k2-means for fast and accurate large scale clustering

TL;DR

k^2-means is a novel clustering algorithm that significantly accelerates large-scale clustering tasks by combining a new initialization method with an optimized assignment step, achieving faster convergence and comparable accuracy.

Contribution

It introduces k^2-means, a scalable clustering method with a new initialization and assignment strategy that reduces computational complexity for large datasets.

Findings

k^2-means is orders of magnitude faster than standard methods.

It achieves low energy solutions comparable to k-means++.

The method performs well on high-dimensional, large-cluster datasets.

Abstract

We propose k^2-means, a new clustering method which efficiently copes with large numbers of clusters and achieves low energy solutions. k^2-means builds upon the standard k-means (Lloyd's algorithm) and combines a new strategy to accelerate the convergence with a new low time complexity divisive initialization. The accelerated convergence is achieved through only looking at k_n nearest clusters and using triangle inequality bounds in the assignment step while the divisive initialization employs an optimal 2-clustering along a direction. The worst-case time complexity per iteration of our k^2-means is O(nk_nd+k^2d), where d is the dimension of the n data points and k is the number of clusters and usually n << k << k_n. Compared to k-means' O(nkd) complexity, our k^2-means complexity is significantly lower, at the expense of slightly increasing the memory complexity by O(nk_n+k^2). In our extensive experiments k^2-means is order(s) of magnitude faster than standard methods in computing accurate clusterings on several standard datasets and settings with hundreds of clusters and high dimensional data. Moreover, the proposed divisive initialization generally leads to clustering energies comparable to those achieved with the standard k-means++ initialization, while being significantly faster.