This paper introduces a straightforward generalization of the well-known LVQ1 algorithm for nearest neighbour classifiers that includes the standard LVQ1 and the k-means algorithms as special cases. It is based on a regularizing parameter that monotonically decreases the upper bound of the training classification error towards a minimum. Experiments using 10 real data sets show the utility of t...

In this study, the general ideas surrounding the k-medians problem are discussed. This involves a look into what k-medians attempts to solve and how it goes about doing so. We take a look at why k-medians is used as opposed to its k-means counterpart, specifically how its robustness enables it to be far more resistant to outliers. We then discuss the areas of study that are prevalent in the rea...

In this paper we give a first set of communication lower bounds for distributed clustering problems, in particular, for k-center, k-median and k-means. When the input is distributed across a large number of machines and the number of clusters k is small, our lower bounds match the current best upper bounds up to a logarithmic factor. We have designed a new composition framework in our proofs fo...

We propose a new clustering algorithm based upon the maximin correlation analysis (MCA), a learning technique that can minimize the maximum misclassification risk. The proposed algorithm resembles conventional partition clustering algorithms such as k-means in that data objects are partitioned into k disjoint partitions. On the other hand, the proposed approach is unique in that an MCA-based ap...

Mini Batch K-means ([11]) has been proposed as an alternative to the K-means algorithm for clustering massive datasets. The advantage of this algorithm is to reduce the computational cost by not using all the dataset each iteration but a subsample of a fixed size. This strategy reduces the number of distance computations per iteration at the cost of lower cluster quality. The purpose of this pa...