Stratified Non-Negative Tensor Factorization
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912136259698688 |
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| author | Sietsema, Alexander Vural, Zerrin Chapman, James Yaniv, Yotam Needell, Deanna |
| author_facet | Sietsema, Alexander Vural, Zerrin Chapman, James Yaniv, Yotam Needell, Deanna |
| contents | Non-negative matrix factorization (NMF) and non-negative tensor factorization (NTF) decompose non-negative high-dimensional data into non-negative low-rank components. NMF and NTF methods are popular for their intrinsic interpretability and effectiveness on large-scale data. Recent work developed Stratified-NMF, which applies NMF to regimes where data may come from different sources (strata) with different underlying distributions, and seeks to recover both strata-dependent information and global topics shared across strata. Applying Stratified-NMF to multi-modal data requires flattening across modes, and therefore loses geometric structure contained implicitly within the tensor. To address this problem, we extend Stratified-NMF to the tensor setting by developing a multiplicative update rule and demonstrating the method on text and image data. We find that Stratified-NTF can identify interpretable topics with lower memory requirements than Stratified-NMF. We also introduce a regularized version of the method and demonstrate its effects on image data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18805 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stratified Non-Negative Tensor Factorization Sietsema, Alexander Vural, Zerrin Chapman, James Yaniv, Yotam Needell, Deanna Machine Learning Numerical Analysis G.1.6; I.5.3; I.5.4 Non-negative matrix factorization (NMF) and non-negative tensor factorization (NTF) decompose non-negative high-dimensional data into non-negative low-rank components. NMF and NTF methods are popular for their intrinsic interpretability and effectiveness on large-scale data. Recent work developed Stratified-NMF, which applies NMF to regimes where data may come from different sources (strata) with different underlying distributions, and seeks to recover both strata-dependent information and global topics shared across strata. Applying Stratified-NMF to multi-modal data requires flattening across modes, and therefore loses geometric structure contained implicitly within the tensor. To address this problem, we extend Stratified-NMF to the tensor setting by developing a multiplicative update rule and demonstrating the method on text and image data. We find that Stratified-NTF can identify interpretable topics with lower memory requirements than Stratified-NMF. We also introduce a regularized version of the method and demonstrate its effects on image data. |
| title | Stratified Non-Negative Tensor Factorization |
| topic | Machine Learning Numerical Analysis G.1.6; I.5.3; I.5.4 |
| url | https://arxiv.org/abs/2411.18805 |