How can I efficiently find the accuracy of a classifier

Question

Even with a simple classifier like the nearest neighbour I cannot seem to judge its accuracy and thus cannot improve it.

For example with the code below:

IDX = knnsearch(train_image_feats, test_image_feats);
    predicted_categories = cell([size(test_image_feats, 1), 1]);
    for i=1:size(IDX,1)
        predicted_categories{i}=train_labels(IDX(i));
    end

Here train_image_feats is a 300 by 256 matrix where each row represents an image. Same is the structure of test_image_feats. train_labels is the label corresponding to each row of the training matrix.

The book I am following simply said that the above method achieves an accuracy of 19%.

How did the author come to this conclusion? Is there any way to judge the accuracy of my results be it with this classifier or other?

The author then uses another method of feature extraction and says it improved accuracy by 30%.

How can I find the accuracy? Be it graphically or just via a simple percentage.

Answer 1

Accuracy when doing machine learning and classification is usually calculated by comparing your predicted outputs from your classifier in comparison to the ground truth. When you're evaluating the classification accuracy of your classifier, you will have already created a predictive model using a training set with known inputs and outputs. At this point, you will have a test set with inputs and outputs that were not used to train the classifier. For the purposes of this post, let's call this the ground truth data set. This ground truth data set helps assess the accuracy of your classifier when you are providing inputs to this classifier that it has not seen before. You take your inputs from your test set, and run them through your classifier. You get outputs for each input and we call the collection of these outputs the predicted values.

For each predicted value, you compare to the associated ground truth value and see if it is the same. You add up all of the instances where the outputs match up between the predicted and the ground truth. Adding all of these values up, and dividing by the total number of points in your test set yields the fraction of instances where your model accurately predicted the result in comparison to the ground truth.

In MATLAB, this is really simple to calculate. Supposing that your categories for your model were enumerated from 1 to N where N is the total number of labels you are classifying with. Let groundTruth be your vector of labels that denote the ground truth while predictedLabels denote your labels that are generated from your classifier. The accuracy is simply calculated by:

accuracy = sum(groundTruth == predictedLabels) / numel(groundTruth);
accuracyPercentage = 100*accuracy;

The first line of code calculates what the accuracy of your model is as a fraction. The second line calculates this as a percentage, where you simply multiply the first line of code by 100. You can use either or when you want to assess accuracy. One is just normalized between [0,1] while the other is a percentage from 0% to 100%. What groundTruth == predictedLabels does is that it compares each element between groundTruth and predictedLabels. If the i^th value in groundTruth matches with the i^th value in predictedLabels, we output a 1. If not, we output a 0. This will be a vector of 0s and 1s and so we simply sum up all of the values that are 1, which is eloquently encapsulated in the sum operation. We then divide by the total number of points in our test set to obtain the final accuracy of the classifier.

With a toy example, supposing I had 4 labels, and my groundTruth and predictedLabels vectors were this:

groundTruth =     [1 2 3 2 3 4 1 1 2 3 3 4 1 2 3];
predictedLabels = [1 2 2 4 4 4 1 2 3 3 4 1 2 3 3];

The accuracy using the above vectors gives us:

>> accuracy

accuracy =

    0.4000

>> accuracyPercentage

accuracyPercentage =

    40

This means that we have a 40% accuracy or an accuracy of 0.40. Using this example, the predictive model was only able to accurately classify 40% of the test set when you put each test set input through the classifier. This makes sense, because between our predicted outputs and ground truth, only 40%, or 6 outputs match up. These are the 1st, 2nd, 6th, 7th, 10th and 15th elements. There are other metrics to calculating accuracy, like ROC curves, but when calculating accuracy in machine learning, this is what is usually done.