Robust continuous clustering

Abstract

Clustering is a fundamental procedure in the analysis of scientific data. It is used ubiquitously across the sciences. Despite decades of research, existing clustering algorithms have limited effectiveness in high dimensions and often require tuning parameters for different domains and datasets. We present a clustering algorithm that achieves high accuracy across multiple domains and scales efficiently to high dimensions and large datasets. The presented algorithm optimizes a smooth continuous objective, which is based on robust statistics and allows heavily mixed clusters to be untangled. The continuous nature of the objective also allows clustering to be integrated as a module in end-to-end feature learning pipelines. We demonstrate this by extending the algorithm to perform joint clustering and dimensionality reduction by efficiently optimizing a continuous global objective. The presented approach is evaluated on large datasets of faces, handwritten digits, objects, newswire articles, sensor readings from the Space Shuttle, and protein expression levels. Our method achieves high accuracy across all datasets, outperforming the best prior algorithm by a factor of 3 in average rank.clustering | data analysis | unsupervised learning C lustering is one of the fundamental experimental procedures in data analysis. It is used in virtually all natural and social sciences and has played a central role in biology, astronomy, psychology, medicine, and chemistry. Data-clustering algorithms have been developed for more than half a century (1). Significant advances in the last two decades include spectral clustering (2-4), generalizations of classic center-based methods (5, 6), mixture models (7, 8), mean shift (9), affinity propagation (10), subspace clustering (11-13), nonparametric methods (14, 15), and feature selection (16)(17)(18)(19)(20).Despite these developments, no single algorithm has emerged to displace the k -means scheme and its variants (21). This is despite the known drawbacks of such center-based methods, including sensitivity to initialization, limited effectiveness in high-dimensional spaces, and the requirement that the number of clusters be set in advance. The endurance of these methods is in part due to their simplicity and in part due to difficulties associated with some of the new techniques, such as additional hyperparameters that need to be tuned, high computational cost, and varying effectiveness across domains. Consequently, scientists who analyze large high-dimensional datasets with unknown distribution must maintain and apply multiple different clustering algorithms in the hope that one will succeed. Books have been written to guide practitioners through the landscape of data-clustering techniques (22).We present a clustering algorithm that is fast, easy to use, and effective in high dimensions. The algorithm optimizes a clear continuous objective, using standard numerical methods that scale to massive datasets. The number of clusters need not be known in advance.The operation of the algorithm ...

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