The traditional clustering algorithm, K-means, is famous for its simplicity and low time complexity. However, the usability of K-means is limited by its shortcoming that the clustering result is heavily dependent on the user-defined variants, i.e., the selection of the initial centroid seeds and the number of clusters (k). A new clustering algorithm, called K-means+, is proposed to extend K-mea...

This paper focuses on the enhanced initial centroids for the K-means algorithm. The original kmeans is using the random choice of init ial seeds which is a major limitation of the orig inal K-means algorithm because it produces less reliab le result of clustering the data. The enhanced method of the k-means algorithm includes the computation of the weighted mean to improve the centroids initial...

This note describes a useful adaptation of thèpeak seeking' regime used in unsupervised learning processes such as competitive learning and`k-means'. The adaptation enables the learning to capture low-order probability eeects and thus to more fully capture the probabilistic structure of the training data.

This paper proposes a fast k-means algorithm for graphs based on Elkan’s k-means for vectors. To accelerate the k-means algorithm for graphs without trading computational time against solution quality, we avoid unnecessary graph distance calculations by exploiting the triangle inequality of the underlying distance metric. In experiments we show that the accelerated k-means for graphs is faster ...

In this paper we propose a new evolutionary clustering algorithm named E-means. E-means is an Evolutionary extension of k-means algorithm that is composed by a revised k-means algorithm and an evolutionary approach to Gaussian mixture model, which estimates automatically the number of clusters and the optimal mean for each cluster. More specifically, the proposed Emeans algorithm defines an ent...

We prove in this paper that the expected value of the objective function of the k-means++ algorithm for samples converges to population expected value. As k-means++, for samples, provides with constant factor approximation for k-means objectives, such an approximation can be achieved for the population with increase of the sample size. This result is of potential practical relevance when one is...

The K-Means Clustering Approach is one of main algorithms in the literature of Pattern recognition and Machine Learning. Yet, due to the random selection of cluster centers and the adherence of results to initial cluster centers, the risk of trapping into local optimality ever exists. In this paper, inspired by a genetic algorithm which is based on the K-means method , a new approach is develop...

and showed the solution G is the leading eigenvectors of the symmetric positive semi definite matrix K. When K = AA> (sample covariance matrix) with A = [x1, ...,xm], xi ∈ Rn, those eigenvectors form a basis to a k-dimensional subspace of Rn which is the closest (in L2 norm sense) to the sample points xi. The axes (called principal axes) g1, ...,gk preserve the variance of the original data in ...

Despite its simplicity and its linear time, a serial K-means algorithm's time complexity remains expensive when it is applied to a problem of large size of multidimensional vectors. In this paper we show an improvement by a factor of O(K/2), where K is the number of desired clusters, by applying theories of parallel computing to the algorithm. In addition to time improvement, the parallel versi...