The paper presents a formula for the reclassification of multidimensional data points (columns of real numbers, "objects", "vectors", etc.). This formula describes the change in the total squared error caused by reclassification of data points from one cluster into another and prompts the way to calculate the sequence of optimal partitions, which are characterized by a minimum value of the tota...

The k-means method is an old but popular clustering algorithm known for its speed and simplicity. Until recently, however, no meaningful theoretical bounds were known on its running time. In this paper, we demonstrate that the worst-case running time of k-means is superpolynomial by improving the best known lower bound from Ω(n) iterations to 2 √ . To complement this lower bound, we show a smoo...

Image segmentation is used to recognizing some objects or something that is more meaningful and easier to analyze In this paper we are focus on the the K means clustering for segmentation of the image. K-means clustering is the most widely used clustering algorithm to position the radial basis function (RBF) centres. Its simplicity and ability to perform on-line clustering may inspire this choi...

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...

Mini-model method (MM-method) is an instance-based learning algorithm similarly as the k-nearest neighbor method, GRNN network or RBF network but its idea is different. MM operates only on data from the local neighborhood of a query. The paper presents new version of the MM-method which is based on k-means clustering algorithm. The domain of the model is calculated using k-means algorithm. Clus...

Clustering is a fundamental problem in computer science with applications ranging from biology to information retrieval and data compression. In a clustering problem, a set of objects, usually represented as points in a high-dimensional space R, is to be partitioned such that objects in the same group share similar properties. The k-means method is a traditional clustering algorithm, originally...

Hedge fund databases vary as to the type of funds to include and in their classification scheme. Investment strategy and/or investment style are the basis for classification. Considerable variation is observed in the definitions, return calculation methodologies, and assumptions. There exists a myriad of classifications, some overlapping and some mutually exclusive. There is a need for an ‘alte...

In this paper we give a first set of communication lower bounds for distributed clustering problems, in particular, for k-center, k-median and k-means. When the input is distributed across a large number of machines and the number of clusters k is small, our lower bounds match the current best upper bounds up to a logarithmic factor. We have designed a new composition framework in our proofs fo...

We propose a new clustering algorithm based upon the maximin correlation analysis (MCA), a learning technique that can minimize the maximum misclassification risk. The proposed algorithm resembles conventional partition clustering algorithms such as k-means in that data objects are partitioned into k disjoint partitions. On the other hand, the proposed approach is unique in that an MCA-based ap...

The k-means method is a widely used clustering algorithm. One of its distinguished features is its speed in practice. Its worst-case running-time, however, is exponential, leaving a gap between practical and theoretical performance. Arthur and Vassilvitskii [3] aimed at closing this gap, and they proved a bound of poly(nk, σ−1) on the smoothed running-time of the k-means method, where n is the ...