Measure of Similarity between GMMs Based on Geometry-Aware Dimensionality Reduction
Gaussian Mixture Models (GMMs) are used in many traditional expert systems and modern artificial intelligence tasks such as automatic speech recognition, image recognition and retrieval, pattern recognition, speaker recognition and verification, financial forecasting applications and others, as simp...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/1/175 |
| _version_ | 1797406770834964480 |
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| author | Branislav Popović Marko Janev Lidija Krstanović Nikola Simić Vlado Delić |
| author_facet | Branislav Popović Marko Janev Lidija Krstanović Nikola Simić Vlado Delić |
| author_sort | Branislav Popović |
| collection | DOAJ |
| description | Gaussian Mixture Models (GMMs) are used in many traditional expert systems and modern artificial intelligence tasks such as automatic speech recognition, image recognition and retrieval, pattern recognition, speaker recognition and verification, financial forecasting applications and others, as simple statistical representations of underlying data. Those representations typically require many high-dimensional GMM components that consume large computing resources and increase computation time. On the other hand, real-time applications require computationally efficient algorithms and for that reason, various GMM similarity measures and dimensionality reduction techniques have been examined to reduce the computational complexity. In this paper, a novel GMM similarity measure is proposed. The measure is based on a recently presented nonlinear geometry-aware dimensionality reduction algorithm for the manifold of Symmetric Positive Definite (SPD) matrices. The algorithm is applied over SPD representations of the original data. The local neighborhood information from the original high-dimensional parameter space is preserved by preserving distance to the local mean. Instead of dealing with high-dimensional parameter space, the method operates on much lower-dimensional space of transformed parameters. Resolving the distance between such representations is reduced to calculating the distance among lower-dimensional matrices. The method was tested within a texture recognition task where superior state-of-the-art performance in terms of the trade-off between recognition accuracy and computational complexity has been achieved in comparison with all baseline GMM similarity measures. |
| first_indexed | 2024-03-09T03:31:26Z |
| format | Article |
| id | doaj.art-5fd25b3e36af4e61ad385715754038bc |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T03:31:26Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-5fd25b3e36af4e61ad385715754038bc2023-12-03T14:55:29ZengMDPI AGMathematics2227-73902022-12-0111117510.3390/math11010175Measure of Similarity between GMMs Based on Geometry-Aware Dimensionality ReductionBranislav Popović0Marko Janev1Lidija Krstanović2Nikola Simić3Vlado Delić4Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, SerbiaInstitute of Mathematics, Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000 Belgrade, SerbiaFaculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, SerbiaFaculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, SerbiaFaculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000 Novi Sad, SerbiaGaussian Mixture Models (GMMs) are used in many traditional expert systems and modern artificial intelligence tasks such as automatic speech recognition, image recognition and retrieval, pattern recognition, speaker recognition and verification, financial forecasting applications and others, as simple statistical representations of underlying data. Those representations typically require many high-dimensional GMM components that consume large computing resources and increase computation time. On the other hand, real-time applications require computationally efficient algorithms and for that reason, various GMM similarity measures and dimensionality reduction techniques have been examined to reduce the computational complexity. In this paper, a novel GMM similarity measure is proposed. The measure is based on a recently presented nonlinear geometry-aware dimensionality reduction algorithm for the manifold of Symmetric Positive Definite (SPD) matrices. The algorithm is applied over SPD representations of the original data. The local neighborhood information from the original high-dimensional parameter space is preserved by preserving distance to the local mean. Instead of dealing with high-dimensional parameter space, the method operates on much lower-dimensional space of transformed parameters. Resolving the distance between such representations is reduced to calculating the distance among lower-dimensional matrices. The method was tested within a texture recognition task where superior state-of-the-art performance in terms of the trade-off between recognition accuracy and computational complexity has been achieved in comparison with all baseline GMM similarity measures.https://www.mdpi.com/2227-7390/11/1/175Gaussian Mixture Modelssimilarity measuresdimensionality reductiontexture recognition |
| spellingShingle | Branislav Popović Marko Janev Lidija Krstanović Nikola Simić Vlado Delić Measure of Similarity between GMMs Based on Geometry-Aware Dimensionality Reduction Mathematics Gaussian Mixture Models similarity measures dimensionality reduction texture recognition |
| title | Measure of Similarity between GMMs Based on Geometry-Aware Dimensionality Reduction |
| title_full | Measure of Similarity between GMMs Based on Geometry-Aware Dimensionality Reduction |
| title_fullStr | Measure of Similarity between GMMs Based on Geometry-Aware Dimensionality Reduction |
| title_full_unstemmed | Measure of Similarity between GMMs Based on Geometry-Aware Dimensionality Reduction |
| title_short | Measure of Similarity between GMMs Based on Geometry-Aware Dimensionality Reduction |
| title_sort | measure of similarity between gmms based on geometry aware dimensionality reduction |
| topic | Gaussian Mixture Models similarity measures dimensionality reduction texture recognition |
| url | https://www.mdpi.com/2227-7390/11/1/175 |
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