Efficient <inline-formula><tex-math>$k$</tex-math><alternatives> <inline-graphic xlink:type="simple" xlink:href="qu-ieq1-2306193.gif"/></alternatives></inline-formula>-Means++ Approximation with MapReduce

Abstract

Abstract--means is undoubtedly one of the most popular clustering algorithms owing to its simplicity and efficiency. However, this algorithm is highly sensitive to the chosen initial centers and a proper initialization is crucial for obtaining an ideal solution. To overcome this problem, -means++ is proposed to sequentially choose the centers so as to achieve a solution that is provably close to the optimal one. However, due to its weak scalability, -means++ becomes inefficient as the size of data increases. To improve its scalability and efficiency, this paper presents MapReduce -means++ method which can drastically reduce the number of MapReduce jobs by using only one MapReduce job to obtain centers. The -means++ initialization algorithm is executed in the Mapper phase and the weighted -means++ initialization algorithm is run in the Reducer phase. As this new MapReduce -means++ method replaces the iterations among multiple machines with a single machine, it can reduce the communication and I/O costs significantly. We also prove that the proposed MapReduce -means++ method obtains ( 2 ) approximation to the optimal solution of -means. To reduce the expensive distance computation of the proposed method, we further propose a pruning strategy that can greatly avoid a large number of redundant distance computations. Extensive experiments on real and synthetic data are conducted and the performance results indicate that the proposed MapReduce -means++ method is much more efficient and can reach a good approximation.

Improving Scalable K-Means++

“…However, for example MapReduce-based implementation of K-means needs multiple MapReduce jobs for the initialization. The MapReduce K-means++ method [7] tries to address this issue, as it uses one MapReduce job to select K initial prototypes, which speeds up the initialization compared to K-means . Suggestions of parallelizing the second, search phase of K-means have been given in several papers (see, e.g., [8,9]).…”

Clustering Balinese Language Documents using the Balinese Stemmer Method and Mini Batch K-Means with K-Means++

“…Metode k-means dan mini batch k-means memiliki kekurangan yang sama yaitu sensitif terhadap pusat cluster awal yang dipilih [8]. Metode k-means++ digunakan untuk mengatasi kekurangan pada k-means dan mini batch k-means dengan cara memilih pusat klaster pertama secara acak dan kemudian dipilih pusat klaster berdasarkan perhitungan jarak terdekat antara titik data dan pusat cluster yang dipilih [9].…”

A Cluster Approach to Cloud Cover Classification over South America and Adjacent Oceans Using a k-means/k-means++ Unsupervised Algorithm on GOES IR Imagery

“…Nevertheless, the performance of k-means was improved by combining it with the k-means++ initialization algorithm, which is a subprocess that seeds the centroids [60]. To this particular aim, k-means++ outperforms k-means both by achieving the classification task quicker and by a faster convergence to a minimal intra-class (intra-cluster) variance [60,61]. The k-means++ algorithm operates as follows:…”