CAREER:Mining biological functions from single cell multi-omics data
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1.Generalized Matrix Local Low Rank Representation by Random Projection and Submatrix Propagation
- 关键词:
- Approximation theory;Computation theory;Local low rank matrix;Low rank approximations;Low-rank matrices;matrix;Matrix approximation;Random projections;Randomized matrix approximation;Representation learning;Sub-matrix detection;Submatrix
- Dang, Pengtao;Zhu, Haiqi;Guo, Tingbo;Wan, Changlin;Zhao, Tong;Salama, Paul;Wang, Yijie;Cao, Sha;Zhang, Chi
- 《29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD 2023》
- 2023年
- August 6, 2023 - August 10, 2023
- Long Beach, CA, United states
- 会议
Matrix low rank approximation is an effective method to reduce or eliminate the statistical redundancy of its components. Compared with the traditional global low rank methods such as singular value decomposition (SVD), local low rank approximation methods are more advantageous to uncover interpretable data structures when clear duality exists between the rows and columns of the matrix. Local low rank approximation is equivalent to low rank submatrix detection. Unfortunately,existing local low rank approximation methods can detect only submatrices of specific mean structure, which may miss a substantial amount of true and interesting patterns. In this work, we develop a novel matrix computational framework called RPSP (Random Probing based submatrix Propagation) that provides an effective solution for the general matrix local low rank representation problem. RPSP detects local low rank patterns that grow from small submatrices of low rank property, which are determined by a random projection approach. RPSP is supported by theories of random projection. Experiments on synthetic data demonstrate that RPSP outperforms all state-of-the-art methods, with the capacity to robustly and correctly identify the low rank matrices when the pattern has a similar mean as the background, background noise is heteroscedastic and multiple patterns present in the data. On real-world datasets, RPSP also demonstrates its effectiveness in identifying interpretable local low rank matrices. © 2023 ACM.
...2.Bias Aware Probabilistic Boolean Matrix Factorization
- 关键词:
- Collaborative filtering;Matrix algebra;Matrix factorization;Probability distributions;Stochastic models;Bias levels;Boolean Matrix;Combinatorial problem;Datapoints;Dimensionality reduction;Factorization methods;Matrix factorizations;Noise models;Probabilistics;Real-world
- Wan, Changlin;Dang, Pengtao;Zhao, Tong;Zang, Yong;Zhang, Chi;Cao, Sha
- 《38th Conference on Uncertainty in Artificial Intelligence, UAI 2022》
- 2022年
- August 1, 2022 - August 5, 2022
- Eindhoven, Netherlands
- 会议
Boolean matrix factorization (BMF) is a combinatorial problem arising from a wide range of applications including recommendation system, collaborative filtering, and dimensionality reduction. Currently, the noise model of existing BMF methods is often assumed to be homoscedastic; however, in real world data scenarios, the deviations of observed data from their true values are almost surely diverse due to stochastic noises, making each data point not equally suitable for fitting a model. In this case, it is not ideal to treat all data points as equally distributed. Motivated by such observations, we introduce a probabilistic BMF model that recognizes the object- and feature-wise bias distribution respectively, called bias aware BMF (BABF). To the best of our knowledge, BABF is the first approach for Boolean decomposition with consideration of the feature-wise and object-wise bias in binary data. We conducted experiments on datasets with different levels of background noise, bias level, and sizes of the signal patterns, to test the effectiveness of our method in various scenarios. We demonstrated that our model outperforms the state-of-the-art factorization methods in both accuracy and efficiency in recovering the original datasets, and the inferred bias level is highly significantly correlated with true existing bias in both simulated and real world datasets. © 2022 UAI. All Rights Reserved.
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