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

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