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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Online Access: | https://arxiv.org/abs/2306.15199 |
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| _version_ | 1866909044156923904 |
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| author | Mo, Xiangbo Chen, Hao |
| author_facet | Mo, Xiangbo Chen, Hao |
| contents | Despite advances in representation learning, high-dimensional classification remains challenging in low-sample-size regimes, where the dominant signal may vary across applications and labeled data are often limited. We propose a dissimilarity-profiling classification framework that represents each observation by its class-wise dissimilarity profile, transforming the original feature space into a low-dimensional representation that summarizes how the observation relates to each class. The key idea is to turn a consequence of the curse of dimensionality into signal: high-dimensional geometry can induce systematic within-class and between-class dissimilarity patterns under location, scale, or other distributional changes, and these patterns are captured by the class-wise profiles. Building on this representation, we introduce a rank-transformed algorithm that converts dissimilarities into class-wise rank profiles, yielding a compact representation for classification. The proposed method delivers competitive or improved performance relative to commonly used classifiers on two-class, multi-class, network, and real high-dimensional low-sample-size datasets. To provide insight into the mechanism underlying the method, we analyze a distance-based surrogate and show that the resulting profiles encode differences in first, second, and higher-order moments, while the rank transformation improves robustness to outliers. Together, these results show that rank-transformed dissimilarity profiles provide an adaptive representation for high-dimensional classification when the signal structure is unknown. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_15199 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rank-Transformed Dissimilarity Profiles for High-Dimensional Classification Mo, Xiangbo Chen, Hao Methodology Despite advances in representation learning, high-dimensional classification remains challenging in low-sample-size regimes, where the dominant signal may vary across applications and labeled data are often limited. We propose a dissimilarity-profiling classification framework that represents each observation by its class-wise dissimilarity profile, transforming the original feature space into a low-dimensional representation that summarizes how the observation relates to each class. The key idea is to turn a consequence of the curse of dimensionality into signal: high-dimensional geometry can induce systematic within-class and between-class dissimilarity patterns under location, scale, or other distributional changes, and these patterns are captured by the class-wise profiles. Building on this representation, we introduce a rank-transformed algorithm that converts dissimilarities into class-wise rank profiles, yielding a compact representation for classification. The proposed method delivers competitive or improved performance relative to commonly used classifiers on two-class, multi-class, network, and real high-dimensional low-sample-size datasets. To provide insight into the mechanism underlying the method, we analyze a distance-based surrogate and show that the resulting profiles encode differences in first, second, and higher-order moments, while the rank transformation improves robustness to outliers. Together, these results show that rank-transformed dissimilarity profiles provide an adaptive representation for high-dimensional classification when the signal structure is unknown. |
| title | Rank-Transformed Dissimilarity Profiles for High-Dimensional Classification |
| topic | Methodology |
| url | https://arxiv.org/abs/2306.15199 |