  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.
