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-Harmonic means clustering algorithm addresses the random initial clusters problem by using a different cost function @cite_17 for numeric datasets. K-Harmonic means clustering algorithm clusters create more stable clusters as compared to K-means clustering algorithm with random initial clusters. Ahmad and Hashmi @cite_15 combine the distance measure and the definition of cluster centres for mixed datasets suggested by Ahmad and Dey @cite_28 with k-Harmonic clustering algorithm @cite_17 to develop the k-Harmonic clustering algorithm for mixed datasets. Their method is less sensitive to the choice of initial cluster centres. The standard deviation of clustering accuracy of this method is small as compared to the random initialization method. However, it does not give the same clustering results in different runs with different initial partitions.
@cite_28 @cite_15 @cite_17
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Use of traditional k-mean type algorithm is limited to numeric data. This paper presents a clustering algorithm based on k-mean paradigm that works well for data with mixed numeric and categorical features. We propose new cost function and distance measure based on co-occurrence of values. The measures also take into account the significance of an attribute towards the clustering process. We present a modified description of cluster center to overcome the numeric data only limitation of k-mean algorithm and provide a better characterization of clusters. The performance of this algorithm has been studied on real world data sets. Comparisons with other clustering algorithms illustrate the effectiveness of this approach. Display Omitted A K-Harmonic clustering algorithm for mixed data has been presented to reduce random initialization problem for partitional algorithms.The proposed clustering algorithm uses a distance measure developed for mixed datasets.The experiment results suggest that clustering results are quite insensitive to random initialization.The proposed algorithm performed better than other clustering algorithms for various datasets. K-means type clustering algorithms for mixed data that consists of numeric and categorical attributes suffer from cluster center initialization problem. The final clustering results depend upon the initial cluster centers. Random cluster center initialization is a popular initialization technique. However, clustering results are not consistent with different cluster center initializations. K-Harmonic means clustering algorithm tries to overcome this problem for pure numeric data. In this paper, we extend the K-Harmonic means clustering algorithm for mixed datasets. We propose a definition for a cluster center and a distance measure. These cluster centers and the distance measure are used with the cost function of K-Harmonic means clustering algorithm in the proposed algorithm. Experiments were carried out with pure categorical datasets and mixed datasets. Results suggest that the proposed clustering algorithm is quite insensitive to the cluster center initialization problem. Comparative studies with other clustering algorithms show that the proposed algorithm produce better clustering results. We propose a new class of center-based iterative clustering algorithms, K-Harmonic Means (KHMp), which is essentially insensitive to the initialization of the centers, demonstrated through many experiments. The insensitivity to initialization is attributed to a dynamic weighting function, which increases the importance of the data points that are far from any centers in the next iteration. The dependency of the K-Means’ and EM’s performance on the initialization of the centers has been a major problem. Many have tried to generate good initializations to solve the sensitivity problem. KHMp addresses the intrinsic problem by replacing the minimum distance from a data point to the centers, used in K-Means, by the Harmonic Averages of the distances from the data point to all centers. KHMp significantly improves the quality of clustering results comparing with both K-Means and EM. The KHMp algorithms have been implemented in both sequential and parallel languages and tested on hundreds of randomly generated datasets with different data distribution and clustering characteristics.