Feature Selection and Reduction of Classifier Complexity

In a further attempt to reduce the dimensionality of the feature set, a subset of 10 features was selected from the combined Zernike and Haralick features using the stepwise discriminant analysis functionality (i.e. the STEPDISC procedure) of SAS. This method uses Wilks' lambda statistic to iteratively determine which features are best able to separate the classes in feature space. The 10 features selected using this method are listed in Table 2.7. Using these 10 features as inputs to a BPNN containing 20 hidden nodes resulted in correct classification rates of 97% for giantin, 93% for Hoechst, 82% for LAMP2, 88% for NOP4, and 54% for tubulin. Although the performance on the first four classes is identical to the Haralick features alone, the performance on the tubulin images is significantly worse (81% vs. 54%) and drops the average classification rate to $83\pm6\%$. Performance of the stepwise discriminant procedure was unsatisfactory in this case.

As an alternative, a different subset of features was identified using Equation 2.14. This procedure selects those features that, on average, widely separate the classes from each other while at the same time keep the individual classes tightly clustered. The 10 features selected using this method are included in Table 2.7. Although 7 of the 10 features selected using this approach are the same ones selected using stepwise discriminant analysis, the performance of the BPNN using these 10 features (Table 2.8) was better (88% vs. 83%). This result is important because it indicates that it is possible to achieve performance at least equal to the best single feature set using a smaller number of features selected from both feature sets.

 

Table 2.7: The 10 best features selected using stepwise discriminant analysis (SDA - left), and using Equation 2.14 (right). Features were selected using the training data only.

 

  

Table 2.8: Confusion matrix generated from the output of a back-propagation neural network trained and tested with the 10 `best' Zernike and Haralick features. The average classification rate for the test data is $88\pm5.1\%$. Performance across the 8 test sets ranged from 70-95%. Average performance on the training data was $97\pm2.6\%$.

True	Output of the BPNN
Classification	Giantin	Hoechst	LAMP2	NOP4	Tubulin
Giantin	97%	0%	3%	0%	0%
Hoechst	3%	97%	0%	0%	0%
LAMP2	12%	0%	83%	2%	3%
NOP4	0%	0%	13%	88%	0%
Tubulin	0%	0%	19%	4%	77%