MC-GTA: Metric-Constrained Model-Based Clustering using Goodness-of-fit Tests with Autocorrelations
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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_ | 1866910469031198720 |
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| author | Wang, Zhangyu Mai, Gengchen Janowicz, Krzysztof Lao, Ni |
| author_facet | Wang, Zhangyu Mai, Gengchen Janowicz, Krzysztof Lao, Ni |
| contents | A wide range of (multivariate) temporal (1D) and spatial (2D) data analysis tasks, such as grouping vehicle sensor trajectories, can be formulated as clustering with given metric constraints. Existing metric-constrained clustering algorithms overlook the rich correlation between feature similarity and metric distance, i.e., metric autocorrelation. The model-based variations of these clustering algorithms (e.g. TICC and STICC) achieve SOTA performance, yet suffer from computational instability and complexity by using a metric-constrained Expectation-Maximization procedure. In order to address these two problems, we propose a novel clustering algorithm, MC-GTA (Model-based Clustering via Goodness-of-fit Tests with Autocorrelations). Its objective is only composed of pairwise weighted sums of feature similarity terms (square Wasserstein-2 distance) and metric autocorrelation terms (a novel multivariate generalization of classic semivariogram). We show that MC-GTA is effectively minimizing the total hinge loss for intra-cluster observation pairs not passing goodness-of-fit tests, i.e., statistically not originating from the same distribution. Experiments on 1D/2D synthetic and real-world datasets demonstrate that MC-GTA successfully incorporates metric autocorrelation. It outperforms strong baselines by large margins (up to 14.3% in ARI and 32.1% in NMI) with faster and stabler optimization (>10x speedup). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18395 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | MC-GTA: Metric-Constrained Model-Based Clustering using Goodness-of-fit Tests with Autocorrelations Wang, Zhangyu Mai, Gengchen Janowicz, Krzysztof Lao, Ni Machine Learning Artificial Intelligence Applications A wide range of (multivariate) temporal (1D) and spatial (2D) data analysis tasks, such as grouping vehicle sensor trajectories, can be formulated as clustering with given metric constraints. Existing metric-constrained clustering algorithms overlook the rich correlation between feature similarity and metric distance, i.e., metric autocorrelation. The model-based variations of these clustering algorithms (e.g. TICC and STICC) achieve SOTA performance, yet suffer from computational instability and complexity by using a metric-constrained Expectation-Maximization procedure. In order to address these two problems, we propose a novel clustering algorithm, MC-GTA (Model-based Clustering via Goodness-of-fit Tests with Autocorrelations). Its objective is only composed of pairwise weighted sums of feature similarity terms (square Wasserstein-2 distance) and metric autocorrelation terms (a novel multivariate generalization of classic semivariogram). We show that MC-GTA is effectively minimizing the total hinge loss for intra-cluster observation pairs not passing goodness-of-fit tests, i.e., statistically not originating from the same distribution. Experiments on 1D/2D synthetic and real-world datasets demonstrate that MC-GTA successfully incorporates metric autocorrelation. It outperforms strong baselines by large margins (up to 14.3% in ARI and 32.1% in NMI) with faster and stabler optimization (>10x speedup). |
| title | MC-GTA: Metric-Constrained Model-Based Clustering using Goodness-of-fit Tests with Autocorrelations |
| topic | Machine Learning Artificial Intelligence Applications |
| url | https://arxiv.org/abs/2405.18395 |