# Scalable Clustering: Large Scale Unsupervised Learning of Gaussian Mixture Models with Outliers

## TL;DR

This paper presents a scalable, theoretically guaranteed clustering algorithm robust to outliers, suitable for large datasets like ImageNet, and effective as an initialization for k-means.

## Contribution

It introduces a new loss minimization-based clustering method with provable guarantees that scales efficiently and handles outliers in large datasets.

## Key findings

- High accuracy with high probability under certain assumptions
- Effective as an initialization for k-means clustering
- Outperforms classic methods in speed and accuracy on large datasets

## Abstract

Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a provably robust clustering algorithm based on loss minimization that performs well on Gaussian mixture models with outliers. It provides theoretical guarantees that the algorithm obtains high accuracy with high probability under certain assumptions. Moreover, it can also be used as an initialization strategy for $k$-means clustering. Experiments on real-world large-scale datasets demonstrate the effectiveness of the algorithm when clustering a large number of clusters, and a $k$-means algorithm initialized by the algorithm outperforms many of the classic clustering methods in both speed and accuracy, while scaling well to large datasets such as ImageNet.