An Improved k-means Algorithm based on BIC Score and Density Radius

Purpose – It is well known that the selection of initial cluster centers can significantly affect K-means clustering results. The purpose of this paper is to propose an improved, efficient methodology to handle such a challenge. Design/methodology/approach – According to the fact that the inner-class distance among samples within the same cluster is supposed to be smaller than the inter-class distance among clusters, the algorithm will dynamically adjust initial cluster centers that are randomly selected. Consequently, such adjusted initial cluster centers will be highly representative in the sense that they are distributed among as many samples as possible. As a result, local optima that are common in K-means clustering can then be effectively reduced. In addition, the algorithm is able to obtain all initial cluster centers simultaneously (instead of one center at a time) during the dynamic adjustment. Findings – Experimental results demonstrate that the proposed algorithm greatly improves the accuracy of traditional K-means clustering results and, in a more efficient manner. Originality/value – The authors presented in this paper an efficient algorithm, which is able to dynamically adjust initial cluster centers that are randomly selected. The adjusted centers are highly representative, i.e. they are distributed among as many samples as possible. As a result, local optima that are common in K-means clustering can be effectively reduced so that the authors can achieve an improved clustering accuracy. In addition, the algorithm is a cost-efficient one and the enhanced clustering accuracy can be obtained in a more efficient manner compared with traditional K-means algorithm.

Clustering is a widely used technique in data mining applications and various pattern recognition applications, in which data objects are divided into groups. K-means algorithm is one of the most classical clustering algorithms. In this algorithm, the initial clustering centers are randomly selected, this results in unstable clustering results. To solve this problem, an optimized algorithm to select the initial centers is proposed. In the proposed algorithm, dispersion degree is defined, which is based on entropy. In the algorithm, all the objects are firstly grouped into a big cluster, and the object that has the maximum dispersion degree and the object that has the minimum dispersion degree are selected as the initial clustering centers from the initial big cluster. And then other objects in the biggest cluster are partitioned to the initial clusters to which the objects are nearest. The partition process will be repeated until the cluster number is equal to the specified value k. Finally, the partitioned k clusters and their cluster centers are applied to k-means algorithm as initial clusters and centers. Several experiments are conducted on real data sets to evaluate the proposed algorithm. The proposed algorithm is compared with traditional k-means algorithm and max-min distance clustering algorithm, and experimental results show that the improved k-means algorithm is stable in selecting initial clustering, because it can select unique initial clustering centers. The optimized algorithm’s effectiveness and feasibility are also verified by experiments, and the algorithm can reduce the times of iterations and has more stable clustering results and higher accuracy.

The traditional K-means clustering algorithm has the problems that the number of clusters needs to be determined artificially, the clustering results are easily affected by the initial clustering centers and isolated points, and the iterative process is computationally complicated. To address above problems, an improved K-means clustering algorithm combining multi-point optimization(MFK-means) is proposed. The proposed algorithm is improved from the following four aspects. Firstly, the number of clusters is jointly determined by combining the contour coefficient method and the elbow rule. Secondly, the optimized outlier detection algorithm is used to exclude the influence of isolated points on the clustering results. Thirdly, the initial clustering centers are gradually determined based on the outlier candidate set and the maximum-minimum distance idea. Finally, the heuristic method is used to reduce the computational effort of the iterative process. The experimental results on the UCI dataset show that the proposed improved algorithm has higher clustering accuracy and better stability than the traditional K-means algorithm and another improved algorithm.

The traditional K-means algorithm is sensitive to the initial clustering center, and randomly selecting different initial clustering centers will result in different clustering results. In this paper, an improved K-means algorithm based on Mean Shift clustering is proposed to solve the existing problems of the K-means algorithm. This algorithm selects a high-density migration vector set MP by Mean Shift, and selects k points with the farthest distance from each other in the high-density region in MP as the initial cluster center. This paper adopts the iris data set and the wine data set from the international standard UCI database, and 150 vowel image texts on the upper part of the baseline for the text analysis of the Ujin body Tibetan ancient books are used to verify the proposed algorithm (The real sample is called the Tibetan dataset). It can be seen from the experimental results that the algorithm can achieve better clustering results with higher accuracy and more stability.

The main influencing factors of the clustering effect of the k-means algorithm are the selection of the initial clustering center and the distance measurement between the sample points. The traditional k-mean algorithm uses Euclidean distance to measure the distance between sample points, thus it suffers from low differentiation of attributes between sample points and is prone to local optimal solutions. For this feature, this paper proposes an improved k-means algorithm based on evidence distance. Firstly, the attribute values of sample points are modelled as the basic probability assignment (BPA) of sample points. Then, the traditional Euclidean distance is replaced by the evidence distance for measuring the distance between sample points, and finally k-means clustering is carried out using UCI data. Experimental comparisons are made with the traditional k-means algorithm, the k-means algorithm based on the aggregation distance parameter, and the Gaussian mixture model. The experimental results show that the improved k-means algorithm based on evidence distance proposed in this paper has a better clustering effect and the convergence of the algorithm is also better.

In the era of big data, text as an information reserve database is very important, in all walks of life. From humanities research to government decision-making, from precision medicine to quantitative finance, from customer management to marketing, massive text, as one of the most important information carriers, plays an important role everywhere. The text data generated in these practical problems of humanities research, financial industry, marketing, and other fields often has obvious domain characteristics, often containing the professional vocabulary and unique language patterns in these fields and often accompanied by a variety of “noise.” Dealing with such texts is a great challenge for the current technical conditions, especially for Chinese texts. A clustering algorithm provides a better solution for text big data information processing. Clustering algorithm is the main body of cluster analysis, K-means algorithm with its implementation principle is simple, low time complexity is widely used in the field of cluster analysis, but its K value needs to be preset, initial clustering center random selection into local optimal solution, other clustering algorithm, such as mean drift clustering, K-means clustering in mining text big data. In view of the problems of the above algorithm, this paper first extracts and analyzes the text big data and then does experiments with the clustering algorithm. Experimental conclusion: by analyzing large-scale text data limited to large-scale and simple data set, the traditional K-means algorithm has low efficiency and reduced accuracy, and the K-means algorithm is susceptible to the influence of initial center and abnormal data. According to the above problems, the K-means cluster analysis algorithm for data sets with large data volumes is analyzed and improved to improve its execution efficiency and accuracy on data sets with large data volume set. Mean shift clustering can be regarded as making many random centers move towards the direction of maximum density gradually, that is, moving their mean centroid continuously according to the probability density of data and finally obtaining multiple maximum density centers. It can also be said that mean shift clustering is a kernel density estimation algorithm.

K-means clustering algorithm is an unsupervised learning method with simple principles, easy implementation, and strong adaptability. Aiming at the disadvantages of this algorithm that the clusters’ number is difficult to determine, sensitive to the initial cluster center, and the clustering result is easily impacted by the outliers, this paper proposes an improved clustering algorithm based on density selection, which compares the neighborhood density of each sample and the average density of all the samples, treats the samples with lower density as the outliers or isolated points, and then deletes them. After data pre-processing, the cluster validity index is modified to obtain the optimal clusters’ number by minimizing the cluster validity index, and then optimizes the initial cluster center by density selection strategy. Finally, it is verified by the experiment that the improved algorithm has better accuracy than the traditional K-means algorithm, and it can converge to the global minimum of SSE faster.

As one of the most important techniques in data mining, clustering has always been highly concerned. Most clustering algorithms have encountered challenges, such as the difficulty of cluster centers selection, the artificial determination of the number of clusters K, low accuracy of clustering, and uneven clustering efficiency of different data sets. Considering the difficulty of cluster centers chosen, a new algorithm of fast selecting the initial cluster centers is proposed in this paper. Generally, cluster centers are those data points with higher density, smaller radius threshold and far away from each other, this method uses MNN (M nearest neighbors), density and distance to determine the initial cluster centers. First, the neighborhood radius r of each point is measured by MNN based on distance, and the average value of all r is marked as r̅; second, the densities ρ of each point in the region within r̅ are calculated; and then, factor f is defined to describe the probability that points become cluster centers, based on which, the initial cluster centers are determined by the candidates with bigger f . In the end, the method proposed in this paper is tested by using 12 groups of typical benchmark data sets and applied in the stellar spectral data of LAMOST survey. The experiment results compared with the other six algorithms indicate that the initial cluster centers obtained by this method are of higher quality than that of the six algorithms. Meanwhile, the initial cluster centers of spectral data are of good agreement with the actual stellar classifications.

For such difficulties as low mining efficiency and large amount of data that the data mining of residential electricity data has to be faced with, the research on improved K-means algorithm and cloud computing-based analysis on massive data of power utilization is performed. Firstly, as the initial cluster center and the value K is difficult to determine in traditional K-means algorithm, an improved K-means algorithm based on density is proposed. Defining the product of sample density, the reciprocal of the average distance between the samples in the cluster, and the distance between the clusters as weight product, the initial center is determined successively according to the maximum weight product method and the accuracy of the clustering is improved. Then, the parallelization of improved K-means algorithm based on MapReduce model is realized and the efficiency of clustering is improved. Finally, the mining experiment of massive power utilization data is carried out on basis of 400 households' electricity data. Taking family as unit, calculate such features as electricity consumption rate during peak hour, load rate, valley load coefficient and the percentage of power using during normal hour, and establish the data vector dimension, completing the clustering of similar user types, while analyzing the behavioral characteristics of each types of users. Experiment results on Hadoop cluster show that the improved algorithm can be stable and efficient operated and it can achieve better clustering effect.

In China, Hangzhou is the first city to set up the Public Bicycle System. Now, the System has been the largest bike- sharing program in the world. The software of Hangzhou Public Bicycle System was developed by our team. There are many and many technology problems in the decision of intelligent dispatch. Among of these problems, determining how to find the key stations to give special care is very important. In this paper, a improved k-means algorithm is used to recognize the key stations of Hangzhou Public Bicycle System. At first, by passing over the two week’s real data, a rent-return database is initialed. Then the algorithm builds minimum spanning tree and splits it to gets k initial cluster centers. The key stations are determined from the rent-return database by the algorithm. Practice examples and comparison with the traditional k-means algorithm are made. The results show that the proposed algorithm is efficient and robust. The research result has been applied in Hangzhou.

Adding spatial penalty to fuzzy C-means (FCM) model is an important way to reduce the influence of noise in image segmentation. However, these improved algorithms easily cause segmentation failures when the image has the characteristics of unequal cluster sizes. Besides, they often fall into local optimal solutions if the initial cluster centers are improper. This paper presents a noise robust hybrid algorithm for segmenting image with unequal cluster sizes based on chaotic crow search algorithm and improved fuzzy c-means to overcome the above defects. Firstly, each size of clusters is integrated into the objective function of noise detecting fuzzy c-means algorithm (NDFCM), which can reduces the contribution of larger clusters to objective function and then the new membership degree and cluster centers are deduced. Secondly, a new expression called compactness, representing the pixel distribution of each cluster, is introduced into the iteration process of clustering. Thirdly, we use two- paths to seek the optimal solutions in each step of iteration: one path is produced by the chaotic crow search algorithm and the other is originated by gradient method. Furthermore, the better solutions of the two-paths go to next generation until the end of the iteration. Finally, the experiments on the synthetic and non–destructive testing (NDT) images show that the proposed algorithm behaves well in noise robustness and segmentation performance.

By analyzing the problem of k-means, we find the traditional k-means algorithm suffers from some shortcomings, such as requiring the user to give out the number of clusters k in advance, being sensitive to the initial cluster centers, being sensitive to the noise and isolated data, only being applied to the type found in globular clusters, and being easily trapped into a local solution et cetera. This improved algorithm uses the potential of data to find the center data and eliminate the noise data. It decomposes big or extended cluster into several small clusters, then merges adjacent small clusters into a big cluster using the information provided by the Safety Area. Experimental results demonstrate that the improved k-means algorithm can determine the number of clusters, distinguish irregular cluster to a certain extent, decrease the dependence on the initial cluster centers, eliminate the effects of the noise data and get a better clustering accuracy.

The K-means algorithm is one of the widely used clustering algorithms in the image classification systems. However, the K-Means algorithm is easily trapped into the local optimal solutions. Several optimization techniques have been proposed to solve this problem such as genetic algorithms, simulated annealing and swarm intelligence. In this paper, we develop hybrid techniques using different particle swarm optimization (PSO) heuristics to optimize the k-means algorithm and examine the reliability of parametric values for different variants of PSO and k-means algorithms. These PSO heuristics include linear inertia reduction, constriction factor, and dynamic inertia and maximum velocity reduction. The performance of these hybridization of PSO and the k-means algorithms was tested on the image segmentation. These PSO heuristics can make the K-means algorithm more stable for finding better solutions and less dependent on the initial cluster centers based on the preliminary experimental results.

K-means algorithm is one of the most popular algorithms for data clustering. With this algorithm, data of similar types are tried to be clustered together from a large data set with brute force strategy which is done by repeated calculations. As a result, the computational complexity of this algorithm is very high. Several researches have been carried out to minimize this complexity. This paper presents the result of our research, which proposes a modified version of k-means algorithm with an improved technique to divide the data set into specific numbers of clusters with the help of several check point values. It requires less computation and has enhanced accuracy than the traditional k-means algorithm as well as some modified variant of the traditional kMeans.

In order to deeply mine the behavior characteristics of power demand-side users and strengthen the accurate interaction between source, grid and load, it is of great significance to identify and analyze load patterns based on massive user load data. In order to solve the problem that the traditional k-means algorithm is sensitive to the initial clustering center and it is difficult to quantify the number of clusters, this paper uses the improved K-means clustering algorithm to cluster the massive user load data. In the data preprocessing stage, t-SNE dimension reduction technology is introduced, and then the GSA-elbow judgment is used to determine the number of clusters. The Huffman tree is constructed based on the density characteristics and dissimilarity attributes of the data to obtain the initial clustering center and obtain the stable clustering result. Based on load clustering, this paper uses SVM classifier for load pattern recognition to extract user load features, and realizes the pattern recognition of unknown user load data.