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Clustering is the process of partitioning elements into a number of groups clusters such that elements in the same cluster are more similar than elements in different clusters. Clustering has been applied in a wide variety of fields, ranging from medical sciences, economics, computer sciences, engineering, social sciences, to earth sciences [1,2], reflecting its important role in scientific research. With several hundred clustering methods in existence [3], there is clearly no shortage of clustering algorithms but, at the same time, satisfactory answers to some basic questions are still to come.

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Breast Cancer Recognition Using a Novel Hybrid Intelligent Method

To browse Academia. Skip to main content. By using our site, you agree to our collection of information through the use of cookies. To learn more, view our Privacy Policy. Log In Sign Up. Download Free PDF. Patrick Flynn. Download PDF. A short summary of this paper. Data clustering: a review. Data Clustering: A Review A. The clustering problem has been addressed in many contexts and by researchers in many disciplines; this reflects its broad appeal and usefulness as one of the steps in exploratory data analysis.

However, clustering is a difficult problem combinatorially, and differences in assumptions and contexts in different communities has made the transfer of useful generic concepts and methodologies slow to occur.

This paper presents an overview of pattern clustering methods from a statistical pattern recognition perspective, with a goal of providing useful advice and references to fundamental concepts accessible to the broad community of clustering practitioners. We present a taxonomy of clustering techniques, and identify cross-cutting themes and recent advances. We also describe some important applications of clustering algorithms such as image segmentation, object recognition, and information retrieval.

Categories and Subject Descriptors: I. Jain and P. Bowyer and N. Ahuja, Eds. Introduction 1. An example of cluster- 1. The input 1. Definitions and Notation the desired clusters are shown in Figure 3. Pattern Representation, Feature Selection and 1 b. Here, points belonging to the same Extraction cluster are given the same label. The 4. Similarity Measures variety of techniques for representing 5. Clustering Techniques data, measuring proximity similarity 5.

Applications label a newly encountered, yet unla- 6. Typically, the given la- 6. Summary in turn are used to label a new pattern. In the case of clustering, the problem is to group a given collection of unlabeled patterns into meaningful clusters.

Data analysis underlies many comput- Clustering is useful in several explor- ing applications, either in a design atory pattern-analysis, grouping, deci- phase or as part of their on-line opera- sion-making, and machine-learning sit- tions.

Data analysis procedures can be uations, including data mining, dichotomized as either exploratory or document retrieval, image segmenta- confirmatory, based on the availability tion, and pattern classification. How- of appropriate models for the data ever, in many such problems, there is source, but a key element in both types little prior information e. Cluster analysis is the organi- lationships among the data points to zation of a collection of patterns usual- make an assessment perhaps prelimi- ly represented as a vector of measure- nary of their structure.

Jain et al. Data clustering. Thus, we face a dilemma regard- 1. The produc- tion of a truly comprehensive survey Typical pattern clustering activity in- would be a monumental task given the volves the following steps [Jain and sheer mass of literature in this area. Where appropriate, references will be 4 data abstraction if needed , and made to key concepts and techniques 5 assessment of output if needed. Some of this infor- broader audience of scientific profes- mation may not be controllable by the ACM Computing Surveys, Vol.

Stages in clustering. Feature selection is the Data abstraction is the process of ex- process of identifying the most effective tracting a simple and compact represen- subset of the original features to use in tation of a data set.

Here, simplicity is clustering. Feature extraction is the use either from the perspective of automatic of one or more transformations of the analysis so that a machine can perform input features to produce new salient further processing efficiently or it is features. Either or both of these tech- human-oriented so that the representa- niques can be used to obtain an appro- tion obtained is easy to comprehend and priate set of features to use in cluster- intuitively appealing. In the clustering ing.

A variety of distance mea- representative patterns such as the cen- sures are in use in the various commu- troid [Diday and Simon ]. A simple rithm evaluated? If the data does contain similarity between patterns [Michalski clusters, some clustering algorithms and Stepp ].

The output clus- One is actually an assessment of the tering or clusterings can be hard a data domain rather than the clustering partition of the data into groups or algorithm itself— data which do not fuzzy where each pattern has a vari- contain clusters should not be processed able degree of membership in each of by a clustering algorithm.

The study of the output clusters. Hierarchical clus- cluster tendency, wherein the input data tering algorithms produce a nested se- are examined to see if there is any merit ries of partitions based on a criterion for to a cluster analysis prior to one being merging or splitting clusters based on performed, is a relatively inactive re- similarity.

Partitional clustering algo- search area, and will not be considered rithms identify the partition that opti- further in this survey. The interested mizes usually locally a clustering cri- reader is referred to Dubes [] and terion.

Additional techniques for the Cheng [] for information. Often this analysis uses a variety of techniques for cluster forma- specific criterion of optimality; however, tion is described in Section 5.

Va- ciently? A vey, and its aim is to provide a perspec- clustering structure is valid if it cannot tive on the state of the art in clustering reasonably have occurred by chance or methodology and algorithms. With such as an artifact of a clustering algorithm. There are on a technique or suite of techniques to three types of validation studies.

An employ in a particular application. An internal examina- the variety of structures present in mul- tion of validity tries to determine if the tidimensional data sets. For example, structure is intrinsically appropriate for consider the two-dimensional data set the data.

A relative test compares two shown in Figure 1 a. Not all clustering structures and measures their relative techniques can uncover all the clusters merit. Indices used for this comparison present here with equal facility, because are discussed in detail in Jain and clustering algorithms often contain im- Dubes [] and Dubes [], and are plicit assumptions about cluster shape not discussed further in this paper. Expertise Humans perform competitively with automatic clustering procedures in two The availability of such a vast collection dimensions, but most real problems in- of clustering algorithms in the litera- volve clustering in higher dimensions.

It ture can easily confound a user attempt- is difficult for humans to obtain an intu- ing to select an algorithm suitable for itive interpretation of data embedded in the problem at hand. In Dubes and Jain a high-dimensional space. This explains the large num- rithms. These admissibility criteria are ber of clustering algorithms which con- based on: 1 the manner in which clus- tinue to appear in the literature; each ters are formed, 2 the structure of the new clustering algorithm performs data, and 3 sensitivity of the cluster- slightly better than the existing ones on ing technique to changes that do not a specific distribution of patterns.

How- It is essential for the user of a cluster- ever, there is no critical analysis of clus- ing algorithm to not only have a thor- tering algorithms dealing with the im- ough understanding of the particular portant questions such as technique being utilized, but also to —How should the data be normalized?

A comparison of vari- resentation [Murty and Jain ]. One example of this is []. Cluster analysis was also sur- mixture resolving [Titterington et al. A review of ], wherein it is assumed that the image segmentation by clustering was data are drawn from a mixture of an reported in Jain and Flynn [].

Com- unknown number of densities often as- parisons of various combinatorial opti- sumed to be multivariate Gaussian. Khan []. The concept of density clustering and a methodology for decomposition of fea- ture spaces [Bajcsy ] have also 1. Sec- tering methodology, yielding a tech- tion 2 presents definitions of terms to be nique for extracting overlapping clus- used throughout the paper.

Section 3 ters. Various approaches to the compu- tation of proximity between patterns Even though there is an increasing in- are discussed in Section 4. Section 5 terest in the use of clustering methods presents a taxonomy of clustering ap- in pattern recognition [Anderberg proaches, describes the major tech- ], image processing [Jain and niques in use, and discusses emerging Flynn ] and information retrieval techniques for clustering incorporating [Rasmussen ; Salton ], cluster- non-numeric constraints and the clus- ing has a rich history in other disci- tering of large sets of patterns.

Section plines [Jain and Dubes ] such as 6 discusses applications of clustering biology, psychiatry, psychology, archae- methods to image analysis and data ology, geology, geography, and market- mining problems. Finally, Section 7 pre- ing. Other terms more or less synony- sents some concluding remarks. The used throughout this paper. The importance and tion, or datum x is a single data item interdisciplinary nature of clustering is used by the clustering algorithm.

It evident through its vast literature. Anderberg ; Hartigan ; Spath ; Duran and Odell ; Everitt —The individual scalar components x i ; Backer ], in addition to some of a pattern x are called features or useful and influential review papers. A attributes. Because of the diffi- or of the pattern space. The i th pattern in - is to clustering.

In many vestigation of the available features and cases a pattern set to be clustered is any available transformations even simple ones can yield significantly im- viewed as an n 3 d pattern matrix. A good pat- —A class, in the abstract, refers to a tern representation can often yield a state of nature that governs the pat- simple and easily understood clustering; tern generation process in some cases. The a probability density specific to the points in this 2D feature space are ar- class.

Unsupervised Learning and Clustering

The fuzzy clustering algorithm has been widely used in the research area and production and life. However, the conventional fuzzy algorithms have a disadvantage of high computational complexity. This article proposes an improved fuzzy C-means FCM algorithm based on K-means and principle of granularity. This algorithm is aiming at solving the problems of optimal number of clusters and sensitivity to the data initialization in the conventional FCM methods. The initialization stage of the K-medoid cluster, which is different from others, has a strong representation and is capable of detecting data with different sizes. Meanwhile, through the combination of the granular computing and FCM, the optimal number of clusters is obtained by choosing accurate validity functions. Finally, the detailed clustering process of the proposed algorithm is presented, and its performance is validated by simulation tests.

For the shortcoming of fuzzy c -means algorithm FCM needing to know the number of clusters in advance, this paper proposed a new self-adaptive method to determine the optimal number of clusters. Firstly, a density-based algorithm was put forward. The algorithm, according to the characteristics of the dataset, automatically determined the possible maximum number of clusters instead of using the empirical rule and obtained the optimal initial cluster centroids, improving the limitation of FCM that randomly selected cluster centroids lead the convergence result to the local minimum. Secondly, this paper, by introducing a penalty function, proposed a new fuzzy clustering validity index based on fuzzy compactness and separation, which ensured that when the number of clusters verged on that of objects in the dataset, the value of clustering validity index did not monotonically decrease and was close to zero, so that the optimal number of clusters lost robustness and decision function. Then, based on these studies, a self-adaptive FCM algorithm was put forward to estimate the optimal number of clusters by the iterative trial-and-error process. At last, experiments were done on the UCI, KDD Cup , and synthetic datasets, which showed that the method not only effectively determined the optimal number of clusters, but also reduced the iteration of FCM with the stable clustering result.

Cluster analysis

Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group called a cluster are more similar in some sense to each other than to those in other groups clusters. It is a main task of exploratory data mining , and a common technique for statistical data analysis , used in many fields, including pattern recognition , image analysis , information retrieval , bioinformatics , data compression , computer graphics and machine learning. Cluster analysis itself is not one specific algorithm , but the general task to be solved. It can be achieved by various algorithms that differ significantly in their understanding of what constitutes a cluster and how to efficiently find them.

Breast cancer is the second largest cause of cancer deaths among women. At the same time, it is also among the most curable cancer types if it can be diagnosed early. This paper presents a novel hybrid intelligent method for recognition of breast cancer tumors.

Data clustering: a review

Motivation: Fuzzy c-means clustering is widely used to identify cluster structures in high-dimensional datasets, such as those obtained in DNA microarray and quantitative proteomics experiments. One of its main limitations is the lack of a computationally fast method to set optimal values of algorithm parameters. Wrong parameter values may either lead to the inclusion of purely random fluctuations in the results or ignore potentially important data. The optimal solution has parameter values for which the clustering does not yield any results for a purely random dataset but which detects cluster formation with maximum resolution on the edge of randomness. Results: Estimation of the optimal parameter values is achieved by evaluation of the results of the clustering procedure applied to randomized datasets. In this case, the optimal value of the fuzzifier follows common rules that depend only on the main properties of the dataset.

It includes contributions from diverse areas of soft computing such as uncertain computation, Z-information processing, neuro-fuzzy approaches, evolutionary computing and others. The topics of the papers include theory of uncertainty computation; theory and application of soft computing; decision theory with imperfect information; neuro-fuzzy technology; image processing with soft computing; intelligent control; machine learning; fuzzy logic in data analytics and data mining; evolutionary computing; chaotic systems; soft computing in business, economics and finance; fuzzy logic and soft computing in the earth sciences; fuzzy logic and soft computing in engineering; soft computing in medicine, biomedical engineering and the pharmaceutical sciences; and probabilistic and statistical reasoning in the social and educational sciences. The book covers new ideas from theoretical and practical perspectives in economics, business, industry, education, medicine, the earth sciences and other fields. In addition to promoting the development and application of soft computing methods in various real-life fields, it offers a useful guide for academics, practitioners, and graduates in fuzzy logic and soft computing fields. Skip to main content Skip to table of contents. Advertisement Hide. This service is more advanced with JavaScript available.

The fuzzy clustering algorithm has been widely used in the research area and production and life. However, the conventional fuzzy algorithms have a disadvantage of high computational complexity. This article proposes an improved fuzzy C-means FCM algorithm based on K-means and principle of granularity. This algorithm is aiming at solving the problems of optimal number of clusters and sensitivity to the data initialization in the conventional FCM methods. The initialization stage of the K-medoid cluster, which is different from others, has a strong representation and is capable of detecting data with different sizes. Meanwhile, through the combination of the granular computing and FCM, the optimal number of clusters is obtained by choosing accurate validity functions. Finally, the detailed clustering process of the proposed algorithm is presented, and its performance is validated by simulation tests.


PDF | The adoption of triangular fuzzy sets to define Strong Fuzzy Partitions (​points of separation between cluster projections on eration of a well-formed triangular fuzzy set (red In IEEE, editor, 18th International Conference or compactness–separability, do not allow to find the optimal partition.


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