Summary of Learnable Similarity and Dissimilarity Guided Symmetric Non-negative Matrix Factorization, by Wenlong Lyu and Yuheng Jia
Learnable Similarity and Dissimilarity Guided Symmetric Non-Negative Matrix Factorization
by Wenlong Lyu, Yuheng Jia
First submitted to arxiv on: 5 Dec 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: None
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary Symmetric nonnegative matrix factorization (SymNMF) is a powerful tool for clustering that uses the k-nearest neighbor (k-NN) method to construct similarity matrices. However, traditional k-NN approaches may lead to inaccurate clustering results due to unreliable neighbors and growing computational complexity as k increases. This paper addresses these limitations by introducing a learnable weighted k-NN graph that incorporates reliability weights and reduces the dimensionality of the similarity matrix learning problem from O(n^2) to n – 1, where n represents the number of samples. Additionally, the authors propose a dual structure dissimilarity matrix and orthogonality regularization, offering an efficient alternative optimization algorithm with theoretical guarantees of convergence to a stationary point satisfying KKT conditions. Compared to nine state-of-the-art clustering methods on eight datasets, the proposed model demonstrates advantages in accuracy and efficiency. The code is available at this URL. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Symmetric nonnegative matrix factorization (SymNMF) is a powerful tool for grouping similar data points together. Currently, SymNMF uses k-nearest neighbors to find similarities between data points, but this approach has some limitations. In this paper, the authors improve this method by introducing a new way of weighting the importance of each neighbor and reducing the amount of calculations needed. They also propose two new ideas: a dissimilarity matrix that helps create more accurate groups, and a special type of regularization to make sure the results are meaningful. The authors tested their approach on eight different datasets and found it outperformed nine other clustering methods. The code for this method is available online. |
Keywords
» Artificial intelligence » Clustering » Nearest neighbor » Optimization » Regularization
