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GENHOP: An Image Generation Method Based on Successive Subspace Learning
Xuejing Lei, Wei Wang, C. -C. Jay Kuo
TL;DR
Direct pixel-domain image generation is difficult because pixels have complicated statistical correlations. GenHop uses successive subspace learning to reduce dimensions, generate seed samples, and restore image details; it ranks first by FID on MNIST and second on Fashion-MNIST and CelebA.
Problem
Complicated statistical correlations among pixels make direct generation in the pixel domain difficult.
Source: §1 · p. 1Method
GenHop builds progressively lower-dimensional subspaces, generates seed samples in the lowest-dimensional space, and expands them using LLE and inverse Saab coloring.
Source: §1 · p. 2, §3.3 · p. 4Results
GenHop has the best FID on MNIST and the second-best FID on Fashion-MNIST and CelebA, outperforming almost all other DL-based benchmark methods.
Source: §4 · p. 5Takeaways & Limitations
Generated MNIST digits capture structure with diversity, Fashion-MNIST examples span classes with natural-looking details, and most CelebA samples are semantically meaningful and realistic.
Source: §4 · p. 5Some CelebA object colors are unnatural, which the authors attribute to LLE being performed only in small image regions.
Source: §4 · p. 5
Abstract
from arXiv · showhide
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.
1 Introduction
Direct pixel-domain generation is difficult because image pixels have complicated statistical correlations, while deep-learning methods are described as black-box tools with mathematically intractable end-to-end nonconvex optimization. GenHop applies successive subspace learning to image generation through dimension reduction, seed generation, and dimension expansion.
1 Introduction
- GenHop is built on successive subspace learning and the PixelHop++ architecture, offering an alternative to deep-learning-based image generation.The paper motivates the approach partly by describing deep-learning methods as black boxes whose end-to-end optimization is mathematically intractable.Source: §1 · p. 1
- GenHop addresses complicated pixel correlations with three stages: high-to-low dimension reduction, seed image generation, and low-to-high dimension expansion.It uses channel-wise Saab whitening to reduce dimensionality, Gaussian noise to generate samples in the lowest-dimensional subspace, and LLE plus inverse Saab coloring to restore detail.Source: §1 · pp. 1–2
2 Review of Related Work
The review contrasts deep-learning generative models with successive subspace learning, which combines spatial and spectral representations to capture both global structure and local detail. GenHop extends SSL-based work toward image generation beyond texture synthesis.
DL-based Generative Models
- GANs train generator–discriminator pairs to make generated and training distributions indistinguishable, while VAEs, flow-based methods, and GLANN are presented as non-adversarial alternatives.The review describes VAEs as approximating density with an encoder/decoder, flow-based methods as transforming Gaussian distributions, and GLANN as mapping through feature and noise spaces.Source: §2 · p. 2
SSL
- Saak and Saab transforms represent images with spatial-spectral trade-offs, combining global structure and local detail; channel-wise Saab reduces model size by processing channels individually.PixelHop and PixelHop++ implement SSL; PixelHop++ replaces Saab with channel-wise Saab.Source: §2 · p. 2
- GenHop examines SSL-based image generation beyond texture synthesis, with extensions aimed at fine-detail generation and quality enhancement through local detail generation.The review notes prior SSL-based texture synthesis work [26] [27].Source: §2 · p. 2
3 Proposed GenHop Method
GenHop constructs progressively lower-dimensional subspaces, generates seed samples in the smallest subspace, then expands them by recovering details and pixel correlations. The method uses PixelHop++ whitening, clustering-based distribution modeling, Gaussian sampling, LLE, and inverse Saab transforms.
3.1 Module 1: High-to-Low Dimension Reduction
- PixelHop++ builds successive subspaces by whitening local neighborhoods: Saab separates DC and AC components and applies PCA to AC components to remove within-block correlations.For 28×28 grayscale images, the example transforms non-overlapping 2×2 blocks into a 14×14×4 joint-spatial-spectral representation in S1; later stages retain low-frequency channels and discard high-frequency channels for dimension reduction.Source: §3.1 · pp. 2–3, Figure 1 · p. 3
3.2 Module 2: Seed Image Generation
- Training seed generation removes spatial correlations with PCA, clusters samples, applies ICA within clusters, and matches component histograms to a standard Gaussian distribution.Generation reverses these operations: it selects a cluster by its sample proportion, maps Gaussian noise through inverse histogram matching, and applies inverse ICA and inverse spatial PCA.Source: §3.2 · pp. 3–4
3.3 Module 3: Low-to-High Dimension Expansion
- Generated low-frequency samples are adjusted with LLE to lie on the training-sample manifold and establish correspondence to samples containing both low- and high-frequency components.LLE operates in 2×2 or 3×3 spatial regions; inverse Saab coloring then rebuilds correlations among spatial pixels.Source: §3.3 · p. 4
4 Experiments
Across MNIST, Fashion-MNIST, and CelebA, GenHop ranks first by FID on MNIST and second on the other two datasets. The experiments also inspect generated-image quality and report a color limitation for some CelebA samples.
Experimental Setup
- The evaluation covers grayscale MNIST and Fashion-MNIST and RGB CelebA, with pixel-wise PCA reducing CelebA to two channels before LLE-based RGB recovery.The experiments use 10K generated and 10K real test images for FID calculation.Source: §4 · p. 4
Performance Comparison
- GenHop has the best FID on MNIST and the second-best FID on Fashion-MNIST and CelebA, outperforming almost all other DL-based benchmark methods.FID evaluates generated and real-image Inception embeddings through Gaussian fits, considering both diversity and fidelity; lower scores indicate better performance.Source: §4 · pp. 4–5, Table 1 · p. 5
Generated Exemplary Images
- Most CelebA samples are semantically meaningful and realistic, while some generated object colors are unnatural because LLE operates only in small image regions.The examples also show captured digit structure and diversity on MNIST, and diverse classes with natural-looking shoe texture and T-shirt printing on Fashion-MNIST.Source: §4 · p. 5
5 Conclusion and Future Work
GenHop combines staged subspace reduction, seed generation, and dimension expansion to generate images without deep learning. It achieved state-of-the-art FID performance on MNIST, Fashion-MNIST, and CelebA, with higher-resolution images and more complex content proposed as future directions.
5 Conclusion and Future Work
- GenHop achieved state-of-the-art FID performance on MNIST, Fashion-MNIST, and CelebA.The conclusion provides no FID values.Source: §5 · p. 5
- Its pipeline removes local pixel correlations with the Saab transform, reduces dimension by discarding high-frequency components, generates seeds with white Gaussian noise, then restores details using LLE and pixel correlations with the inverse Saab transform.The reduction and restoration tasks can each be executed in multiple stages.Source: §5 · p. 5
- Future work includes generating higher-resolution images with more complicated content and exploring transfer learning and image inpainting.Transfer learning examples include transfer between horses and zebras.Source: §5 · p. 5