Fast Approximate KK-Means via Cluster Closures

$K$-means, a simple and effective clustering algorithm, is one of the most widely used algorithms in multimedia and computer vision community. Traditional $k$-means is an iterative algorithm---in each iteration new cluster centers are computed and each data point is re-assigned to its nearest center. The cluster re-assignment step becomes prohibitively expensive when the number of data points and cluster centers are large. In this paper, we propose a novel approximate $k$-means algorithm to greatly reduce the computational complexity in the assignment step. Our approach is motivated by the observation that most active points changing their cluster assignments at each iteration are located on or near cluster boundaries. The idea is to efficiently identify those active points by pre-assembling the data into groups of neighboring points using multiple random spatial partition trees, and to use the neighborhood information to construct a closure for each cluster, in such a way only a small number of cluster candidates need to be considered when assigning a data point to its nearest cluster. Using complexity analysis, image data clustering, and applications to image retrieval, we show that our approach out-performs state-of-the-art approximate $k$-means algorithms in terms of clustering quality and efficiency

Low-rank SIFT: An Affine Invariant Feature for Place Recognition

In this paper, we present a novel affine-invariant feature based on SIFT, leveraging the regular appearance of man-made objects. The feature achieves full affine invariance without needing to simulate over affine parameter space. Low-rank SIFT, as we name the feature, is based on our observation that local tilt, which are caused by changes of camera axis orientation, could be normalized by converting local patches to standard low-rank forms. Rotation, translation and scaling invariance could be achieved in ways similar to SIFT. As an extension of SIFT, our method seeks to add prior to solve the ill-posed affine parameter estimation problem and normalizes them directly, and is applicable to objects with regular structures. Furthermore, owing to recent breakthrough in convex optimization, such parameter could be computed efficiently. We will demonstrate its effectiveness in place recognition as our major application. As extra contributions, we also describe our pipeline of constructing geotagged building database from the ground up, as well as an efficient scheme for automatic feature selection