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

arXiv: https://arxiv.org/abs/2002.03141 · HTML: https://mlsanity.com/paper/2002.03141/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2020.

## Built on by (most cited first, 30 of 37)

- [AMMU : A Survey of Transformer-based Biomedical Pretrained Language Models](https://mlsanity.com/paper/2105.00827/) (2021)
- [DefakeHop: A Light-Weight High-Performance Deepfake Detector](https://mlsanity.com/paper/2103.06929/) (2021)
- [Green Learning: Introduction, Examples and Outlook](https://mlsanity.com/paper/2210.00965/) (2022)
- [On Supervised Feature Selection from High Dimensional Feature Spaces](https://mlsanity.com/paper/2203.11924/) (2022)
- [BERTHop: An Effective Vision-and-Language Model for Chest X-ray Disease Diagnosis](https://mlsanity.com/paper/2108.04938/) (2021)
- [VoxelHop: Successive Subspace Learning for ALS Disease Classification Using Structural MRI](https://mlsanity.com/paper/2101.05131/) (2021)
- [A scoping review on multimodal deep learning in biomedical images and texts](https://mlsanity.com/paper/2307.07362/) (2023)
- [AnomalyHop: An SSL-based Image Anomaly Localization Method](https://mlsanity.com/paper/2105.03797/) (2021)
- [Successive Subspace Learning: An Overview](https://mlsanity.com/paper/2103.00121/) (2021)
- [Bi-VLGM : Bi-Level Class-Severity-Aware Vision-Language Graph Matching for Text Guided Medical Image Segmentation](https://mlsanity.com/paper/2305.12231/) (2023)
- [E-PixelHop: An Enhanced PixelHop Method for Object Classification](https://mlsanity.com/paper/2107.02966/) (2021)
- [TGHop: An Explainable, Efficient and Lightweight Method for Texture Generation](https://mlsanity.com/paper/2107.04020/) (2021)
- [Segmentation of Cardiac Structures via Successive Subspace Learning with Saab Transform from Cine MRI](https://mlsanity.com/paper/2107.10718/) (2021)
- [GSIP: Green Semantic Segmentation of Large-Scale Indoor Point Clouds](https://mlsanity.com/paper/2109.11835/) (2021)
- [DefakeHop++: An Enhanced Lightweight Deepfake Detector](https://mlsanity.com/paper/2205.00211/) (2022)
- [PAGER: Progressive Attribute-Guided Extendable Robust Image Generation](https://mlsanity.com/paper/2206.00162/) (2022)
- [Bridging Gap between Image Pixels and Semantics via Supervision: A Survey](https://mlsanity.com/paper/2107.13757/) (2021)
- [Subspace Learning Machine (SLM): Methodology and Performance](https://mlsanity.com/paper/2205.05296/) (2022)
- [GENHOP: An Image Generation Method Based on Successive Subspace Learning](https://mlsanity.com/paper/2210.03689/) (2022)
- [Design of Supervision-Scalable Learning Systems: Methodology and Performance Benchmarking](https://mlsanity.com/paper/2206.09061/) (2022)
- [S3I-PointHop: SO(3)-Invariant PointHop for 3D Point Cloud Classification](https://mlsanity.com/paper/2302.11506/) (2023)
- [Enhancing Edge Intelligence with Highly Discriminant LNT Features](https://mlsanity.com/paper/2312.14968/) (2023)
- [Fighting Malicious Media Data: A Survey on Tampering Detection and Deepfake Detection](https://mlsanity.com/paper/2212.05667/) (2022)
- [GreenCOD: A Green Camouflaged Object Detection Method](https://mlsanity.com/paper/2405.16144/) (2024)
- [Statistical Attention Localization (SAL): Methodology and Application to Object Classification](https://mlsanity.com/paper/2208.01823/) (2022)
- [PointFlowHop: Green and Interpretable Scene Flow Estimation from Consecutive Point Clouds](https://mlsanity.com/paper/2302.14193/) (2023)
- [Green Steganalyzer: A Green Learning Approach to Image Steganalysis](https://mlsanity.com/paper/2306.04008/) (2023)
- [HyperBank: A Differentiable Bank of Classical Priors for Few-Shot Spheroid Microscopy Segmentation](https://mlsanity.com/paper/2607.10684/) (2026)
- [Evaluation of Multimodal Semantic Segmentation using RGB-D Data](https://mlsanity.com/paper/2103.16758/) (2021)
- [Lightweight Image Codec via Multi-Grid Multi-Block-Size Vector Quantization (MGBVQ)](https://mlsanity.com/paper/2209.12139/) (2022)

## Abstract (arXiv)

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.