# A deep matrix factorization method for learning attribute representations

arXiv: https://arxiv.org/abs/1509.03248 · HTML: https://mlsanity.com/paper/1509.03248/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2015.

## Built on by (most cited first, 24 of 24)

- [Hyperspectral Unmixing Based on Nonnegative Matrix Factorization: A Comprehensive Review](https://mlsanity.com/paper/2205.09933/) (2022)
- [Consistency and Diversity induced Human Motion Segmentation](https://mlsanity.com/paper/2202.04861/) (2022)
- [Nonnegative Matrix Factorization in Dimensionality Reduction: A Survey](https://mlsanity.com/paper/2405.03615/) (2024)
- [A Generalized Hierarchical Nonnegative Tensor Decomposition](https://mlsanity.com/paper/2109.14820/) (2021)
- [A consistent and flexible framework for deep matrix factorizations](https://mlsanity.com/paper/2206.10693/) (2022)
- [A Complete Loss Landscape Analysis of Regularized Deep Matrix Factorization](https://mlsanity.com/paper/2506.20344/) (2025)
- [DEMAND: Deep Matrix Approximately Nonlinear Decomposition to Identify Meta, Canonical, and Sub-Spatial Pattern of functional Magnetic Resonance Imaging in the Human Brain](https://mlsanity.com/paper/2205.10264/) (2022)
- [DELMAR: Deep Linear Matrix Approximately Reconstruction to Extract Hierarchical Functional Connectivity in the Human Brain](https://mlsanity.com/paper/2205.10374/) (2022)
- [Neural Nonnegative Matrix Factorization for Hierarchical Multilayer Topic Modeling](https://mlsanity.com/paper/2303.00058/) (2023)
- [Deep Nonnegative Matrix Factorization with Beta Divergences](https://mlsanity.com/paper/2309.08249/) (2023)
- [Error Bound Analysis for the Regularized Loss of Deep Linear Neural Networks](https://mlsanity.com/paper/2502.11152/) (2025)
- [Deep Variational Models for Collaborative Filtering-based Recommender Systems](https://mlsanity.com/paper/2107.12677/) (2021)
- [Transformed K-means Clustering](https://mlsanity.com/paper/2111.13921/) (2021)
- [SENDER: SEmi-Nonlinear Deep Efficient Reconstructor for Extraction Canonical, Meta, and Sub Functional Connectivity in the Human Brain](https://mlsanity.com/paper/2209.05627/) (2022)
- [Deep State-Space Model for Predicting Cryptocurrency Price](https://mlsanity.com/paper/2311.14731/) (2023)
- [Interpretable factorization of clinical questionnaires to identify latent factors of psychopathology](https://mlsanity.com/paper/2312.07762/) (2023)
- [Input Guided Multiple Deconstruction Single Reconstruction neural network models for Matrix Factorization](https://mlsanity.com/paper/2405.13449/) (2024)
- [Multi-layer matrix factorization for cancer subtyping using full and partial multi-omics dataset](https://mlsanity.com/paper/2411.15180/) (2024)
- [Balanced Multi-view Clustering](https://mlsanity.com/paper/2501.02564/) (2025)
- [HOME-3: High-Order Momentum Estimator with Third-Power Gradient for Convex and Smooth Nonconvex Optimization](https://mlsanity.com/paper/2505.11748/) (2025)
- [Permutation Randomization on Nonsmooth Nonconvex Optimization: A Theoretical and Experimental Study](https://mlsanity.com/paper/2505.11752/) (2025)
- [Automating Historical Insight Extraction from Large-Scale Newspaper Archives via Neural Topic Modeling](https://mlsanity.com/paper/2512.11635/) (2025)
- [Supervised Deep Multimodal Matrix Factorization for Interpretable Brain Network Analysis](https://mlsanity.com/paper/2605.13312/) (2026)
- [A Generalized Deep Non-negative Matrix Factorization Approach for SAR Automatic Target Recognition](https://mlsanity.com/paper/2607.09779/) (2026)

## Abstract (arXiv)

Semi-Non-negative Matrix Factorization is a technique that learns a low-dimensional representation of a dataset that lends itself to a clustering interpretation. It is possible that the mapping between this new representation and our original data matrix contains rather complex hierarchical information with implicit lower-level hidden attributes, that classical one level clustering methodologies can not interpret. In this work we propose a novel model, Deep Semi-NMF, that is able to learn such hidden representations that allow themselves to an interpretation of clustering according to different, unknown attributes of a given dataset. We also present a semi-supervised version of the algorithm, named Deep WSF, that allows the use of (partial) prior information for each of the known attributes of a dataset, that allows the model to be used on datasets with mixed attribute knowledge. Finally, we show that our models are able to learn low-dimensional representations that are better suited for clustering, but also classification, outperforming Semi-Non-negative Matrix Factorization, but also other state-of-the-art methodologies variants.