Spectral Clustering with a Convex Regularizer on Millions of Images

Abstract

This paper focuses on efficient algorithms for single and multi-view spectral clustering with a convex regularization term for very large scale image datasets. In computer vision applications, multiple views denote distinct image-derived feature representations that inform the clustering. Separately, the regularization encodes high level advice such as tags or user interaction in identifying similar objects across examples. Depending on the specific task, schemes to exploit such information may lead to a smooth or non-smooth regularization function. We present stochastic gradient descent methods for optimizing spectral clustering objectives with such convex regularizers for datasets with up to a hundred million examples. We prove that under mild conditions the local convergence rate is $O(1/\sqrt{T})$ where T is the number of iterations; further, our analysis shows that the convergence improves linearly by increasing the number of threads. We give extensive experimental results on a range of vision datasets demonstrating the algorithm’s empirical behavior.