Multi-Class Perceptron

The multi-class perceptron algorithm is a supervised learning algorithm for classification of data into one of a series of classes. The following implementation was built as part of my project to build a domain-specific natural language question answering algorithm (interview_qa), to classify questions into categories based on their content.

This algorithm is built in such a way that it can be generalized to any use-case, with details on how to format data in the sections below. It is meant to be easy to use and understand, without any significant performance issues.

For added benefit, this module also contains functions to facilitate training, building, and testing the classifier, providing useful metrics and statistics to judge performance.

Algorithm Summary

This algorithm, like most perceptron algorithms is based on the biological model of a neuron, and it's activation. In the case of a normal perceptron (binary classifier), the data is broken up into a series of attributes, or features, each with a specific value. When this feature vector is received by the artificial neuron as a stimulus, it is multiplied (dot product) by a weight vector, to calculate the activation value of the specific data point. If the activation energy is high enough, the neuron fires (the data meets the classification criteria).

In the case of a multi-class perceptron, things are a little different. The data comes in the same way, but instead of the respecting feature vector being multiplied by a single weight vector (for a single class), it is multiplied (dot product) by a number of weight vectors (a separate vector of weights for each unique class). Whichever weight vector that yields the highest activation energy product is the class the data belongs to. This decision process is known as the Multi-Class Decision Rule.

Training Process

To train the algorithm, the following process is taken. Unlike some other popular classification algorithms that require a single pass through the supervised data set (like Naive Bayes), the multi-class perceptron algorithm requires multiple training iterations to fully learn the data. The iteration count can be easily set as a parameter.

During each iteration of training, the data (formatted as a feature vector) is read in, and the dot product is taken with each unique weight vector (which are all initially set to 0). The class that yields the highest product is the class to which the data belongs. In the case this class is the correct value (matches with the actual category to which the data belongs), nothing happens, and the next data point is read in. However, in the case that the predicted value is wrong, the weight vectors are corrected as follows: The feature vector is subtracted from the predicted weight vector, and added to the actual (correct) weight vector. This makes sense, as we want to reject the wrong answer, and accept the correct one.

After the final iteration, the final weight vectors should be somewhat stable (it is of importance to note that unlike the assumptions of the binary perceptron, there is no guarantee the multi-class perceptron will reach a steady state), and the classifier will be ready to be put to use.

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Classifier Building

The following sections detail how to format the data for use with the classifier builder, as well as how to train and save the classifier for later use. The last section deals with how to build an analytics report for the data.

Formatting the Data

The bulk of the classifier is abstracted away into a Python class, that takes the following parameters as input:

1. classes

   • List of categories/classes that data is divided into. This should be a Python list of strings, and each string should be an exact match of the class tag in the actual feature data.

2. feature_list

   • List of features, as strings in a Python list.

3. feature_data

   • A python list of tagged feature data, in the following format:

     feature_data = [("class1", { "feature1": 1, "feature2": 0, "feature3": 0 }),
                    ("class2", { "feature1": 3, "feature2": 1, "feature3": 1 }),
                    ("class3", { "feature1": 3, "feature2": 1, "feature3": 0 })]

4. train_test_ratio

   • Ratio of data to be used in training vs. testing. Set to 75% by default.

5. iterations

   • Number of iterations to run training data through. Set to 100 by default.

A clear example of how all these parameters should look for a given data set can be found in the shapes_example.py file in the feature_data module.

Training and Saving the Classifier

To build and save a classifier once the example data has been properly formatted and written to the feature_data directory, follow the example formatting provided in the main method of the mc_perceptron.py file:

Instantiate a Perceptron object, call the train method, and finally call the save method (providing a name for the given model). Altogether, it will look something like this (using the provided shape classifier example):

shape_classifier = MultiClassPerceptron(shape_classes, shape_feature_list, shape_feature_data)
shape_classifier.train()
shape_classifier.save_classifier("shape_classifier")

When calling the save class method, the classifier model will by default be saved to shape_classifier.pik in the classifier_models directory. This can be changed depending on your needs.

Building an Analytics Report

Finally, to build an analytics report, create and train a model (as shown above), and finally, call the class method run_analytics() to print the model statistics to screen. These statistics include precision and recall values for each category classifier, as well as f-beta and accuracy statistics. You can also retrieve these values dynamically by accessing the actual fields for each statistic as follows:

precision_dictionary = shape_classifier.precision
recall_dictionary = shape_classifier.recall
fbeta_dictionary = shape_classifier.fbeta_score

# Actually print the comprehensive analytics report
shape_classifier.run_analytics()