Fast k-means algorithm clustering

k-means has recently been recognized as one of the best algorithms for clustering unsupervised data. Since k-means depends mainly on distance calculation between all data points and the centers, the time cost will be high when the size of the dataset is large (for example more than 500millions of points). We propose a two stage algorithm to reduce the time cost of distance calculation for huge datasets. The first stage is a fast distance calculation using only a small portion of the data to produce the best possible location of the centers. The second stage is a slow distance calculation in which the initial centers used are taken from the first stage. The fast and slow stages represent the speed of the movement of the centers. In the slow stage, the whole dataset can be used to get the exact location of the centers. The time cost of the distance calculation for the fast stage is very low due to the small size of the training data chosen. The time cost of the distance calculation for the slow stage is also minimized due to small number of iterations. Different initial locations of the clusters have been used during the test of the proposed algorithms. For large datasets, experiments show that the 2-stage clustering method achieves better speed-up (1-9 times).Comment: 16 pages, Wimo2011; International Journal of Computer Networks & Communications (IJCNC) Vol.3, No.4, July 201

Reducing the Time Requirement of k-Means Algorithm

Traditional k-means and most k-means variants are still computationally expensive for large datasets, such as microarray data, which have large datasets with large dimension size d. In k-means clustering, we are given a set of n data points in ddimensional space Rd and an integer k. The problem is to determine a set of k points in Rd, called centers, so as to minimize the mean squared distance from each data point to its nearest center. In this work, we develop a novel k-means algorithm, which is simple but more efficient than the traditional k-means and the recent enhanced k-means. Our new algorithm is based on the recently established relationship between principal component analysis and the k-means clustering. We provided the correctness proof for this algorithm. Results obtained from testing the algorithm on three biological data and six non-biological data (three of these data are real, while the other three are simulated) also indicate that our algorithm is empirically faster than other known k-means algorithms. We assessed the quality of our algorithm clusters against the clusters of a known structure using the Hubert-Arabie Adjusted Rand index (ARIHA). We found that when k is close to d, the quality is good (ARIHA.0.8) and when k is not close to d, the quality of our new k-means algorithm is excellent (ARIHA.0.9). In this paper, emphases are on the reduction of the time requirement of the k-means algorithm and its application to microarray data due to the desire to create a tool for clustering and malaria research. However, the new clustering algorithm can be used for other clustering needs as long as an appropriate measure of distance between the centroids and the members is used. This has been demonstrated in this work on six non-biological data

Study of document clustering using the k-means algorithm

One of the most commonly used data mining techniques is document clustering or unsupervised document classification which deals with the grouping of documents based on some document similarity function; This thesis deals with research issues associated with categorizing documents using the k-means clustering algorithm which groups objects into K number of groups based on document representations and similarities; The proposed hypothesis of this thesis is to prove that unsupervised clustering of a set of documents produces similar results to that of their supervised categorization

Clustering with Spectral Norm and the k-means Algorithm

There has been much progress on efficient algorithms for clustering data points generated by a mixture of $k$ probability distributions under the assumption that the means of the distributions are well-separated, i.e., the distance between the means of any two distributions is at least $\Omega(k)$ standard deviations. These results generally make heavy use of the generative model and particular properties of the distributions. In this paper, we show that a simple clustering algorithm works without assuming any generative (probabilistic) model. Our only assumption is what we call a "proximity condition": the projection of any data point onto the line joining its cluster center to any other cluster center is $\Omega(k)$ standard deviations closer to its own center than the other center. Here the notion of standard deviations is based on the spectral norm of the matrix whose rows represent the difference between a point and the mean of the cluster to which it belongs. We show that in the generative models studied, our proximity condition is satisfied and so we are able to derive most known results for generative models as corollaries of our main result. We also prove some new results for generative models - e.g., we can cluster all but a small fraction of points only assuming a bound on the variance. Our algorithm relies on the well known $k$-means algorithm, and along the way, we prove a result of independent interest -- that the $k$-means algorithm converges to the "true centers" even in the presence of spurious points provided the initial (estimated) centers are close enough to the corresponding actual centers and all but a small fraction of the points satisfy the proximity condition. Finally, we present a new technique for boosting the ratio of inter-center separation to standard deviation

A Faster kk-means++ Algorithm

K-means++ is an important algorithm to choose initial cluster centers for the k-means clustering algorithm. In this work, we present a new algorithm that can solve the $k$-means++ problem with near optimal running time. Given $n$ data points in $\mathbb{R}^d$, the current state-of-the-art algorithm runs in $\widetilde{O}(k )$ iterations, and each iteration takes $\widetilde{O}(nd k)$ time. The overall running time is thus $\widetilde{O}(n d k^2)$. We propose a new algorithm \textsc{FastKmeans++} that only takes in $\widetilde{O}(nd + nk^2)$ time, in total