Collaborative Filter Pre-processing for Improved Corrupted Image Classification

This paper investigates the effects of collaborative filtering on the classification of corrupted digit images. Several experiments were carried out using the MNIST digit dataset by applying a corruption model to the original images, two reconstruction algorithms, and an SVM classifier to measure classification accuracy at each stage of processing. The results demonstrate that collaborative filtering, when properly fit to the data, achieves higher accuracy than not filtering or using a Gaussian filter, and retains high accuracy even up to 85% image corruption. The experiments also show that classification performance drops precipitously when the collaborative filter is allowed to over-fit the training images during reconstruction. Introduction Collaborative filtering is widely known as the winning algorithm of the Netflix challenge for its ability to predict user preferences given highly sparse data [3]. More generally, it can be applied to matrix completion problems [1]. This paper investigates collaborative filtering as it relates to digit image classification on corrupted images using a support vector machine, with corruption simulating the sparse matrix completion problem. corrupt Original MNIST digit images SVM classifier Corrupted digit images SVM classifier Filtered digit images SVM classifier filter Figure 1 – Experimental setup for assessing SVM classifier accuracy on corrupted and reconstructed images. Figure 1 shows the experimental setup. The MNIST digit image dataset is taken as input, and contains 70,000 images of digits, each 28 2 pixels [8]. Each digit has been centered and normalized, but the dataset contains multiple handwriting styles; digits can be written multiple ways (e.g. “2” with or without a loop). Example digits are shown in Figure 2 (left). Using the raw images, an SVM was trained and tested, and the confusion matrix was computed as well as the mean digit classification accuracy. This provided a baseline accuracy for comparing other classifiers. A corruption algorithm was then applied to the MNIST images resulting in degraded image quality (Figure 2 right). The SVM classifier was run to compare the mean classification accuracy of digits. The final processing step applied two filtering algorithms to reconstruct the missing pixels, with the goal of improving SVM classifier accuracy. From these experiments, the effect of corruption and reconstruction was measured having isolated the individual algorithms. Figure 2 – (left) example digits from the MNIST dataset, (right) the same digits with 85% of the pixels removed, simulating sparse data. Note that some digits remain human-recognizable, but others do not. Methodology First, it is interesting to note that while the MNIST dataset appears to have a large number of features (one feature per pixel, 28 2 =784 total), these features are largely redundant. For instance, 8% of the pixels are always set to zero, as can be seen in the heat map of unique pixel values (Figure 3 left). Moreover, PCA indicates that 87 out of 784 features in the eigenbasis capture 90% of the variation in the dataset (Figure 3 right). Therefore, it is reasonable to