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Next: Reconstruction from Zernike Moments Up: Materials and Methods Previous: Feature Selection

   
Classification

Before classification, the image feature data were separated into distinct training and test sets in order to assess performance on images not seen by the classifier during training. Numbers of train/test images for each class were as follows: giantin, 47/30; Hoechst, 39/30; LAMP2, 37/60; NOP4, 25/8; tubulin, 25/26. These values were chosen so that there would be no less than 25 images from any class available for training purposes. After this separation, the training data were used to calculate the mean and variance of each feature. These values were then used to normalize the training data to have a mean of zero and a variance of one for each feature. The same mean and variance were then used to normalize the test data (the resulting means and variances for the test set therefore differed somewhat from zero and one respectively). The normalized training and test sets were used with the neural network classifier and the non-normalized sets were used with the classification tree.

Classification trees were implemented using the tree function of S-Plus (version 3.4 for the HP 9000, MathSoft, Seattle, WA USA). The tree-generating algorithm was allowed to run to completion using the 173 image training set and the performance of that tree on the 154 images in the test set was recorded. The tree function in S-Plus utilizes a measure called `deviance' to determine splits. The splitting process continues until a given node contains only one class of data, or until there are less than five samples left in a node. Test samples that reached a leaf node where they were assigned equally to more than one class were considered to be `unknown'.

Back-propagation neural networks were implemented using PDP++ (http://www.cnbc.cmu.edu/PDP++). Networks were configured with the number of inputs equal to the number of features being used at any particular time, 20 hidden nodes (unless specified otherwise), and 5 output nodes (one for each class of input). The learning rate was empirically chosen to be 0.1, and the momentum was 0.9. The desired outputs of the network for each training sample were defined as 0.9 for the node corresponding to the input class and 0.1 for the other nodes. To minimize any bias in the training and testing process, the aforementioned test set was divided into eight pairs of `stop' and `evaluation' sets. Each pairing placed roughly one-eighth of the test images in an evaluation set and the remainder of the test images in a stop set - see Table 2.3. Each sample in the single test set appears in only one of the eight evaluation sets. Networks were then trained and tested using these eight stop/evaluation pairings. The BPNN was always trained using the single training data set defined above. After every third epoch of training, the sum of squared error was calculated for the stop data, where the error of a particular output node is defined as the difference between its desired and actual output values. Training of the network was terminated when the sum of squared error for the stop set reached a minimum. The performance of the network at the stopping point was measured using the corresponding evaluation set. This process was repeated for the eight pairs of stop and evaluation sets and the classification results summed to generate the confusion matrices in Tables 2.4, 2.6, and 2.8. When measuring the performance of the network using the evaluation data, each sample was classified as belonging to the class corresponding to the largest of the five network output values.


 

 
Table 2.3: The number of images from each class in each of the eight stop/evaluation pairs. Each sample in the original test set was used in only one of the eight evaluation sets. The same 173 image training data were used to train the network in each case.
  Stop/Evaluation samples from each class
Stop/Eval. Pair Giantin DNA LAMP2 NOP4 Tubulin
1 26/4 26/4 52/8 7/1 22/4
2 26/4 26/4 52/8 7/1 22/4
3 26/4 26/4 52/8 7/1 23/3
4 26/4 26/4 52/8 7/1 23/3
5 26/4 26/4 52/8 7/1 23/3
6 26/4 26/4 52/8 7/1 23/3
7 27/3 26/3 54/6 7/1 23/3
8 27/3 26/3 54/6 7/1 23/3


next up previous contents
Next: Reconstruction from Zernike Moments Up: Materials and Methods Previous: Feature Selection
Copyright ©1999 Michael V. Boland
1999-09-18