# One-Pass Sparsified Gaussian Mixtures

## TL;DR

This paper introduces a one-pass sparsified Gaussian mixture model (SGMM) that efficiently clusters high-dimensional data by subsampling features, significantly reducing computation time while maintaining accuracy, suitable for streaming data applications.

## Contribution

The paper proposes a novel one-pass SGMM that operates in reduced feature space, with theoretical derivation of maximum likelihood estimators and demonstrated efficiency over traditional GMM.

## Key findings

- SGMM achieves faster clustering than GMM.
- SGMM maintains comparable accuracy to full GMM.
- SGMM is suitable for streaming high-dimensional data.

## Abstract

We present a one-pass sparsified Gaussian mixture model (SGMM). Given $N$ data points in $P$ dimensions, $X$, the model fits $K$ Gaussian distributions to $X$ and (softly) classifies each point to these clusters. After paying an up-front cost of $\mathcal{O}(NP\log P)$ to precondition the data, we subsample $Q$ entries of each data point and discard the full $P$-dimensional data. SGMM operates in $\mathcal{O}(KNQ)$ time per iteration for diagonal or spherical covariances, independent of $P$, while estimating the model parameters in the full $P$-dimensional space, making it one-pass and hence suitable for streaming data. We derive the maximum likelihood estimators for the parameters in the sparsified regime, demonstrate clustering on synthetic and real data, and show that SGMM is faster than GMM while preserving accuracy.