PixelHop++: A Small Successive-Subspace-Learning-Based (SSL-based) Model for Image Classification

The successive subspace learning (SSL) principle was developed and used to design an interpretable learning model, known as the PixelHop method, for image classification in our prior work. Here, we propose an improved PixelHop method and call it PixelHop++. First, to make the PixelHop model size smaller, we decouple a joint spatial-spectral input tensor to multiple spatial tensors (one for each spectral component) under the spatial-spectral separability assumption and perform the Saab transform in a channel-wise manner, called the channel-wise (c/w) Saab transform. Second, by performing this operation from one hop to another successively, we construct a channel-decomposed feature tree whose leaf nodes contain features of one dimension (1D). Third, these 1D features are ranked according to their cross-entropy values, which allows us to select a subset of discriminant features for image classification. In PixelHop++, one can control the learning model size of fine-granularity, offering a flexible tradeoff between the model size and the classification performance. We demonstrate the flexibility of PixelHop++ on MNIST, Fashion MNIST, and CIFAR-10 three datasets.