Efficient Sketching Algorithm for Sparse Binary Data Recent advancement of the WWW, IOT, social network, ecommerce, etc. have generated a large volume of data. These datasets are mostly represented by high dimensional and sparse datasets. Many fundamental subroutines of common data analytic tasks such as clustering, classification, ranking, nearest neighbour search, etc. scale poorly with the dimension of the dataset. In this work, we address this problem and propose a sketching (alternatively, dimensionality reduction) algorithm xe2x80x93 BinSketch (Binary Data Sketch) xe2x80x93 for sparse binary datasets. BinSketch preserves the binary version of the dataset after sketching and maintains estimates for multiple similarity measures such as Jaccard, Cosine, InnerProduct similarities, and Hamming distance, on the same sketch. We present a theoretical analysis of our algorithm and complement it with extensive experimentation on several realworld datasets. We compare the performance of our algorithm with the stateoftheart algorithms on the task of meansquareerror and ranking. Our proposed algorithm offers a comparable accuracy while suggesting a significant speedup in the dimensionality reduction time, with respect to the other candidate algorithms. Our proposal is simple, easy to implement, and therefore can be adopted in practice.

A Binary Linear ProgrammingBased KMeans Approach for the Capacitated Centered Clustering Problem The kmeans algorithm is one of the most popular clustering algorithms in the machine learning community. Its simplicity and scalability make it the primary choice for many clustering applications. We introduce here a variant of the kmeans algorithm that can account for complex side constraints. The key idea is to use binary linear programming for assigning objects to clusters. Unlike existing extensions of the kmeans algorithm that are designed for accommodating specific types of constraints, our approach can be applied to a wide range of constrained clustering problems with minor modifications. We demonstrate the effectiveness and efficiency of the proposed approach by comparing it to a stateoftheart algorithm on a test set that comprises 18 instances of the capacitated centered clustering problem. The proposed approach performed particularly well on largesized instances with more than 100 clusters. It even found new bestknown solutions for the four largest instances in the test set.