L1-Norm Tucker Tensor Decomposition
Tucker decomposition is a standard multi-way generalization of Principal-Component Analysis (PCA), appropriate for processing tensor data. Similar to PCA, Tucker decomposition has been shown to be sensitive against faulty data, due to its L2-norm-based formulation which places squared emphasis to pe...
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| Veröffentlicht in: | IEEE access 2019, Vol.7, p.178454-178465 |
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| creator | Chachlakis, Dimitris G. Prater-Bennette, Ashley Markopoulos, Panos P. |
| description | Tucker decomposition is a standard multi-way generalization of Principal-Component Analysis (PCA), appropriate for processing tensor data. Similar to PCA, Tucker decomposition has been shown to be sensitive against faulty data, due to its L2-norm-based formulation which places squared emphasis to peripheral/outlying entries. In this work, we explore L1-Tucker, an L1-norm based reformulation of Tucker decomposition, and present two algorithms for its solution, namely L1-norm Higher-Order Singular Value Decomposition (L1-HOSVD) and L1-norm Higher-Order Orthogonal Iterations (L1-HOOI). The proposed algorithms are accompanied by complexity and convergence analysis. Our numerical studies on tensor reconstruction and classification corroborate that L1-Tucker decomposition, implemented by means of the proposed algorithms, attains similar performance to standard Tucker when the processed data are corruption-free, while it exhibits sturdy resistance against heavily corrupted entries. |
| doi_str_mv | 10.1109/ACCESS.2019.2955134 |
| format | Article |
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Similar to PCA, Tucker decomposition has been shown to be sensitive against faulty data, due to its L2-norm-based formulation which places squared emphasis to peripheral/outlying entries. In this work, we explore L1-Tucker, an L1-norm based reformulation of Tucker decomposition, and present two algorithms for its solution, namely L1-norm Higher-Order Singular Value Decomposition (L1-HOSVD) and L1-norm Higher-Order Orthogonal Iterations (L1-HOOI). The proposed algorithms are accompanied by complexity and convergence analysis. 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Our numerical studies on tensor reconstruction and classification corroborate that L1-Tucker decomposition, implemented by means of the proposed algorithms, attains similar performance to standard Tucker when the processed data are corruption-free, while it exhibits sturdy resistance against heavily corrupted entries.</description><subject>Algorithms</subject><subject>Approximation algorithms</subject><subject>Arrays</subject><subject>Data analysis</subject><subject>Decomposition</subject><subject>L1-norm</subject><subject>Mathematical analysis</subject><subject>Matrix decomposition</subject><subject>multi-modal data</subject><subject>Principal component analysis</subject><subject>Resistance</subject><subject>Singular value decomposition</subject><subject>tensor decomposition</subject><subject>Tensors</subject><subject>Tucker</subject><issn>2169-3536</issn><issn>2169-3536</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>ESBDL</sourceid><sourceid>RIE</sourceid><sourceid>DOA</sourceid><recordid>eNpNUE1PAjEUbIwmEuQXcCHhvNjX7x7JikpC9ACem-62axaBYrsc_PcWlxDf5b1MZuZNBqEx4BkA1o_zslys1zOCQc-I5hwou0EDAkIXlFNx----R6OUtjiPyhCXAzRdQfEW4n6yOdVfPk42_pBCnDz5OuyPIbVdGw4P6K6xu-RHlz1EH8-LTflarN5fluV8VdQMq66wrlbUOcodaM8UboS0TmBGwWttnbM5W6UwtoxIYr1klRNaWkxcpQhvCB2iZe_rgt2aY2z3Nv6YYFvzB4T4aWzs2nrnDc506UHTRirWSF_RyspagXVNJTyB7DXtvY4xfJ986sw2nOIhxzeEcS4oh6weItqz6hhSir65fgVszuWavlxzLtdcys2qca9qvfdXhdKABWD6C1tFc0w</recordid><startdate>2019</startdate><enddate>2019</enddate><creator>Chachlakis, Dimitris G.</creator><creator>Prater-Bennette, Ashley</creator><creator>Markopoulos, Panos P.</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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| subjects | Algorithms Approximation algorithms Arrays Data analysis Decomposition L1-norm Mathematical analysis Matrix decomposition multi-modal data Principal component analysis Resistance Singular value decomposition tensor decomposition Tensors Tucker |
| title | L1-Norm Tucker Tensor Decomposition |
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