Efficient Parallel K-Means on MapReduce Using Triangle Inequality

K-Means is one of the most efficient and popular clustering algorithms that has been around for more than 50 years. The naive implementation of K-Means spends the vast majority of its time computing redundant distance calculations from each point to all cluster centres. This issue has been extensively studied and methods based on the triangle inequality principle have been used to eliminate unnecessary distance calculations. Most triangle inequality optimisations cache extra information (distance bounds and cluster assignments) from one iteration to eliminate the need of computing exact distances in the next. This work takes these optimisations one step further and integrates them into an accelerated version of K-Means on a well-known distributed computing framework known as MapReduce to produce an efficient and highly scalable K-Means for big data. Although MapReduce is considered as one of the most reliable and fault tolerant distributed computing frameworks, one of its major drawback is that it does not support iterative algorithms such as K-Means, and does not cache any data between two consecutive iterations, which is required in most triangle inequality optimisations. Therefore, this work introduces two new approaches to pass information from one iteration to the next to accelerate K-Means. The first approach is called K-Means on MapReduce using Extended Vector (KMMR-EV). The second approach is called K-Means on MapReduce using Bounds Files (KMMR-BF). These approaches achieve speedups up to 4.5x for KMMR-EV and 6.8x for KMMR-BF, with respect to the naive implementation of K-Means on MapReduce (KMMR-N). An extensive experimental work, with real and synthetic datasets, has been conducted on Apache Hadoop (an open-source implementation of MapReduce), along with an overhead analysis to show the effectiveness of both approaches.