Mixed datasets consist of both numeric and categorical attributes. Various K-means-based clustering algorithms have been developed to cluster these datasets. Generally, these algorithms use random partition as a starting point, which tend to produce different clustering results in different runs. This inconsistency of clustering results may lead to unreliable inferences from the data. A few initialization algorithms have been developed to compute initial partition for mixed datasets; however, they are either computationally expensive or they do not produce consistent clustering results in different runs. In this paper, we propose, initKmix, a novel approach to find initial partition for K-means-based clustering algorithms for mixed datasets. The initKmix is based on the experimental observations that (i) some data points in a dataset remain in the same clusters created by k-means-based clustering algorithm irrespective of the choice of initial clusters, and (ii) individual attribute information can be used to create initial clusters. In initKmix method, a k-means-based clustering algorithm is run many times, in each run one of the attribute is used to produce initial partition. The clustering results of various runs are combined to produce initial partition. This initial partition is then be used as a seed to a k-means-based clustering algorithm to cluster mixed data. The initial partitions produced by initKmix are always fixed, do not change over different runs or by changing the order of the data objects. Experiments with various categorical and mixed datasets showed that initKmix produced accurate and consistent results, and outperformed random initialization and other state-of-the-art initialization methods. Experiments also showed that K-means-based clustering for mixed datasets with initKmix outperformed many state-of-the-art clustering algorithms.
K-means clustering algorithm is a popular clustering algorithm for datasets consisting of numeric attributes because of its low computational complexity @cite_10 . The complexity is linear with respect to the number of data points and scales well for large datasets. It minimizes the optimization function presented in Equation 1 iteratively,
@cite_10
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K-means, a simple and effective clustering algorithm, is one of the most widely used algorithms in computer vision community. Traditional k-means is an iterative algorithm — in each iteration new cluster centers are computed and each data point is re-assigned to its nearest center. The cluster re-assignment step becomes prohibitively expensive when the number of data points and cluster centers are large. In this paper, we propose a novel approximate k-means algorithm to greatly reduce the computational complexity in the assignment step. Our approach is motivated by the observation that most active points changing their cluster assignments at each iteration are located on or near cluster boundaries. The idea is to efficiently identify those active points by pre-assembling the data into groups of neighboring points using multiple random spatial partition trees, and to use the neighborhood information to construct a closure for each cluster, in such a way only a small number of cluster candidates need to be considered when assigning a data point to its nearest cluster. Using complexity analysis, real data clustering, and applications to image retrieval, we show that our approach out-performs state-of-the-art approximate k-means algorithms in terms of clustering quality and efficiency. Clustering is a popular problem with many applications. We consider the k-means problem in the situation where the data is too large to be stored in main memory and must be accessed sequentially, such as from a disk, and where we must use as little memory as possible. Our algorithm is based on recent theoretical results, with significant improvements to make it practical. Our approach greatly simplifies a recently developed algorithm, both in design and in analysis, and eliminates large constant factors in the approximation guarantee, the memory requirements, and the running time. We then incorporate approximate nearest neighbor search to compute k-means in o(nk) (where n is the number of data points; note that computing the cost, given a solution, takes Θ(nk) time). We show that our algorithm compares favorably to existing algorithms - both theoretically and experimentally, thus providing state-of-the-art performance in both theory and practice. K-means is undoubtedly the most widely used partitional clustering algorithm. Unfortunately, due to its gradient descent nature, this algorithm is highly sensitive to the initial placement of the cluster centers. Numerous initialization methods have been proposed to address this problem. In this paper, we first present an overview of these methods with an emphasis on their computational efficiency. We then compare eight commonly used linear time complexity initialization methods on a large and diverse collection of data sets using various performance criteria. Finally, we analyze the experimental results using non-parametric statistical tests and provide recommendations for practitioners. We demonstrate that popular initialization methods often perform poorly and that there are in fact strong alternatives to these methods. We present a k-means-based clustering algorithm, which optimizes mean square error, for given cluster sizes. A straightforward application is balanced clustering, where the sizes of each cluster are equal. In k-means assignment phase, the algorithm solves the assignment problem by Hungarian algorithm. This is a novel approach, and makes the assignment phase time complexity On 3, which is faster than the previous Ok 3.5 n 3.5 time linear programming used in constrained k-means. This enables clustering of bigger datasets of size over 5000 points.