Clustering is a separation of data into groups of similar objects. Every group called cluster consists of objects that are similar to one another and dissimilar to objects of other groups. In this paper, the K-Means algorithm is implemented by three distance functions and to identify the optimal distance function for clustering methods. The proposed K-Means algorithm is compared with K-Means, S...

K-means (MacQueen, 1967) [1] is one of the simplest unsupervised learning algorithms that solve the well-known clustering problem. The procedure follows a simple and easy way to classify a given data set to a predefined, say K number of clusters. Determination of K is a difficult job and it is not known that which value of K can partition the objects as per our intuition. To overcome this probl...

This paper presents a generalized version of the conventional k-means clustering algorithm [Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability, 1, University of California Press, Berkeley, 1967, p. 281]. Not only is this new one applicable to ellipse-shaped data clusters without dead-unit problem, but also performs correct clustering without pre-assigning the exact...

We present a new clustering algorithm called k-means-u* which in many cases is able to significantly improve the clusterings found by k-means++, the current de-facto standard for clustering in Euclidean spaces. First we introduce the k-means-u algorithm which starts from a result of k-means++ and attempts to improve it with a sequence of non-local “jumps” alternated by runs of standard k-means....

The k-means++ seeding algorithm is one of the most popular algorithms that is used for finding the initial k centers when using the k-means heuristic. The algorithm is a simple sampling procedure and can be described as follows: Pick the first center randomly from the given points. For i > 1, pick a point to be the i center with probability proportional to the square of the Euclidean distance o...

One way of representing semantics could be via a high dimensional conceptual space constructed by certain lexical semantic space models. Concepts (words), represented as a vector of other words in the semantic space, can be categorized via clustering techniques into a number of regions reflecting different contexts. The conventional clustering algorithms, e.g., K-means method, however, normally...

A new clustering algorithm based on grid projections is proposed. This algorithm, called U*C, uses distance information together with density structures. The number of clusters is determined automatically. The validity of the clusters found can be judged by the U*-Matrix visualization on top of the grid. A U*-Matrix gives a combined visualization of distance and density structures of a high dim...

K-means clustering algorithm has been used to classify patterns of Japanese candlesticks which accompany the prices of several assets registered in the Warsaw stock exchange (GPW). It has been found that the trend reversals seem to be preceded by specific combinations of candlesticks with notable frequency. Surprisingly, the same patterns appear in both bullish and bearish trend reversals. The ...

A method for the initialisation step of clustering algorithms is presented. It is based on the concept of cluster as a high density region of points. The search space is modelled as a set of d-dimensional cells. A sample of points is chosen and located into the appropriate cells. Cells are iteratively split as the number of points they receive increases. The regions of the search space having a...