Selecting the right MBA schools – An application of self-organizing map networks

The self-organizing map (SOM) network, an unsupervised neural computing network, is a categorization network developed by Kohonen. The SOM network was designed for solving problems that involve tasks such as clustering, visualization, and abstraction. In this study, we apply the clustering and visualization capabilities of SOM to group and plot the top 79 MBA schools as ranked by US News and World Report (USN&WR) into a two-dimensional map with four segments. The map should assist prospective students in searching for the MBA programs that best meet their personal requirements. Comparative analysis with the outputs from two popular clustering techniques K-means analysis and a two-step Factor analysis/K-means procedure are also included.     

Quantum annealing for combinatorial clustering

Clustering is a powerful machine learning technique that groups “similar” data points based on their characteristics. Many clustering algorithms work by approximating the minimization of an objective function, namely the sum of within-the-cluster distances between points. The straightforward approach involves examining all the possible assignments of points to each of the clusters. This approach guarantees the solution will be a global minimum; however, the number of possible assignments scales quickly with the number of data points and becomes computationally intractable even for very small datasets. In order to circumvent this issue, cost function minima are found using popular local search-based heuristic approaches such as k-means and hierarchical clustering. Due to their greedy nature, such techniques do not guarantee that a global minimum will be found and can lead to sub-optimal clustering assignments. Other classes of global search-based techniques, such as simulated annealing, tabu search, and genetic algorithms, may offer better quality results but can be too time-consuming to implement. In this work, we describe how quantum annealing can be used to carry out clustering. We map the clustering objective to a quadratic binary optimization problem and discuss two clustering algorithms which are then implemented on commercially available quantum annealing hardware, as well as on a purely classical solver “qbsolv.” The first algorithm assigns N data points to K clusters, and the second one can be used to perform binary clustering in a hierarchical manner. We present our results in the form of benchmarks against well-known k-means clustering and discuss the advantages and disadvantages of the proposed techniques.     

Harmony K-means algorithm for document clustering

Fast and high quality document clustering is a crucial task in organizing information, search engine results, enhancing web crawling, and information retrieval or filtering. Recent studies have shown that the most commonly used partition-based clustering algorithm, the K-means algorithm, is more suitable for large datasets. However, the K-means algorithm can generate a local optimal solution. In this paper we propose a novel Harmony K-means Algorithm (HKA) that deals with document clustering based on Harmony Search (HS) optimization method. It is proved by means of finite Markov chain theory that the HKA converges to the global optimum. To demonstrate the effectiveness and speed of HKA, we have applied HKA algorithms on some standard datasets. We also compare the HKA with other meta-heuristic and model-based document clustering approaches. Experimental results reveal that the HKA algorithm converges to the best known optimum faster than other methods and the quality of clusters are comparable.     

An effective web document clustering algorithm based on bisection and merge

To cluster web documents, all of which have the same name entities, we attempted to use existing clustering algorithms such as K-means and spectral clustering. Unexpectedly, it turned out that these algorithms are not effective to cluster web documents. According to our intensive investigation, we found that clustering such web pages is more complicated because (1) the number of clusters (known as ground truth) is larger than two or three clusters as in general clustering problems and (2) clusters in the data set have extremely skewed distributions of cluster sizes. To overcome the aforementioned problem, in this paper, we propose an effective clustering algorithm to boost up the accuracy of K-means and spectral clustering algorithms. In particular, to deal with skewed distributions of cluster sizes, our algorithm performs both bisection and merge steps based on normalized cuts of the similarity graph G to correctly cluster web documents. Our experimental results show that our algorithm improves the performance by approximately 56% compared to spectral bisection and 36% compared to K-means.     

A two-leveled symbiotic evolutionary algorithm for clustering problems

Because of its unsupervised nature, clustering is one of the most challenging problems, considered as a NP-hard grouping problem. Recently, several evolutionary algorithms (EAs) for clustering problems have been presented because of their efficiency for solving the NP-hard problems with high degree of complexity. Most previous EA-based algorithms, however, have dealt with the clustering problems given the number of clusters (K) in advance. Although some researchers have suggested the EA-based algorithms for unknown K clustering, they still have some drawbacks to search efficiently due to their huge search space. This paper proposes the two-leveled symbiotic evolutionary clustering algorithm (TSECA), which is a variant of coevolutionary algorithm for unknown K clustering problems. The clustering problems considered in this paper can be divided into two sub-problems: finding the number of clusters and grouping the data into these clusters. The two-leveled framework of TSECA and genetic elements suitable for each sub-problem are proposed. In addition, a neighborhood-based evolutionary strategy is employed to maintain the population diversity. The performance of the proposed algorithm is compared with some popular evolutionary algorithms using the real-life and simulated synthetic data sets. Experimental results show that TSECA produces more compact clusters as well as the accurate number of clusters.     

Interval Set Clustering of Web Users with Rough K-Means

Data collection and analysis in web mining faces certain unique challenges. Due to a variety of reasons inherent in web browsing and web logging, the likelihood of bad or incomplete data is higher than conventional applications. The analytical techniques in web mining need to accommodate such data. Fuzzy and rough sets provide the ability to deal with incomplete and approximate information. Fuzzy set theory has been shown to be useful in three important aspects of web and data mining, namely clustering, association, and sequential analysis. There is increasing interest in research on clustering based on rough set theory. Clustering is an important part of web mining that involves finding natural groupings of web resources or web users. Researchers have pointed out some important differences between clustering in conventional applications and clustering in web mining. For example, the clusters and associations in web mining do not necessarily have crisp boundaries. As a result, researchers have studied the possibility of using fuzzy sets in web mining clustering applications. Recent attempts have used genetic algorithms based on rough set theory for clustering. However, the genetic algorithms based clustering may not be able to handle the large amount of data typical in a web mining application. This paper proposes a variation of the K-means clustering algorithm based on properties of rough sets. The proposed algorithm represents clusters as interval or rough sets. The paper also describes the design of an experiment including data collection and the clustering process. The experiment is used to create interval set representations of clusters of web visitors.     

Weighted adjacent matrix for K-means clustering

K-means clustering is one of the most popular clustering algorithms and has been embedded in other clustering algorithms, e.g. the last step of spectral clustering. In this paper, we propose two techniques to improve previous k-means clustering algorithm by designing two different adjacent matrices. Extensive experiments on public UCI datasets showed the clustering results of our proposed algorithms significantly outperform three classical clustering algorithms in terms of different evaluation metrics.

     

A clustering method combining differential evolution with the K-means algorithm

The present paper considers the problem of partitioning a dataset into a known number of clusters using the sum of squared errors criterion (SSE). A new clustering method, called DE-KM, which combines differential evolution algorithm (DE) with the well known K-means procedure is described. In the method, the K-means algorithm is used to fine-tune each candidate solution obtained by mutation and crossover operators of DE. Additionally, a reordering procedure which allows the evolutionary algorithm to tackle the redundant representation problem is proposed. The performance of the DE-KM clustering method is compared to the performance of differential evolution, global K-means method, genetic K-means algorithm and two variants of the K-means algorithm. The experimental results show that if the number of clusters K is sufficiently large, DE-KM obtains solutions with lower SSE values than the other five algorithms.     

An efficient hybrid approach based on PSO, ACO and k-means for cluster analysis

Clustering is a popular data analysis and data mining technique. A popular technique for clustering is based on k-means such that the data is partitioned into K clusters. However, the k-means algorithm highly depends on the initial state and converges to local optimum solution. This paper presents a new hybrid evolutionary algorithm to solve nonlinear partitional clustering problem. The proposed hybrid evolutionary algorithm is the combination of FAPSO (fuzzy adaptive particle swarm optimization), ACO (ant colony optimization) and k-means algorithms, called FAPSO-ACO–K, which can find better cluster partition. The performance of the proposed algorithm is evaluated through several benchmark data sets. The simulation results show that the performance of the proposed algorithm is better than other algorithms such as PSO, ACO, simulated annealing (SA), combination of PSO and SA (PSO–SA), combination of ACO and SA (ACO–SA), combination of PSO and ACO (PSO–ACO), genetic algorithm (GA), Tabu search (TS), honey bee mating optimization (HBMO) and k-means for partitional clustering problem.     

A hierarchical evolutionary algorithm for automatic medical image segmentation

Image segmentation denotes a process of partitioning an image into distinct regions. A large variety of different segmentation approaches for images have been developed. Among them, the clustering methods have been extensively investigated and used. In this paper, a clustering based approach using a hierarchical evolutionary algorithm (HEA) is proposed for medical image segmentation. The HEA can be viewed as a variant of conventional genetic algorithms. By means of a hierarchical structure in the chromosome, the proposed approach can automatically classify the image into appropriate classes and avoid the difficulty of searching for the proper number of classes. The experimental results indicate that the proposed approach can produce more continuous and smoother segmentation results in comparison with four existing methods, competitive Hopfield neural networks (CHNN), dynamic thresholding, k-means, and fuzzy c-means methods.     

一种半监督K均值多关系数据聚类算法

提出了一种半监督K均值多关系数据聚类算法.该算法在K均值聚类算法的基础上扩展了其初始类簇的选择方法和对象相似性度量方法,以用于多关系数据的半监督学习.为了获取高性能,该算法在聚类过程中充分利用了标记数据、对象属性及各种关系信息.多关系数据库Movie上的实验结果验证了该算法的有效性.     

Clustering properties of hierarchical self-organizing maps

A multilayer hierarchical self-organizing map (HSOM) is discussed as an unsupervised clustering method. The HSOM is shown to form arbitrarily complex clusters, in analogy with multilayer feedforward networks. In addition, the HSOM provides a natural measure for the distance of a point from a cluster that weighs all the points belonging to the cluster appropriately. In experiments with both artificial and real data it is demonstrated that the multilayer SOM forms clusters that match better to the desired classes than do direct SOM's, classical k-means, or Isodata algorithms.     

Clustering for malware classification

In this research, we apply clustering techniques to the malware classification problem. We compute clusters using the well-known K-means and Expectation Maximization algorithms, with the underlying scores based on Hidden Markov Models. We compare the results obtained from these two clustering approaches and we carefully consider the interplay between the dimension (i.e., number of models used for clustering), and the number of clusters, with respect to the accuracy of the clustering.     

GAKREM: A novel hybrid clustering algorithm

We introduce a novel clustering algorithm named GAKREM (Genetic Algorithm K-means Logarithmic Regression Expectation Maximization) that combines the best characteristics of the K-means and EM algorithms but avoids their weaknesses such as the need to specify a priori the number of clusters, termination in local optima, and lengthy computations. To achieve these goals, genetic algorithms for estimating parameters and initializing starting points for the EM are used first. Second, the log-likelihood of each configuration of parameters and the number of clusters resulting from the EM is used as the fitness value for each chromosome in the population. The novelty of GAKREM is that in each evolving generation it efficiently approximates the log-likelihood for each chromosome using logarithmic regression instead of running the conventional EM algorithm until its convergence. Another novelty is the use of K-means to initially assign data points to clusters. The algorithm is evaluated by comparing its performance with the conventional EM algorithm, the K-means algorithm, and the likelihood cross-validation technique on several datasets.     

A New Line Symmetry Distance and Its Application to Data Clustering

In this paper,at first a new line-symmetry-based distance is proposed.The properties of the proposed distance are then elaborately described.Kd-tree-based nearest neighbor search is used to reduce the complexity of computing the proposed line-symmetry-based distance.Thereafter an evolutionary clustering technique is developed that uses the new linesymmetry -based distance measure for assigning points to different clusters.Adaptive mutation and crossover probabilities are used to accelerate the proposed c...     

基于熵加权K-means全局信息聚类的高光谱图像分类

目的 高光谱图像波段数目巨大，导致在解译及分类过程中出现“维数灾难”的现象。针对该问题，在K-means聚类算法基础上，考虑各个波段对不同聚类的重要程度，同时顾及类间信息，提出一种基于熵加权K-means全局信息聚类的高光谱图像分类算法。方法 首先，引入波段权重，用来刻画各个波段对不同聚类的重要程度，并定义熵信息测度表达该权重。其次，为避免局部最优聚类，引入类间距离测度实现全局最优聚类。最后，将上述两类测度引入K-means聚类目标函数，通过最小化目标函数得到最优分类结果。结果 为了验证提出的高光谱图像分类方法的有效性，对Salinas高光谱图像和Pavia University高光谱图像标准图中的地物类别根据其光谱反射率差异程度进行合并，将合并后的标准图作为新的标准分类图。分别采用本文算法和传统K-means算法对Salinas高光谱图像和Pavia University高光谱图像进行实验，并定性、定量地评价和分析了实验结果。对于图像中合并后的地物类别，光谱反射率差异程度大，从视觉上看，本文算法较传统K-means算法有更好的分类结果；从分类精度看，本文算法的总精度分别为92.20%和82.96%， K-means算法的总精度分别为83.39%和67.06%，较K-means算法增长8.81%和15.9%。结论 提出一种基于熵加权K-means全局信息聚类的高光谱图像分类算法，实验结果表明，本文算法对高光谱图像中具有不同光谱反射率差异程度的各类地物目标均能取得很好的分类结果。     

A genetic algorithm approach to cluster analysis

A common problem in the social and agricultural sciences is to find clusters in experimental data; the standard attack is a deterministic search terminating in a locally optimal clustering. We propose here a genetic algorithm (GA) for performing cluster analysis. GAs have been used profitably in a variety of contexts in which it is either impractical or impossible to directly solve for a globally optimal solution to complex numerical problems. In the present case, our GA clustering technique attempted to maximize a variance-ratio (VR) based goodness-of-fit criterion defined in terms of external cluster isolation and internal cluster homogeneity. Although our GA-based clustering algorithm cannot guarantee to recover the cluster solution that exhibits the global maximum of this fitness function, it does explicitly work toward this goal (in marked contrast to existing clustering algorithms, especially hierarchical agglomerative ones such as Ward's method). Using both constrained and unconstrained simulated datasets, Monte Carlo results showed that in some conditions the genetic clustering algorithm did indeed surpass the performance of conventional clustering techniques (Ward's and K-means) in terms of an internal (VR) criterion. Suggestions for future refinement and study are offered.     

A survey of kernel and spectral methods for clustering

Clustering algorithms are a useful tool to explore data structures and have been employed in many disciplines. The focus of this paper is the partitioning clustering problem with a special interest in two recent approaches: kernel and spectral methods. The aim of this paper is to present a survey of kernel and spectral clustering methods, two approaches able to produce nonlinear separating hypersurfaces between clusters. The presented kernel clustering methods are the kernel version of many classical clustering algorithms, e.g., K-means, SOM and neural gas. Spectral clustering arise from concepts in spectral graph theory and the clustering problem is configured as a graph cut problem where an appropriate objective function has to be optimized. An explicit proof of the fact that these two paradigms have the same objective is reported since it has been proven that these two seemingly different approaches have the same mathematical foundation. Besides, fuzzy kernel clustering methods are presented as extensions of kernel K-means clustering algorithm.     

Classification System for Serial Criminal Patterns

The data mining field in computer science specializes in extracting implicit information that is distributed across the stored data records and/or exists as associations among groups of records. Criminal databases contain information on the crimes themselves, the offenders, the victims as well as the vehicles that were involved in the crime. Among these records lie groups of crimes that can be attributed to serial criminals who are responsible for multiple criminal offenses and usually exhibit patterns in their operations, by specializing in a particular crime category (i.e., rape, murder, robbery, etc.), and applying a specific method for implementing their crimes. Discovering serial criminal patterns in crime databases is, in general, a clustering activity in the area of data mining that is concerned with detecting trends in the data by classifying and grouping similar records. In this paper, we report on the different statistical and neural network approaches to the clustering problem in data mining in general, and as it applies to our crime domain in particular. We discuss our approach of using a cascaded network of Kohonen neural networks followed by heuristic processing of the networks outputs that best simulated the experts in the field. We address the issues in this project and the reasoning behind this approach, including: the choice of neural networks, in general, over statistical algorithms as the main tool, and the use of Kohonen networks in particular, the choice for the cascaded approach instead of the direct approach, and the choice of a heuristics subsystem as a back-end subsystem to the neural networks. We also report on the advantages of this approach over both the traditional approach of using a single neural network to accommodate all the attributes, and that of applying a single clustering algorithm on all the data attributes.     

Text document clustering based on neighbors

Clustering is a very powerful data mining technique for topic discovery from text documents. The partitional clustering algorithms, such as the family of k-means, are reported performing well on document clustering. They treat the clustering problem as an optimization process of grouping documents into k clusters so that a particular criterion function is minimized or maximized. Usually, the cosine function is used to measure the similarity between two documents in the criterion function, but it may not work well when the clusters are not well separated. To solve this problem, we applied the concepts of neighbors and link, introduced in [S. Guha, R. Rastogi, K. Shim, ROCK: a robust clustering algorithm for categorical attributes, Information Systems 25 (5) (2000) 345–366], to document clustering. If two documents are similar enough, they are considered as neighbors of each other. And the link between two documents represents the number of their common neighbors. Instead of just considering the pairwise similarity, the neighbors and link involve the global information into the measurement of the closeness of two documents. In this paper, we propose to use the neighbors and link for the family of k-means algorithms in three aspects: a new method to select initial cluster centroids based on the ranks of candidate documents; a new similarity measure which uses a combination of the cosine and link functions; and a new heuristic function for selecting a cluster to split based on the neighbors of the cluster centroids. Our experimental results on real-life data sets demonstrated that our proposed methods can significantly improve the performance of document clustering in terms of accuracy without increasing the execution time much.