This paper presents a new approach to overcome one of the most known disadvantages of the well-known Kmeans clustering algorithm. The problems of classical Kmeans are such as the problem of random initialization of prototypes and the requirement of predefined number of clusters in the dataset. Randomly initialized prototypes can often yield results to converge to local rather than global optimum. A better result of Kmeans may be obtained by running it many times to get satisfactory results. The proposed algorithms are based on a new novel definition of densities of data points which is based on the k-nearest neighbor method. By this definition we detect noise and outliers which affect Kmeans strongly, and obtained good initial prototypes from one run with automatic determination of K number of clusters. This algorithm is referred to as Efficient Initialization of Kmeans (EI-Kmeans). Still Kmeans algorithm used to cluster data with convex shapes, similar sizes, and densities. Thus we develop a new clustering algorithm called Efficient Data Clustering Algorithm (EDCA) that uses our new definition of densities of data points. The results show that the proposed algorithms improve the data clustering by Kmeans. EDCA is able to detect clusters with different non-convex shapes, different sizes and densities.

Partition-based clustering technique is one of several clustering techniques that attempt to directly decompose the dataset into a set of disjoint clusters. K-means algorithm dependence on partition-based clustering technique is popular and widely used and applied to a variety of domains. K-means clustering results are extremely sensitive to the initial centroid; this is one of the major drawbacks of k-means algorithm. Due to such sensitivity; several different initialization approaches were proposed for the K-means algorithm in the last decades. This paper proposes a selection method for initial cluster centroid in K-means clustering instead of the random selection method. Research provides a detailed performance assessment of the proposed initialization method over many datasets with different dimensions, numbers of observations, groups and clustering complexities. Ability to identify the true clusters is the performance evaluation standard in this research. The experimental results show that the proposed initialization method is more effective and converges to more accurate clustering results than those of the random initialization method.

One of the main categories in Data Clustering is density based clustering. Density based clustering techniques like DBSCAN are attractive because they can find arbitrary shaped clusters along with noisy outlier. The main weakness of the traditional density based algorithms like DBSCAN is clustering the different density level data sets. DBSCAN calculations done according to given parameters applied to all points in a data set, while densities of the data set clusters may be totally different. The proposed algorithm overcomes this weakness of the traditional density based algorithms. The algorithm starts with partitioning the data within a cluster to units based on a user parameter and compute the density for each unit separately. Consequently, the algorithm compares the results and merges neighboring units with closer approximate density values to become a new cluster. The experimental results of the simulation show that the proposed algorithm gives good results in finding clusters for different density cluster data set.