Pixelhop++: A Small Successive-Subspace-Learning-Based (Ssl-Based) Model For Image Classification

Abstract

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 Pixel-Hop++. 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 Pixel-Hop++, 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.

TGHop: an explainable, efficient, and lightweight method for texture generation

“…To reduce the computational burden in training and inference of DL-based methods, we adopt spatial-spectral representations for texture images based on the successive subspace learning (SSL) framework [32][33][34]. To implement SSL, PixelHop [35] and PixelHop++ [27] offers powerful hierarchical representations and plays a key role of dimension reduction in TGHop. SSL-based solutions have been proposed to tackle quite a few problems, including [36][37][38][39][40][41][42][43][44][45].…”

“…Specifically, we can apply the c/w Saab transform in each stage to conduct the analysis. In the following, we provide a brief review on the Saab transform [34] and the c/w Saab transform [27].…”

“…First, given an exemplary texture, TGHop crops numerous sample patches out of it to form a collection of sample patches called the source. Second, it analyzes pixel statistics of samples from the source and obtains a sequence of fine-to-coarse subspaces for these patches by using the PixelHop++ framework [27]. Third, to generate realistic texture patches, it begins with generating samples in the coarsest subspace, which is called the core, by matching the distribution of real and generated samples, and attempts to generate spatial pixels given spectral coefficients from coarse to fine subspaces.…”

DefakeHop: A Light-Weight High-Performance Deepfake Detector

“…DefakeHop consists of three main modules: 1) PixelHop++, 2) feature distillation and 3) ensemble classification. To derive the rich feature representation of faces, DefakeHop extracts features using PixelHop++ units [12] from various parts of face images. The theory of PixelHop++ have been developed by Kuo et al using SSL [13,14,12].…”

“…To derive the rich feature representation of faces, DefakeHop extracts features using PixelHop++ units [12] from various parts of face images. The theory of PixelHop++ have been developed by Kuo et al using SSL [13,14,12]. PixelHop++ has been recently used for feature learning from low-resolution face images [15,16] but, to the best of our knowledge, this is the first time that it is used for feature learning from patches extracted from high-resolution color face images.…”