On September 9, 2026, Chen Luonan's team at Guangdong Institute of Intelligence Science and Technology (GDIIST) published a research paper online in the internationally renowned academic journal Nature Communications, titled "Explainable data generation from observed small samples by matrix tri-factorization," proposing an explainable small-sample data generation method (EDG) based on matrix tri-factorization.

Aimed at the challenging problem of extreme data scarcity in real biomedical scenarios (such as a single available sample from the index patient of an entirely new rare disease), the method proposes an explainable data generation approach, EDG, for scenarios of extreme sample scarcity. Unlike traditional approaches that rely on large numbers of training samples, EDG mines the complete information inherent in high-dimensional data itself, mapping observable high-dimensional small samples into a low-dimensional latent representation space and generating low-dimensional latent representations far larger in scale than the original sample size. Relying on the transparency of the matrix factorization and reconstruction process, it enables explainable sample generation while preserving the original biological characteristics of the data.

The method can provide high-quality data support for core tasks such as disease classification, feature selection, and pre-disease critical point prediction, to make up for the industry shortcomings of difficult sample collection, high costs, and scarcity in biomedicine, help mine the potential patterns of high-dimensional biological data, and provide reliable technical support for emerging disease research, early warning, pathogenic mechanism analysis, and biomarker mining, with sound theoretical and application value.

Against the backdrop of the rapid development of big data and artificial intelligence, the performance of machine learning models depends to a large extent on sufficient, high-quality training data. However, in biomedical research, data acquisition is often constrained by multiple factors such as experimental costs and privacy protection, especially in scenarios such as rare disease research, early monitoring of emerging diseases, and identification of key turning points in the occurrence and development of diseases, where available samples may be extremely limited.

Traditional data augmentation methods, such as SMOTE and Mixup, mainly construct new data through interpolation between existing samples, and it is difficult for them to fully characterize the complex structures and dependencies within high-dimensional data. Deep generative models represented by generative adversarial networks (GANs) and variational autoencoders (VAEs) usually require relatively sufficient training samples and high computational resources, and their application in extreme small-sample scenarios remains limited. In addition, the "black-box" nature of such models limits interpretability and reduces their credibility in biomedical applications. Therefore, there is an urgent need for efficient, explainable generation technologies capable of generating high-quality data, especially for tricky research scenarios where samples of each class are scarce or even only a single sample exists (such as the index patient).

Figure 1. Framework of the explainable small-sample data generation method (EDG) based on matrix tri-factorization.

To address the above problems, Chen Luonan's team proposed the EDG method. Its core idea is that high-dimensional observed data may contain deeper latent structural information; even when the number of observed samples is limited, the associations among high-dimensional features can be mined to construct a feature basis capable of characterizing the intrinsic structure of the data, and new samples can be generated based on the feature basis (the framework is shown in Figure 1). Specifically, EDG represents the observed data in the form X = U·Y·V through matrix tri-factorization, where the matrix Y carries the latent structural information of the data, and its sample scale can be expanded to exceed the number of original observed samples, thereby providing the basis for data reconstruction and new sample generation. On this basis, EDG introduces two key constraints to further improve the consistency between the generated data and the original data distribution. On the one hand, the Hilbert–Schmidt Independence Criterion (HSIC) is introduced to constrain the statistical relationships among relevant representations, preserving important structural information of the original data; on the other hand, optimal transport (OT) is introduced to constrain the distribution discrepancy between the generated data and the original data at the data distribution level, improving the authenticity of the generated data. Ultimately, through the synergistic effect of matrix factorization and the two constraints, EDG grounds the data generation process in a factorization and reconstruction mechanism with a clear mathematical structure, which can both alleviate the problem of insufficient data under extreme small-sample conditions and provide a clearer view for understanding the generation results.

The research team systematically verified the data generation capability, downstream analysis performance, and generalization ability of EDG on simulated omics data and real single-cell data for tasks such as classification, clustering, feature selection, and critical warning.

Figure 2. Visualization experimental results of EDG on simulated omics data.

On simulated omics data, faced with high-dimensional data with only 10 samples per class and a feature dimension as high as 3,980, EDG showed good performance improvements in multiple tasks such as classification, clustering, feature selection, and critical warning. As shown in the experimental results in Figure 2, in the visualization of generated data, the generated data are consistent with the original data distribution (Figure 2a); in the feature selection task, features with stronger class-discriminative ability can be selected based on the data generated by EDG (Figure 2b); in the clustering task, better cluster centers can be learned based on the data generated by EDG (Figures 2c and 2d); and in the critical point prediction task, the critical point can be accurately predicted based on the data generated by EDG (Figure 2e).

Table 1. Experimental results on real single-cell data.

EDG is designed for real biomedical application scenarios and is especially suitable for extreme situations such as early-stage diseases or emerging diseases (for example, the index patient of an entirely new rare disease with only a single sample). Therefore, in the experimental setup on real single-cell data (experimental results are shown in Table 1), the team simulated the condition in which only n samples can be obtained in real biomedical scenarios, and set the experiments to cover the complete stages of disease development (n = 1–50), including both the early stage of the disease with extremely limited sample size (n < 10) and cases with relatively sufficient samples (n > 20). The experimental results show that under the extreme scarcity condition of only 1 to 10 samples per class, EDG can still generate effective new samples and significantly improve the performance of downstream classification tasks. Furthermore, the team carried out validation on 10 additional datasets covering different species and organs, and the results show that EDG achieved optimal or tied-optimal performance on most datasets with high stability, demonstrating its application potential across different data types and research scenarios.

Figure 3. Experimental results on the critical warning task.

In addition to tasks such as classification, clustering, and feature selection, the research team also applied EDG to disease critical point prediction to explore its application value in early warning of the occurrence and development of diseases. In the analysis of real prostate cancer data (as shown in Figure 3), the critical state could not be clearly identified on either the original data or the data generated by comparison methods, whereas after augmenting samples through EDG, the warning signals near the critical point were significantly enhanced. Therefore, EDG provides a new analytical approach for identifying disease state transitions and capturing potential early warning signals.

In summary, the EDG method proposed in this study, with matrix tri-factorization as its core and synergizing the two constraints of HSIC and OT, achieves explainable, high-quality data generation that conforms to the original data distribution under extreme small samples, and its effectiveness has been comprehensively verified in the four types of tasks: classification, clustering, feature selection, and critical point prediction. The method provides a reliable data augmentation solution for data-scarce biomedical scenarios and also enables researchers to gain deep insight into the underlying structure behind the data. The team noted that in the future they will combine the generated low-dimensional feature basis with biological knowledge such as pathway annotations and gene regulatory networks to further enhance its biological interpretability, and explore directions for integrating it with deep generative models.

Zhang Bin, a young researcher at GDIIST, is the first author of this paper; Chen Luonan, a distinguished researcher at GDIIST, is the corresponding author of this paper; and GDIIST is the first corresponding institution. This research was funded by projects such as the National Natural Science Foundation of China and the National Key Research and Development Program.

Original link:

https://www.nature.com/articles/s41467-026-77343-0