# VoxelHop: Successive Subspace Learning for ALS Disease Classification Using Structural MRI

arXiv: https://arxiv.org/abs/2101.05131 · HTML: https://mlsanity.com/paper/2101.05131/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 44 references that are in the map.
- First posted on arXiv 13 Jan 2021.

## Builds on (most cited first, 9 of 9)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Deep Learning for Medical Image Analysis](https://mlsanity.com/paper/1708.08987/) (2017)
- [3D Deep Learning on Medical Images: A Review](https://mlsanity.com/paper/2004.00218/) (2020)
- [Interpretable Convolutional Neural Networks via Feedforward Design](https://mlsanity.com/paper/1810.02786/) (2018)
- [Residual and Plain Convolutional Neural Networks for 3D Brain MRI Classification](https://mlsanity.com/paper/1701.06643/) (2017)
- [PointHop: An Explainable Machine Learning Method for Point Cloud Classification](https://mlsanity.com/paper/1907.12766/) (2019)
- [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)

## Built on by (most cited first, 18 of 18)

- [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)
- [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)
- [E-PixelHop: An Enhanced PixelHop Method for Object Classification](https://mlsanity.com/paper/2107.02966/) (2021)
- [Geo-DefakeHop: High-Performance Geographic Fake Image Detection](https://mlsanity.com/paper/2110.09795/) (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)
- [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)
- [GENHOP: An Image Generation Method Based on Successive Subspace Learning](https://mlsanity.com/paper/2210.03689/) (2022)
- [Enhancing Edge Intelligence with Highly Discriminant LNT Features](https://mlsanity.com/paper/2312.14968/) (2023)
- [SF2Former: Amyotrophic Lateral Sclerosis Identification From Multi-center MRI Data Using Spatial and Frequency Fusion Transformer](https://mlsanity.com/paper/2302.10859/) (2023)
- [LG-NuSegHop: A Local-to-Global Self-Supervised Pipeline For Nuclei Instance Segmentation](https://mlsanity.com/paper/2511.04892/) (2025)
- [Interpretable and backpropagation-free Green Learning for efficient multi-task echocardiographic segmentation and classification](https://mlsanity.com/paper/2601.19743/) (2026)
- [MedSaab-US: A Backpropagation-Free Multi-Scale Wavelet-Saab Framework for Thyroid Nodule Segmentation in Ultrasound Images](https://mlsanity.com/paper/2607.02209/) (2026)

## Abstract (arXiv)

Deep learning has great potential for accurate detection and classification of diseases with medical imaging data, but the performance is often limited by the number of training datasets and memory requirements. In addition, many deep learning models are considered a "black-box," thereby often limiting their adoption in clinical applications. To address this, we present a successive subspace learning model, termed VoxelHop, for accurate classification of Amyotrophic Lateral Sclerosis (ALS) using T2-weighted structural MRI data. Compared with popular convolutional neural network (CNN) architectures, VoxelHop has modular and transparent structures with fewer parameters without any backpropagation, so it is well-suited to small dataset size and 3D imaging data. Our VoxelHop has four key components, including (1) sequential expansion of near-to-far neighborhood for multi-channel 3D data; (2) subspace approximation for unsupervised dimension reduction; (3) label-assisted regression for supervised dimension reduction; and (4) concatenation of features and classification between controls and patients. Our experimental results demonstrate that our framework using a total of 20 controls and 26 patients achieves an accuracy of 93.48% and an AUC score of 0.9394 in differentiating patients from controls, even with a relatively small number of datasets, showing its robustness and effectiveness. Our thorough evaluations also show its validity and superiority to the state-of-the-art 3D CNN classification methods. Our framework can easily be generalized to other classification tasks using different imaging modalities.