Spectral Methods for Data Clustering

2011 ◽  
pp. 1823-1829
Author(s):  
Wenyuan Li
Keyword(s):  
Data Mining ◽  
Spectral Methods ◽  
Data Clustering ◽  
Clustering Algorithms ◽  
The Internet ◽  
Data Sets ◽  
Local Optima ◽  
Clustering Problem ◽  
Close Relationship ◽  
Technological University

With the rapid growth of the World Wide Web and the capacity of digital data storage, tremendous amount of data are generated daily from business and engineering to the Internet and science. The Internet, financial realtime data, hyperspectral imagery, and DNA microarrays are just a few of the common sources that feed torrential streams of data into scientific and business databases worldwide. Compared to statistical data sets with small size and low dimensionality, traditional clustering techniques are challenged by such unprecedented high volume, high dimensionality complex data. To meet these challenges, many new clustering algorithms have been proposed in the area of data mining (Han & Kambr, 2001). Spectral techniques have proven useful and effective in a variety of data mining and information retrieval applications where massive amount of real-life data is available (Deerwester et al., 1990; Kleinberg, 1998; Lawrence et al., 1999; Azar et al., 2001). In recent years, a class of promising and increasingly popular approaches — spectral methods — has been proposed in the context of clustering task (Shi & Malik, 2000; Kannan et al., 2000; Meila & Shi, 2001; Ng et al., 2001). Spectral methods have the following reasons to be an attractive approach to clustering problem: • Spectral approaches to the clustering problem offer the potential for dramatic improvements in efficiency and accuracy relative to traditional iterative or greedy algorithms. They do not intrinsically suffer from the problem of local optima. • Numerical methods for spectral computations are extremely mature and well understood, allowing clustering algorithms to benefit from a long history of implementation efficiencies in other fields (Golub & Loan, 1996). • Components in spectral methods have the naturally close relationship with graphs (Chung, 1997). This characteristic provides an intuitive and semantic understanding of elements in spectral methods. It Spectral Methods for Data Clustering Wenyuan Li Nanyang Technological University, Singapore Wee Keong Ng Nanyang Technological University, Singapore is important when the data is graph-based, such as links of WWW, or can be converted to graphs. In this paper, we systematically discuss applications of spectral methods to data clustering.

Clustering techniques and their applications in engineering

2007 ◽  
Vol 221 (11) ◽  
pp. 1445-1459 ◽  
Author(s):  
D T Pham ◽  
A A Afify
Keyword(s):  
Data Mining ◽  
Clustering Algorithms ◽  
Large Data ◽  
Large Data Sets ◽  
Data Sets ◽  
Monitoring And Control ◽  
Design Quality ◽  
Clustering Problem ◽  
Manufacturing System Design ◽  
And Control

Clustering is an important data exploration technique with many applications in different areas of engineering, including engineering design, manufacturing system design, quality assurance, production planning and process planning, modelling, monitoring, and control. The clustering problem has been addressed by researchers from many disciplines. However, efforts to perform effective and efficient clustering on large data sets only started in recent years with the emergence of data mining. The current paper presents an overview of clustering algorithms from a data mining perspective. Attention is paid to techniques of scaling up these algorithms to handle large data sets. The paper also describes a number of engineering applications to illustrate the potential of clustering algorithms as a tool for handling complex real-world problems.

scholarly journals Big Data Clustering And Its Applications Examination

2019 ◽  
Vol 8 (2S11) ◽  
pp. 3687-3693
Keyword(s):  
Data Mining ◽  
Big Data ◽  
Data Clustering ◽  
Clustering Algorithms ◽  
Large Data ◽  
Data Sets ◽  
Clustering Methods ◽  
Time Saving ◽  
Data Set ◽  
The Many

Clustering is a type of mining process where the data set is categorized into various sub classes. Clustering process is very much essential in classification, grouping, and exploratory pattern of analysis, image segmentation and decision making. And we can explain about the big data as very large data sets which are examined computationally to show techniques and associations and also which is associated to the human behavior and their interactions. Big data is very essential for several organisations but in few cases very complex to store and it is also time saving. Hence one of the ways of overcoming these issues is to develop the many clustering methods, moreover it suffers from the large complexity. Data mining is a type of technique where the useful information is extracted, but the data mining models cannot utilized for the big data because of inherent complexity. The main scope here is to introducing a overview of data clustering divisions for the big data And also explains here few of the related work for it. This survey concentrates on the research of several clustering algorithms which are working basically on the elements of big data. And also the short overview of clustering algorithms which are grouped under partitioning, hierarchical, grid based and model based are seenClustering is major data mining and it is used for analyzing the big data.the problems for applying clustering patterns to big data and also we phase new issues come up with big data

scholarly journals Improved minimum-minimum roughness algorithm for clustering categorical data

2021 ◽  
Vol 8 (10) ◽  
pp. 43-50
Author(s):  
Truong et al. ◽  
Keyword(s):  
Machine Learning ◽  
Data Mining ◽  
Hierarchical Clustering ◽  
Categorical Data ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Experimental Results ◽  
Data Sets ◽  
Top Down ◽  
Hierarchical Clustering Algorithm

Clustering is a fundamental technique in data mining and machine learning. Recently, many researchers are interested in the problem of clustering categorical data and several new approaches have been proposed. One of the successful and pioneering clustering algorithms is the Minimum-Minimum Roughness algorithm (MMR) which is a top-down hierarchical clustering algorithm and can handle the uncertainty in clustering categorical data. However, MMR tends to choose the category with less value leaf node with more objects, leading to undesirable clustering results. To overcome such shortcomings, this paper proposes an improved version of the MMR algorithm for clustering categorical data, called IMMR (Improved Minimum-Minimum Roughness). Experimental results on actual data sets taken from UCI show that the IMMR algorithm outperforms MMR in clustering categorical data.

Uncertainty-Based Clustering Algorithms for Large Data Sets

2018 ◽  
pp. 1-33 ◽  
Author(s):  
B. K. Tripathy ◽  
Hari Seetha ◽  
M. N. Murty
Keyword(s):  
Big Data ◽  
Data Clustering ◽  
Clustering Algorithms ◽  
Large Data ◽  
Large Data Sets ◽  
Mining Machine ◽  
Data Sets ◽  
Fuzzy C Means ◽  
Intuitionistic Fuzzy ◽  
New Algorithms

Data clustering plays a very important role in Data mining, machine learning and Image processing areas. As modern day databases have inherent uncertainties, many uncertainty-based data clustering algorithms have been developed in this direction. These algorithms are fuzzy c-means, rough c-means, intuitionistic fuzzy c-means and the means like rough fuzzy c-means, rough intuitionistic fuzzy c-means which base on hybrid models. Also, we find many variants of these algorithms which improve them in different directions like their Kernelised versions, possibilistic versions, and possibilistic Kernelised versions. However, all the above algorithms are not effective on big data for various reasons. So, researchers have been trying for the past few years to improve these algorithms in order they can be applied to cluster big data. The algorithms are relatively few in comparison to those for datasets of reasonable size. It is our aim in this chapter to present the uncertainty based clustering algorithms developed so far and proposes a few new algorithms which can be developed further.

A Data Distribution View of Clustering Algorithms

2011 ◽  
pp. 374-381 ◽  
Author(s):  
Junjie Wu ◽  
Jian Chen ◽  
Hui Xiong
Keyword(s):  
Data Mining ◽  
Cluster Analysis ◽  
Clustering Analysis ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Data Distribution ◽  
Point Of View ◽  
Group Method ◽  
Data Sets ◽  
Distribution Point

Cluster analysis (Jain & Dubes, 1988) provides insight into the data by dividing the objects into groups (clusters), such that objects in a cluster are more similar to each other than objects in other clusters. Cluster analysis has long played an important role in a wide variety of fields, such as psychology, bioinformatics, pattern recognition, information retrieval, machine learning, and data mining. Many clustering algorithms, such as K-means and Unweighted Pair Group Method with Arithmetic Mean (UPGMA), have been wellestablished. A recent research focus on clustering analysis is to understand the strength and weakness of various clustering algorithms with respect to data factors. Indeed, people have identified some data characteristics that may strongly affect clustering analysis including high dimensionality and sparseness, the large size, noise, types of attributes and data sets, and scales of attributes (Tan, Steinbach, & Kumar, 2005). However, further investigation is expected to reveal whether and how the data distributions can have the impact on the performance of clustering algorithms. Along this line, we study clustering algorithms by answering three questions: 1. What are the systematic differences between the distributions of the resultant clusters by different clustering algorithms? 2. How can the distribution of the “true” cluster sizes make impact on the performances of clustering algorithms? 3. How to choose an appropriate clustering algorithm in practice? The answers to these questions can guide us for the better understanding and the use of clustering methods. This is noteworthy, since 1) in theory, people seldom realized that there are strong relationships between the clustering algorithms and the cluster size distributions, and 2) in practice, how to choose an appropriate clustering algorithm is still a challenging task, especially after an algorithm boom in data mining area. This chapter thus tries to fill this void initially. To this end, we carefully select two widely used categories of clustering algorithms, i.e., K-means and Agglomerative Hierarchical Clustering (AHC), as the representative algorithms for illustration. In the chapter, we first show that K-means tends to generate the clusters with a relatively uniform distribution on the cluster sizes. Then we demonstrate that UPGMA, one of the robust AHC methods, acts in an opposite way to K-means; that is, UPGMA tends to generate the clusters with high variation on the cluster sizes. Indeed, the experimental results indicate that the variations of the resultant cluster sizes by K-means and UPGMA, measured by the Coefficient of Variation (CV), are in the specific intervals, say [0.3, 1.0] and [1.0, 2.5] respectively. Finally, we put together K-means and UPGMA for a further comparison, and propose some rules for the better choice of the clustering schemes from the data distribution point of view.

A Dynamic Genetic Algorithm for Clustering Problems

2013 ◽  
Vol 411-414 ◽  
pp. 1884-1893
Author(s):  
Yong Chun Cao ◽  
Ya Bin Shao ◽  
Shuang Liang Tian ◽  
Zheng Qi Cai
Keyword(s):  
Genetic Algorithm ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Real Life ◽  
Search Space ◽  
Adaptive Mutation ◽  
Data Sets ◽  
Data Set ◽  
Local Optima ◽  
Clustering Problems

Due to many of the clustering algorithms based on GAs suffer from degeneracy and are easy to fall in local optima, a novel dynamic genetic algorithm for clustering problems (DGA) is proposed. The algorithm adopted the variable length coding to represent individuals and processed the parallel crossover operation in the subpopulation with individuals of the same length, which allows the DGA algorithm clustering to explore the search space more effectively and can automatically obtain the proper number of clusters and the proper partition from a given data set; the algorithm used the dynamic crossover probability and adaptive mutation probability, which prevented the dynamic clustering algorithm from getting stuck at a local optimal solution. The clustering results in the experiments on three artificial data sets and two real-life data sets show that the DGA algorithm derives better performance and higher accuracy on clustering problems.

scholarly journals Serial Crystallography with Multi-stage Merging oi 1000’s of Images

2017 ◽  
Author(s):  
Herbert J. Bernstein ◽  
Lawrence C. Andrews ◽  
James Foadi ◽  
Martin R. Fuchs ◽  
Jean Jakoncic ◽  
...  
Keyword(s):  
Data Clustering ◽  
Clustering Algorithms ◽  
Unit Cell ◽  
Physical Parameters ◽  
Data Sets ◽  
Cell Parameters ◽  
Cell Clustering ◽  
Multi Stage ◽  
Cluster Data ◽  
Serial Crystallography

KAMO and Blend provide particularly effective tools to automatically manage the merging of large numbers of data sets from serial crystallography. The requirement for manual intervention in the process can be reduced by extending Blend to support additional clustering options to increase the sensitivity to differences in unit cell parameters and to allow for clustering of nearly complete datasets on the basis of intensity or amplitude differences. If datasets are already sufficiently complete to permit it, apply KAMO once, just for reflections. If starting from incomplete datasets, one applies KAMO twice, first using cell parameters. In this step either the simple cell vector distance of the original Blend is used, or the more sensitive NCDist, to find clusters to merge to achieve sufficient completeness to allow intensities or amplitudes to be compared. One then uses KAMO again using the correlation between the reflections at the common HKLs to merge clusters in a way sensitive to structural differences that may not perturb the cell parameters sufficiently to make meaningful clusters.Many groups have developed effective clustering algorithms that use a measurable physical parameter from each diffraction still or wedge to cluster the data into categories which can then be merged to, hopefully, yield the electron density from a single protein iso-form. What is striking about many of these physical parameters is that they are largely independent from one another. Consequently, it should be possible to greatly improve the efficacy of data clustering software by using a multi-stage partitioning strategy. Here, we have demonstrated one possible approach to multi-stage data clustering. Our strategy was to use unit-cell clustering until merged data was of sufficient completeness to then use intensity based clustering. We have demonstrated that, using this strategy, we were able to accurately cluster data sets from crystals that had subtle differences.

scholarly journals A New Method on Data Clustering Based on Hybrid K-Harmonic Means and Imperialist Competitive Algorithm

2013 ◽  
Vol 10 (7) ◽  
pp. 1848-1857
Author(s):  
Marjan Abdeyazdan
Keyword(s):  
Data Clustering ◽  
Particle Swarm Optimization Algorithm ◽  
Clustering Algorithms ◽  
Optimization Technique ◽  
Imperialist Competitive Algorithm ◽  
Swarm Optimization ◽  
Local Optima ◽  
Evolutionary Genetic ◽  
Harmonic Means ◽  
Global Optimization Technique

Data clustering is one of the commonest data mining techniques. The K-means algorithm is one of the most wellknown clustering algorithms thatare increasingly popular due to the simplicity of implementation and speed of operation. However, its performancecouldbe affected by some issues concerningsensitivity to the initialization and getting stuck in local optima. The K-harmonic means clustering method manages the issue of sensitivity to initialization but the local optimaissue still compromises the algorithm. Particle Swarm Optimization algorithm is a stochastic global optimization technique which is a good solution to the above-mentioned problems. In the present article, the PSOKHM, a hybrid algorithm which draws upon the advantages of both of the algorithms, strives not only to overcome the issue of local optima in KHM but also the slow convergence speed of PSO. In this article, the proposed GSOKHM method, which is a combination of PSO and the evolutionary genetic algorithmwithin PSOKHM,has been positedto enhancethe PSO operation. To carry out this experiment, four real datasets have been employed whose results indicate thatGSOKHMoutperforms PSOKHM.

scholarly journals Clustering, factor discovery and optimal transport

2020 ◽  
Author(s):  
Hongkang Yang ◽  
Esteban G Tabak
Keyword(s):  
Latent Variables ◽  
Optimal Transport ◽  
Clustering Algorithms ◽  
Data Sets ◽  
Affine Transformations ◽  
Real World Data ◽  
Continuous Version ◽  
Clustering Problem ◽  
Latent Space ◽  
Transport Maps

Abstract The clustering problem, and more generally latent factor discovery or latent space inference, is formulated in terms of the Wasserstein barycenter problem from optimal transport. The objective proposed is the maximization of the variability attributable to class, further characterized as the minimization of the variance of the Wasserstein barycenter. Existing theory, which constrains the transport maps to rigid translations, is extended to affine transformations. The resulting non-parametric clustering algorithms include $k$-means as a special case and exhibit more robust performance. A continuous version of these algorithms discovers continuous latent variables and generalizes principal curves. The strength of these algorithms is demonstrated by tests on both artificial and real-world data sets.

scholarly journals Density-based clustering with constraints

2019 ◽  
Vol 16 (2) ◽  
pp. 469-489 ◽  
Author(s):  
Piotr Lasek ◽  
Jarek Gryz
Keyword(s):  
Data Clustering ◽  
Clustering Algorithms ◽  
Background Knowledge ◽  
Data Sets ◽  
Benchmark Data ◽  
Density Based Clustering

In this paper we present our ic-NBC and ic-DBSCAN algorithms for data clustering with constraints. The algorithms are based on density-based clustering algorithms NBC and DBSCAN but allow users to incorporate background knowledge into the process of clustering by means of instance constraints. The knowledge about anticipated groups can be applied by specifying the so-called must-link and cannot-link relationships between objects or points. These relationships are then incorporated into the clustering process. In the proposed algorithms this is achieved by properly merging resulting clusters and introducing a new notion of deferred points which are temporarily excluded from clustering and assigned to clusters based on their involvement in cannot-link relationships. To examine the algorithms, we have carried out a number of experiments. We used benchmark data sets and tested the efficiency and quality of the results. We have also measured the efficiency of the algorithms against their original versions. The experiments prove that the introduction of instance constraints improves the quality of both algorithms. The efficiency is only insignificantly reduced and is due to extra computation related to the introduced constraints.

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