# GENHOP: An Image Generation Method Based on Successive Subspace Learning

arXiv: https://arxiv.org/abs/2210.03689 · HTML: https://mlsanity.com/paper/2210.03689/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 38 references that are in the map.
- First posted on arXiv 7 Oct 2022.

## Builds on (most cited first, 29 of 29)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Least Squares Generative Adversarial Networks](https://mlsanity.com/paper/1611.04076/) (2016)
- [Are GANs Created Equal? A Large-Scale Study](https://mlsanity.com/paper/1711.10337/) (2017)
- [Optimizing the Latent Space of Generative Networks](https://mlsanity.com/paper/1707.05776/) (2017)
- [BEGAN: Boundary Equilibrium Generative Adversarial Networks](https://mlsanity.com/paper/1703.10717/) (2017)
- [Implicit Maximum Likelihood Estimation](https://mlsanity.com/paper/1809.09087/) (2018)
- [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)
- [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)
- [Non-Adversarial Image Synthesis with Generative Latent Nearest Neighbors](https://mlsanity.com/paper/1812.08985/) (2018)
- [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)
- [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)
- [TGHop: An Explainable, Efficient and Lightweight Method for Texture Generation](https://mlsanity.com/paper/2107.04020/) (2021)
- [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, 4 of 4)

- [An Overview on Generative AI at Scale with Edge-Cloud Computing](https://mlsanity.com/paper/2306.17170/) (2023)
- [Enhancing Edge Intelligence with Highly Discriminant LNT Features](https://mlsanity.com/paper/2312.14968/) (2023)
- [Green Steganalyzer: A Green Learning Approach to Image Steganalysis](https://mlsanity.com/paper/2306.04008/) (2023)
- [A Tiny Machine Learning Model for Point Cloud Object Classification](https://mlsanity.com/paper/2303.10898/) (2023)

## Abstract (arXiv)

Being different from deep-learning-based (DL-based) image generation methods, a new image generative model built upon successive subspace learning principle is proposed and named GenHop (an acronym of Generative PixelHop) in this work. GenHop consists of three modules: 1) high-to-low dimension reduction, 2) seed image generation, and 3) low-to-high dimension expansion. In the first module, it builds a sequence of high-to-low dimensional subspaces through a sequence of whitening processes, each of which contains samples of joint-spatial-spectral representation. In the second module, it generates samples in the lowest dimensional subspace. In the third module, it finds a proper high-dimensional sample for a seed image by adding details back via locally linear embedding (LLE) and a sequence of coloring processes. Experiments show that GenHop can generate visually pleasant images whose FID scores are comparable or even better than those of DL-based generative models for MNIST, Fashion-MNIST and CelebA datasets.