A latent variable model for two-dimensional canonical correlation analysis and the variational inference
Abstract The probabilistic dimension reduction has been and is a major concern. Probabilistic models provide a better interpretability of the dimension reduction methods and present a framework for their further extensions. In pattern recognition problems, data that have a matrix or tensor structure...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Safayani, Mehran [verfasserIn] Momenzadeh, Saeid [verfasserIn] Mirzaei, Abdolreza [verfasserIn] Razavi, Masoomeh Sadat [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Schlagwörter: |
Canonical correlation analysis |
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| Übergeordnetes Werk: |
Enthalten in: Soft Computing - Springer-Verlag, 2003, 24(2020), 12 vom: 06. Apr., Seite 8737-8749 |
|---|---|
| Übergeordnetes Werk: |
volume:24 ; year:2020 ; number:12 ; day:06 ; month:04 ; pages:8737-8749 |
| Links: |
|---|
| DOI / URN: |
10.1007/s00500-020-04906-8 |
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SPR039733254 |
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| 520 | |a Abstract The probabilistic dimension reduction has been and is a major concern. Probabilistic models provide a better interpretability of the dimension reduction methods and present a framework for their further extensions. In pattern recognition problems, data that have a matrix or tensor structure is initially transformed into a vector format. This eliminates the internal structure of the data. The available perspective is to maintain the internal structure of each data while reducing the dimensionality, which can reduce the small sample size problem. Canonical correlation analysis is one of the most important techniques in dimension reduction in multi-view data. A two-dimensional canonical correlation analysis as an extension of canonical correlation analysis has been proposed to preserve the matrix structure of the data. Here, a new probabilistic framework for two-dimensional canonical correlation analysis is proposed, where the matrix-variate distributions are applied to model the relation between the latent matrix and the two-view matrix-variate observed data. These distributions, specific to the matrix data, can provide better understanding of two-dimensional canonical correlation analysis and pave the way for further extensions. In general, there does not exist any analytical maximum likelihood solution for this model; therefore, here the two approaches, one based on the expectation maximization and other on variational expected maximization, are proposed for learning the model parameters. The synthetic data are applied to evaluate the convergence and quality of the mapping of these algorithms. The functionalities of these methods and their counterparts are compared on the real face datasets. | ||
| 650 | 4 | |a Canonical correlation analysis |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Probabilistic dimension reduction |7 (dpeaa)DE-He213 | |
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| 650 | 4 | |a Variational expectation maximization |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Momenzadeh, Saeid |e verfasserin |4 aut | |
| 700 | 1 | |a Mirzaei, Abdolreza |e verfasserin |4 aut | |
| 700 | 1 | |a Razavi, Masoomeh Sadat |e verfasserin |4 aut | |
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10.1007/s00500-020-04906-8 doi (DE-627)SPR039733254 (SPR)s00500-020-04906-8-e DE-627 ger DE-627 rakwb eng Safayani, Mehran verfasserin aut A latent variable model for two-dimensional canonical correlation analysis and the variational inference 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The probabilistic dimension reduction has been and is a major concern. Probabilistic models provide a better interpretability of the dimension reduction methods and present a framework for their further extensions. In pattern recognition problems, data that have a matrix or tensor structure is initially transformed into a vector format. This eliminates the internal structure of the data. The available perspective is to maintain the internal structure of each data while reducing the dimensionality, which can reduce the small sample size problem. Canonical correlation analysis is one of the most important techniques in dimension reduction in multi-view data. A two-dimensional canonical correlation analysis as an extension of canonical correlation analysis has been proposed to preserve the matrix structure of the data. Here, a new probabilistic framework for two-dimensional canonical correlation analysis is proposed, where the matrix-variate distributions are applied to model the relation between the latent matrix and the two-view matrix-variate observed data. These distributions, specific to the matrix data, can provide better understanding of two-dimensional canonical correlation analysis and pave the way for further extensions. In general, there does not exist any analytical maximum likelihood solution for this model; therefore, here the two approaches, one based on the expectation maximization and other on variational expected maximization, are proposed for learning the model parameters. The synthetic data are applied to evaluate the convergence and quality of the mapping of these algorithms. The functionalities of these methods and their counterparts are compared on the real face datasets. Canonical correlation analysis (dpeaa)DE-He213 Probabilistic dimension reduction (dpeaa)DE-He213 Matrix-variate distribution (dpeaa)DE-He213 Variational expectation maximization (dpeaa)DE-He213 Momenzadeh, Saeid verfasserin aut Mirzaei, Abdolreza verfasserin aut Razavi, Masoomeh Sadat verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 24(2020), 12 vom: 06. Apr., Seite 8737-8749 (DE-627)SPR006469531 nnns volume:24 year:2020 number:12 day:06 month:04 pages:8737-8749 https://dx.doi.org/10.1007/s00500-020-04906-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 24 2020 12 06 04 8737-8749 |
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10.1007/s00500-020-04906-8 doi (DE-627)SPR039733254 (SPR)s00500-020-04906-8-e DE-627 ger DE-627 rakwb eng Safayani, Mehran verfasserin aut A latent variable model for two-dimensional canonical correlation analysis and the variational inference 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The probabilistic dimension reduction has been and is a major concern. Probabilistic models provide a better interpretability of the dimension reduction methods and present a framework for their further extensions. In pattern recognition problems, data that have a matrix or tensor structure is initially transformed into a vector format. This eliminates the internal structure of the data. The available perspective is to maintain the internal structure of each data while reducing the dimensionality, which can reduce the small sample size problem. Canonical correlation analysis is one of the most important techniques in dimension reduction in multi-view data. A two-dimensional canonical correlation analysis as an extension of canonical correlation analysis has been proposed to preserve the matrix structure of the data. Here, a new probabilistic framework for two-dimensional canonical correlation analysis is proposed, where the matrix-variate distributions are applied to model the relation between the latent matrix and the two-view matrix-variate observed data. These distributions, specific to the matrix data, can provide better understanding of two-dimensional canonical correlation analysis and pave the way for further extensions. In general, there does not exist any analytical maximum likelihood solution for this model; therefore, here the two approaches, one based on the expectation maximization and other on variational expected maximization, are proposed for learning the model parameters. The synthetic data are applied to evaluate the convergence and quality of the mapping of these algorithms. The functionalities of these methods and their counterparts are compared on the real face datasets. Canonical correlation analysis (dpeaa)DE-He213 Probabilistic dimension reduction (dpeaa)DE-He213 Matrix-variate distribution (dpeaa)DE-He213 Variational expectation maximization (dpeaa)DE-He213 Momenzadeh, Saeid verfasserin aut Mirzaei, Abdolreza verfasserin aut Razavi, Masoomeh Sadat verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 24(2020), 12 vom: 06. Apr., Seite 8737-8749 (DE-627)SPR006469531 nnns volume:24 year:2020 number:12 day:06 month:04 pages:8737-8749 https://dx.doi.org/10.1007/s00500-020-04906-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 24 2020 12 06 04 8737-8749 |
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10.1007/s00500-020-04906-8 doi (DE-627)SPR039733254 (SPR)s00500-020-04906-8-e DE-627 ger DE-627 rakwb eng Safayani, Mehran verfasserin aut A latent variable model for two-dimensional canonical correlation analysis and the variational inference 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The probabilistic dimension reduction has been and is a major concern. Probabilistic models provide a better interpretability of the dimension reduction methods and present a framework for their further extensions. In pattern recognition problems, data that have a matrix or tensor structure is initially transformed into a vector format. This eliminates the internal structure of the data. The available perspective is to maintain the internal structure of each data while reducing the dimensionality, which can reduce the small sample size problem. Canonical correlation analysis is one of the most important techniques in dimension reduction in multi-view data. A two-dimensional canonical correlation analysis as an extension of canonical correlation analysis has been proposed to preserve the matrix structure of the data. Here, a new probabilistic framework for two-dimensional canonical correlation analysis is proposed, where the matrix-variate distributions are applied to model the relation between the latent matrix and the two-view matrix-variate observed data. These distributions, specific to the matrix data, can provide better understanding of two-dimensional canonical correlation analysis and pave the way for further extensions. In general, there does not exist any analytical maximum likelihood solution for this model; therefore, here the two approaches, one based on the expectation maximization and other on variational expected maximization, are proposed for learning the model parameters. The synthetic data are applied to evaluate the convergence and quality of the mapping of these algorithms. The functionalities of these methods and their counterparts are compared on the real face datasets. Canonical correlation analysis (dpeaa)DE-He213 Probabilistic dimension reduction (dpeaa)DE-He213 Matrix-variate distribution (dpeaa)DE-He213 Variational expectation maximization (dpeaa)DE-He213 Momenzadeh, Saeid verfasserin aut Mirzaei, Abdolreza verfasserin aut Razavi, Masoomeh Sadat verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 24(2020), 12 vom: 06. Apr., Seite 8737-8749 (DE-627)SPR006469531 nnns volume:24 year:2020 number:12 day:06 month:04 pages:8737-8749 https://dx.doi.org/10.1007/s00500-020-04906-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 24 2020 12 06 04 8737-8749 |
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10.1007/s00500-020-04906-8 doi (DE-627)SPR039733254 (SPR)s00500-020-04906-8-e DE-627 ger DE-627 rakwb eng Safayani, Mehran verfasserin aut A latent variable model for two-dimensional canonical correlation analysis and the variational inference 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The probabilistic dimension reduction has been and is a major concern. Probabilistic models provide a better interpretability of the dimension reduction methods and present a framework for their further extensions. In pattern recognition problems, data that have a matrix or tensor structure is initially transformed into a vector format. This eliminates the internal structure of the data. The available perspective is to maintain the internal structure of each data while reducing the dimensionality, which can reduce the small sample size problem. Canonical correlation analysis is one of the most important techniques in dimension reduction in multi-view data. A two-dimensional canonical correlation analysis as an extension of canonical correlation analysis has been proposed to preserve the matrix structure of the data. Here, a new probabilistic framework for two-dimensional canonical correlation analysis is proposed, where the matrix-variate distributions are applied to model the relation between the latent matrix and the two-view matrix-variate observed data. These distributions, specific to the matrix data, can provide better understanding of two-dimensional canonical correlation analysis and pave the way for further extensions. In general, there does not exist any analytical maximum likelihood solution for this model; therefore, here the two approaches, one based on the expectation maximization and other on variational expected maximization, are proposed for learning the model parameters. The synthetic data are applied to evaluate the convergence and quality of the mapping of these algorithms. The functionalities of these methods and their counterparts are compared on the real face datasets. Canonical correlation analysis (dpeaa)DE-He213 Probabilistic dimension reduction (dpeaa)DE-He213 Matrix-variate distribution (dpeaa)DE-He213 Variational expectation maximization (dpeaa)DE-He213 Momenzadeh, Saeid verfasserin aut Mirzaei, Abdolreza verfasserin aut Razavi, Masoomeh Sadat verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 24(2020), 12 vom: 06. Apr., Seite 8737-8749 (DE-627)SPR006469531 nnns volume:24 year:2020 number:12 day:06 month:04 pages:8737-8749 https://dx.doi.org/10.1007/s00500-020-04906-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 24 2020 12 06 04 8737-8749 |
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10.1007/s00500-020-04906-8 doi (DE-627)SPR039733254 (SPR)s00500-020-04906-8-e DE-627 ger DE-627 rakwb eng Safayani, Mehran verfasserin aut A latent variable model for two-dimensional canonical correlation analysis and the variational inference 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The probabilistic dimension reduction has been and is a major concern. Probabilistic models provide a better interpretability of the dimension reduction methods and present a framework for their further extensions. In pattern recognition problems, data that have a matrix or tensor structure is initially transformed into a vector format. This eliminates the internal structure of the data. The available perspective is to maintain the internal structure of each data while reducing the dimensionality, which can reduce the small sample size problem. Canonical correlation analysis is one of the most important techniques in dimension reduction in multi-view data. A two-dimensional canonical correlation analysis as an extension of canonical correlation analysis has been proposed to preserve the matrix structure of the data. Here, a new probabilistic framework for two-dimensional canonical correlation analysis is proposed, where the matrix-variate distributions are applied to model the relation between the latent matrix and the two-view matrix-variate observed data. These distributions, specific to the matrix data, can provide better understanding of two-dimensional canonical correlation analysis and pave the way for further extensions. In general, there does not exist any analytical maximum likelihood solution for this model; therefore, here the two approaches, one based on the expectation maximization and other on variational expected maximization, are proposed for learning the model parameters. The synthetic data are applied to evaluate the convergence and quality of the mapping of these algorithms. The functionalities of these methods and their counterparts are compared on the real face datasets. Canonical correlation analysis (dpeaa)DE-He213 Probabilistic dimension reduction (dpeaa)DE-He213 Matrix-variate distribution (dpeaa)DE-He213 Variational expectation maximization (dpeaa)DE-He213 Momenzadeh, Saeid verfasserin aut Mirzaei, Abdolreza verfasserin aut Razavi, Masoomeh Sadat verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 24(2020), 12 vom: 06. Apr., Seite 8737-8749 (DE-627)SPR006469531 nnns volume:24 year:2020 number:12 day:06 month:04 pages:8737-8749 https://dx.doi.org/10.1007/s00500-020-04906-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 24 2020 12 06 04 8737-8749 |
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A latent variable model for two-dimensional canonical correlation analysis and the variational inference |
| abstract |
Abstract The probabilistic dimension reduction has been and is a major concern. Probabilistic models provide a better interpretability of the dimension reduction methods and present a framework for their further extensions. In pattern recognition problems, data that have a matrix or tensor structure is initially transformed into a vector format. This eliminates the internal structure of the data. The available perspective is to maintain the internal structure of each data while reducing the dimensionality, which can reduce the small sample size problem. Canonical correlation analysis is one of the most important techniques in dimension reduction in multi-view data. A two-dimensional canonical correlation analysis as an extension of canonical correlation analysis has been proposed to preserve the matrix structure of the data. Here, a new probabilistic framework for two-dimensional canonical correlation analysis is proposed, where the matrix-variate distributions are applied to model the relation between the latent matrix and the two-view matrix-variate observed data. These distributions, specific to the matrix data, can provide better understanding of two-dimensional canonical correlation analysis and pave the way for further extensions. In general, there does not exist any analytical maximum likelihood solution for this model; therefore, here the two approaches, one based on the expectation maximization and other on variational expected maximization, are proposed for learning the model parameters. The synthetic data are applied to evaluate the convergence and quality of the mapping of these algorithms. The functionalities of these methods and their counterparts are compared on the real face datasets. |
| abstractGer |
Abstract The probabilistic dimension reduction has been and is a major concern. Probabilistic models provide a better interpretability of the dimension reduction methods and present a framework for their further extensions. In pattern recognition problems, data that have a matrix or tensor structure is initially transformed into a vector format. This eliminates the internal structure of the data. The available perspective is to maintain the internal structure of each data while reducing the dimensionality, which can reduce the small sample size problem. Canonical correlation analysis is one of the most important techniques in dimension reduction in multi-view data. A two-dimensional canonical correlation analysis as an extension of canonical correlation analysis has been proposed to preserve the matrix structure of the data. Here, a new probabilistic framework for two-dimensional canonical correlation analysis is proposed, where the matrix-variate distributions are applied to model the relation between the latent matrix and the two-view matrix-variate observed data. These distributions, specific to the matrix data, can provide better understanding of two-dimensional canonical correlation analysis and pave the way for further extensions. In general, there does not exist any analytical maximum likelihood solution for this model; therefore, here the two approaches, one based on the expectation maximization and other on variational expected maximization, are proposed for learning the model parameters. The synthetic data are applied to evaluate the convergence and quality of the mapping of these algorithms. The functionalities of these methods and their counterparts are compared on the real face datasets. |
| abstract_unstemmed |
Abstract The probabilistic dimension reduction has been and is a major concern. Probabilistic models provide a better interpretability of the dimension reduction methods and present a framework for their further extensions. In pattern recognition problems, data that have a matrix or tensor structure is initially transformed into a vector format. This eliminates the internal structure of the data. The available perspective is to maintain the internal structure of each data while reducing the dimensionality, which can reduce the small sample size problem. Canonical correlation analysis is one of the most important techniques in dimension reduction in multi-view data. A two-dimensional canonical correlation analysis as an extension of canonical correlation analysis has been proposed to preserve the matrix structure of the data. Here, a new probabilistic framework for two-dimensional canonical correlation analysis is proposed, where the matrix-variate distributions are applied to model the relation between the latent matrix and the two-view matrix-variate observed data. These distributions, specific to the matrix data, can provide better understanding of two-dimensional canonical correlation analysis and pave the way for further extensions. In general, there does not exist any analytical maximum likelihood solution for this model; therefore, here the two approaches, one based on the expectation maximization and other on variational expected maximization, are proposed for learning the model parameters. The synthetic data are applied to evaluate the convergence and quality of the mapping of these algorithms. The functionalities of these methods and their counterparts are compared on the real face datasets. |
| collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER |
| container_issue |
12 |
| title_short |
A latent variable model for two-dimensional canonical correlation analysis and the variational inference |
| url |
https://dx.doi.org/10.1007/s00500-020-04906-8 |
| remote_bool |
true |
| author2 |
Momenzadeh, Saeid Mirzaei, Abdolreza Razavi, Masoomeh Sadat |
| author2Str |
Momenzadeh, Saeid Mirzaei, Abdolreza Razavi, Masoomeh Sadat |
| ppnlink |
SPR006469531 |
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c |
| isOA_txt |
false |
| hochschulschrift_bool |
false |
| doi_str |
10.1007/s00500-020-04906-8 |
| up_date |
2024-07-04T01:19:09.393Z |
| _version_ |
1803609387193860096 |
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| score |
7.401165 |