The ALLs are closer to
AML samples than in the even numbered p value runs. This is in agreement to the
number of misclassifications counted for odd numbered p value runs.
Conclusions
The GA/KNN algorithm did not work really well for this study. It misclassified 12 -14
samples out of 34 test samples. It was observed that the output of the GA/KNN algorithm
changes with changing the p parameter. The even numbered p parameters seem to
perform better than the odd numbered values. The odd ones fail to classify any AML
samples, the reason for which remains unexplored.
References
1. Computational Analysis of Leukemia Microarray Expression Data using the
GA/KNN Method by Leping Li, Lee G. Pedersen, Thomas A. Darden, and
Clarice R. Weinberg
The PCA graphs:
For each value of p, the algo
was run and PCA was done
using the top 50 genes
obtained.
Green circles- B-cell ALL
Green squares-T-cell ALL
Red circles – M1 type AML
Red square – M2 type AML
Red diamond- M4 type
AML
Red Stars – M5 type AML

2. A tutorial on Principal Component Analysis by Lindsay I Smith. Feb 26,2002.
3 .Molecular Classification ofCancer: Class Discovery andClass Prediction by Gene
Expression Monitoring by Golub et al. 1999

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