# E-PixelHop: An Enhanced PixelHop Method for Object Classification

arXiv: https://arxiv.org/abs/2107.02966 · HTML: https://mlsanity.com/paper/2107.02966/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 46 references that are in the map.
- First posted on arXiv 7 Jul 2021.

## Builds on (most cited first, 30 of 31)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model size](https://mlsanity.com/paper/1602.07360/) (2016)
- [Learn To Pay Attention](https://mlsanity.com/paper/1804.02391/) (2018)
- [Do Convolutional Neural Networks Learn Class Hierarchy?](https://mlsanity.com/paper/1710.06501/) (2017)
- [Interpretable Convolutional Neural Networks via Feedforward Design](https://mlsanity.com/paper/1810.02786/) (2018)
- [PointHop: An Explainable Machine Learning Method for Point Cloud Classification](https://mlsanity.com/paper/1907.12766/) (2019)
- [B-CNN: Branch Convolutional Neural Network for Hierarchical Classification](https://mlsanity.com/paper/1709.09890/) (2017)
- [PixelHop++: A Small Successive-Subspace-Learning-Based (SSL-based) Model for Image Classification](https://mlsanity.com/paper/2002.03141/) (2020)
- [Understanding Convolutional Neural Networks with A Mathematical Model](https://mlsanity.com/paper/1609.04112/) (2016)
- [DefakeHop: A Light-Weight High-Performance Deepfake Detector](https://mlsanity.com/paper/2103.06929/) (2021)
- [R-PointHop: A Green, Accurate, and Unsupervised Point Cloud Registration Method](https://mlsanity.com/paper/2103.08129/) (2021)
- [On Data-Driven Saak Transform](https://mlsanity.com/paper/1710.04176/) (2017)
- [PointHop++: A Lightweight Learning Model on Point Sets for 3D Classification](https://mlsanity.com/paper/2002.03281/) (2020)
- [Unsupervised Point Cloud Registration via Salient Points Analysis (SPA)](https://mlsanity.com/paper/2009.01293/) (2020)
- [VoxelHop: Successive Subspace Learning for ALS Disease Classification Using Structural MRI](https://mlsanity.com/paper/2101.05131/) (2021)
- [Unsupervised Feedforward Feature (UFF) Learning for Point Cloud Classification and Segmentation](https://mlsanity.com/paper/2009.01280/) (2020)
- [FaceHop: A Light-Weight Low-Resolution Face Gender Classification Method](https://mlsanity.com/paper/2007.09510/) (2020)
- [GraphHop: An Enhanced Label Propagation Method for Node Classification](https://mlsanity.com/paper/2101.02326/) (2021)
- [NITES: A Non-Parametric Interpretable Texture Synthesis Method](https://mlsanity.com/paper/2009.01376/) (2020)
- [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)
- [The Treasure beneath Convolutional Layers: Cross-convolutional-layer Pooling for Image Classification](https://mlsanity.com/paper/1411.7466/) (2014)
- [A Saak Transform Approach to Efficient, Scalable and Robust Handwritten Digits Recognition](https://mlsanity.com/paper/1710.10714/) (2017)
- [An Interpretable Compression and Classification System: Theory and Applications](https://mlsanity.com/paper/1907.08952/) (2019)
- [Visualization, Discriminability and Applications of Interpretable Saak Features](https://mlsanity.com/paper/1902.09107/) (2019)

## Built on by (most cited first, 9 of 9)

- [Green Learning: Introduction, Examples and Outlook](https://mlsanity.com/paper/2210.00965/) (2022)
- [GSIP: Green Semantic Segmentation of Large-Scale Indoor Point Clouds](https://mlsanity.com/paper/2109.11835/) (2021)
- [Bridging Gap between Image Pixels and Semantics via Supervision: A Survey](https://mlsanity.com/paper/2107.13757/) (2021)
- [Design of Supervision-Scalable Learning Systems: Methodology and Performance Benchmarking](https://mlsanity.com/paper/2206.09061/) (2022)
- [Enhancing Edge Intelligence with Highly Discriminant LNT Features](https://mlsanity.com/paper/2312.14968/) (2023)
- [Statistical Attention Localization (SAL): Methodology and Application to Object Classification](https://mlsanity.com/paper/2208.01823/) (2022)
- [A Tiny Machine Learning Model for Point Cloud Object Classification](https://mlsanity.com/paper/2303.10898/) (2023)
- [On filter design in deep convolutional neural network](https://mlsanity.com/paper/2410.21644/) (2024)
- [LG-NuSegHop: A Local-to-Global Self-Supervised Pipeline For Nuclei Instance Segmentation](https://mlsanity.com/paper/2511.04892/) (2025)

## Abstract (arXiv)

Based on PixelHop and PixelHop++, which are recently developed using the successive subspace learning (SSL) framework, we propose an enhanced solution for object classification, called E-PixelHop, in this work. E-PixelHop consists of the following steps. First, to decouple the color channels for a color image, we apply principle component analysis and project RGB three color channels onto two principle subspaces which are processed separately for classification. Second, to address the importance of multi-scale features, we conduct pixel-level classification at each hop with various receptive fields. Third, to further improve pixel-level classification accuracy, we develop a supervised label smoothing (SLS) scheme to ensure prediction consistency. Forth, pixel-level decisions from each hop and from each color subspace are fused together for image-level decision. Fifth, to resolve confusing classes for further performance boosting, we formulate E-PixelHop as a two-stage pipeline. In the first stage, multi-class classification is performed to get a soft decision for each class, where the top 2 classes with the highest probabilities are called confusing classes. Then,we conduct a binary classification in the second stage. The main contributions lie in Steps 1, 3 and 5.We use the classification of the CIFAR-10 dataset as an example to demonstrate the effectiveness of the above-mentioned key components of E-PixelHop.