1. Breast Cancer Diagnosis via Neural Network Classification Jing Jiang May 10, 2000

2. Outline Introduction and Motivation K-mean, k-nearest neighbor and maximum likelihood classification Back propagating multi-layer perceptron Support vector machine (SVM) Learning vector quantization (LVQ) Linear programming

3. Introduction and Motivation The data file contains the 30 attributes of both benign and malignant fine needle aspirates (FNAs). Our goals are to find a discriminating function to determine if an unknown sample is benign or malignant and choose a pair of the 30 attributes which will be used in diagnosis. Linear program has done a good job in solving this problem. We expect the neural network classification algorithms can be useful for this problem.

4. K-mean First we use k-mean algorithm to find the cluster of the training data set. K-mean algorithm doesn’t give up the discriminating function

5. KNN and ML For 100 nearest neighbors we have, For 20 nearest neighbors we have For maximum likelihood algorithm we have,

6. BP-MLP After careful choice of network parameters, we get the same Cmat and C-rate for the 30 attribute and any 2 attribute problem. It is interesting to note they are the same as the result we get for ML method The low classification rate can be due to the fact that the data is not linearly separable.

7. Support Vector Machine For attribute 1 and 23, we have 6 errors in the testing. For attribute 14 and 28, we have 8 errors in testing. It takes a long time to train a SVM for the 30 attribute problem, even for 2 attribute, it is time consuming too.

8. LVQ While using LVQ for attribute 1 and 23, the number of errors is 8. For attribute 14 and 18, we have 25 errors. The training is faster than SVQ, but so far we are only able to handle the 2 attribute problem, not a 30 attribute problem.

9. LVQ Training data and Weights

10. Linear Program The algorithm used is similar to SVM, but simpler. We device a separation plane and try to minimize the error. For 30 attribute we have only 3 errors For 2 attribute, the best combinations give 2 errors.

11. Linear Program

12. Conclusion We tried various neural network classification algorithm. It seems as far the simpler linear programming gives a better result. More exploration need to be done. BP is not very good at dealing with non-separable data. SVM is a good candidate, but takes a long time to train. LVQ is comparable with SVM. An question remain to be answered, why the maximum likelihood method give the same result as the BP.