# MC-GTA: Metric-Constrained Model-Based Clustering using Goodness-of-fit Tests with Autocorrelations

arXiv: https://arxiv.org/abs/2405.18395 · HTML: https://mlsanity.com/paper/2405.18395/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 75 references that are in the map.
- First posted on arXiv 28 May 2024.

## Builds on (most cited first, 9 of 9)

- [Large Scale Fine-Grained Categorization and Domain-Specific Transfer Learning](https://mlsanity.com/paper/1806.06193/) (2018)
- [Presence-Only Geographical Priors for Fine-Grained Image Classification](https://mlsanity.com/paper/1906.05272/) (2019)
- [CSP: Self-Supervised Contrastive Spatial Pre-Training for Geospatial-Visual Representations](https://mlsanity.com/paper/2305.01118/) (2023)
- [GeoLLM: Extracting Geospatial Knowledge from Large Language Models](https://mlsanity.com/paper/2310.06213/) (2023)
- [SustainBench: Benchmarks for Monitoring the Sustainable Development Goals with Machine Learning](https://mlsanity.com/paper/2111.04724/) (2021)
- [Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data](https://mlsanity.com/paper/1706.03161/) (2017)
- [Sphere2Vec: A General-Purpose Location Representation Learning over a Spherical Surface for Large-Scale Geospatial Predictions](https://mlsanity.com/paper/2306.17624/) (2023)
- [STICC: A multivariate spatial clustering method for repeated geographic pattern discovery with consideration of spatial contiguity](https://mlsanity.com/paper/2203.09611/) (2022)
- [Constrained Clustering and Multiple Kernel Learning without Pairwise Constraint Relaxation](https://mlsanity.com/paper/2203.12546/) (2022)

## Built on by (most cited first, 2 of 2)

- [Enhancing Contrastive Learning for Geolocalization by Discovering Hard Negatives on Semivariograms](https://mlsanity.com/paper/2509.21573/) (2025)
- [NARA: Anchor-Conditioned Representation Learning for Heterogeneous Vector Geoentities](https://mlsanity.com/paper/2605.12276/) (2026)

## Abstract (arXiv)

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).