Average Silhouette Coefficient Research Articles

A Novel Ensemble Framework Based on K-Means and Resampling for Imbalanced Data

Imbalanced classification is one of the most important problems of machine learning and data mining, existing in many real datasets. In the past, many basic classifiers such as SVM, KNN, and so on have been used for imbalanced datasets in which the number of one sample is larger than that of another, but the classification effect is not ideal. Some data preprocessing methods have been proposed to reduce the imbalance ratio of data sets and combine with the basic classifiers to get better performance. In order to improve the whole classification accuracy, we propose a novel classifier ensemble framework based on K-means and resampling technique (EKR). First, we divide the data samples in the majority class into several sub-clusters using K-means, k-value is determined by Average Silhouette Coefficient, and then adjust the number of data samples of each sub-cluster to be the same as that of the minority classes through resampling technology, after that each adjusted sub-cluster and the minority class are combined into several balanced subsets, the base classifier is trained on each balanced subset separately, and finally integrated into a strong ensemble classifier. In this paper, the extensive experimental results on 16 imbalanced datasets demonstrate the effectiveness and feasibility of the proposed algorithm in terms of multiple evaluation criteria, and EKR can achieve better performance when compared with several classical imbalanced classification algorithms using different data preprocessing methods.

A novel variant of social spider optimization using single centroid representation and enhanced mating for data clustering.

Nature-inspired algorithms are based on the concepts of self-organization and complex biological systems. They have been designed by researchers and scientists to solve complex problems in various environmental situations by observing how naturally occurring phenomena behave. The introduction of nature-inspired algorithms has led to new branches of study such as neural networks, swarm intelligence, evolutionary computation, and artificial immune systems. Particle swarm optimization (PSO), social spider optimization (SSO), and other nature-inspired algorithms have found some success in solving clustering problems but they may converge to local optima due to the lack of balance between exploration and exploitation. In this paper, we propose a novel implementation of SSO, namely social spider optimization for data clustering using single centroid representation and enhanced mating operation (SSODCSC) in order to improve the balance between exploration and exploitation. In SSODCSC, we implemented each spider as a collection of a centroid and the data instances close to it. We allowed non-dominant male spiders to mate with female spiders by converting them into dominant males. We found that SSODCSC produces better values for the sum of intra-cluster distances, the average CPU time per iteration (in seconds), accuracy, the F-measure, and the average silhouette coefficient as compared with the K-means and other nature-inspired techniques. When the proposed algorithm is compared with other nature-inspired algorithms with respect to Patent corpus datasets, the overall percentage increase in the accuracy is approximately 13%. When it is compared with other nature-inspired algorithms with respect to UCI datasets, the overall percentage increase in the F-measure value is approximately 10%. For completeness, the best K cluster centroids (the best K spiders) returned by SSODCSC were specified. To show the significance of the proposed algorithm, we conducted a one-way ANOVA test on the accuracy values and the F-measure values returned by the clustering algorithms.

Classification of Collegiate Athletes Based on Their Injury History

Sports-related injuries can have a significant impact on an athlete’s performance and career. While some injuries are inevitable, many can be prevented. Cluster analysis is a useful statistical technique that can assign individuals into groups (i.e., latent subgroups) based on common characteristics. PURPOSE: To utilize cluster analysis to 1) identify the latent subgroups based on athletes’ injury history; and 2) examine the characteristics of latent subgroups among athletes. METHODS: A total of 1,538 college athletes competing in the South Eastern Conference in NCAA division I were segmented by three criteria; 1) Injury parts indicate the body part sustaining the injury, 2) Injury types describe the detail of their injury status such as strain, contusion or tendonitis. 3) Injury duration refers to how long the athlete was unable to participate in training. K-means clustering analysis with the Euclidean similarity of injury log vectors was conducted to label players. The number of groups(k) was determined by applying the average silhouette method. The characteristics of clusters were analyzed descriptively, and the sports were allocated to each group followed by the athlete clusters. RESULTS: Five clusters were identified by the maximum average silhouette coefficient (0.153) among coefficients for randomly drawn k’s between 2 to 20. The first group, mainly baseball, men’s basketball, and men’s tennis, had injury to their ankle, arm, and hamstring for contusion and strain for a few weeks. The second group was mostly from football, with injury to their ankle, knee, and shoulder with the most extended injury durations. The third group, mostly football or track and field, were the athletes likely to have knee inflammation, and the duration was nearly half of a year. The injured body parts of the fourth group were back, finger, and hamstring, and the types of injuries were fracture and tendonitis. This cluster was mainly women’s basketball and track and field athletes. The members of the last group had head injury (e.g., concussion), and were soccer, softball or volleyball athletes. CONCLUSION: This study may help practitioners in recognizing the likelihood of an athletes’ injury according to their sport. Additionally, coaches could also consider this information in daily practices.

Blind Estimation PN Sequence in Soft Spread Spectrum Signal of Improved K-means Algorithm

For the problem of the soft spread spectrum signal Pseudo-Noise (PN) sequence is difficult to estimate by using the coding technology, a blind estimation PN sequence method of soft spread spectrum signal is proposed based on improved K-means algorithm. Firstly, the received signal is divided into continuous non-overlapping temporal vectors according to one period of PN sequence to construct observation data matrix. Secondly, the similarity measure theory is applied to find out the optimal initial clustering center point of K-means algorithm from the observed matrix. Then the number of scale of PN sequence can be estimated by searching for the maximum absolute value of the average Silhouette Coefficient (SC). Finally, the estimated clustering center point corresponding to the number of scale of PN sequence is found, the blind estimation PN sequence of the soft spread spectrum signal is further completed. The simulation results show that the proposed method improves the Signal-to-Noise Ratio (SNR) about 4 dB compared to the traditional method under the condition of the estimation error probability of PN sequence is less than 0.1. Moreover, the blind dispreading performance is also better than unmodified method under the same condition.

Application of k-means clustering to environmental risk zoning of the chemical industrial area

The homogeneous risk characteristics within a sub-area and the heterogeneous from one sub-area to another are unclear using existing environmental risk zoning methods. This study presents a new zoning method by determining and categorizing the risk characteristics using the k-means clustering data mining technology. The study constructs indices and develops index quantification models for environmental risk zoning by analyzing the mechanism of environmental risk occurrence. We calculate the source risk index, air risk field index, water risk field index, and target vulnerability of the study area with Nanjing Chemical Industrial Park using a 100 m × 100 m mesh grid as the basic zoning unit, and then use k-means clustering to analyze the environmental risk in the area. We obtain the optimal clustering number with the largest average silhouette coefficient by calculating the average silhouette coefficients of clustering at different k-values. The clustering result with the optimal clustering number is then used for the environmental risk zoning, and the zoning result is mapped using the geographic information system. The study area is divided into five sub-areas. The common environmental risk characteristics within the same sub-area, as well as the differences between subareas, are presented. The zoning is helpful in risk management and is convenient for decision makers to distribute limited resources to different sub-areas in the design of risk reducing intervention.

A FAST k-MEANS IMPLEMENTATION USING CORESETS

In this paper we develop an efficient implementation for a k-means clustering algorithm. The algorithm is based on a combination of Lloyd's algorithm with random swapping of centers to avoid local minima. This approach was proposed by Mount 30. The novel feature of our algorithms is the use of coresets to speed up the algorithm. A coreset is a small weighted set of points that approximates the original point set with respect to the considered problem. We use a coreset construction described in 12. Our algorithm first computes a solution on a very small coreset. Then in each iteration the previous solution is used as a starting solution on a refined, i.e. larger, coreset. To evaluate the performance of our algorithm we compare it with algorithm KMHybrid 30 on typical 3D data sets for an image compression application and on artificially created instances. Our data sets consist of 300,000 to 4.9 million points. Our algorithm outperforms KMHybrid on most of these input instances. Additionally, the quality of the solutions computed by our algorithm deviates significantly less than that of KMHybrid. We conclude that the use of coresets has two effects. First, it can speed up algorithms significantly. Secondly, in variants of Lloyd's algorithm, it reduces the dependency on the starting solution and thus makes the algorithm more stable. Finally, we propose the use of coresets as a heuristic to approximate the average silhouette coefficient of clusterings. The average silhouette coefficient is a measure for the quality of a clustering that is independent of the number of clusters k. Hence, it can be used to compare the quality of clusterings for different sizes of k. To show the applicability of our approach we computed clusterings and approximate average silhouette coefficient for k = 1,…, 100 for our input instances and discuss the performance of our algorithm in detail.