Unsupervised and semi-supervised clustering with learnable cluster dependent kernels.

Despite the large number of existing clustering methods, clustering remains a challenging task especially when the structure of the data does not correspond to easily separable categories, and when clusters vary in size, density and shape. Existing kernel based approaches allow to adapt a specific similarity measure in order to make the problem easier. Although good results were obtained using the Gaussian kernel function, its performance depends on the selection of the scaling parameter. Moreover, since one global parameter is used for the entire data set, it may not be possible to find one optimal scaling parameter when there are large variations between the distributions of the different clusters in the feature space. One way to learn optimal scaling parameters is through an exhaustive search of one optimal scaling parameter for each cluster. However, this approach is not practical since it is computationally expensive especially when the data includes a large number of clusters and when the dynamic range of possible values of the scaling parameters is large. Moreover, it is not trivial to evaluate the resulting partition in order to select the optimal parameters. To overcome this limitation, we introduce two new fuzzy relational clustering techniques that learn cluster dependent Gaussian kernels. The first algorithm called clustering and Local Scale Learning algorithm (LSL) minimizes one objective function for both the optimal partition and for cluster dependent scaling parameters that reflect the intra-cluster characteristics of the data. The second algorithm, called Fuzzy clustering with Learnable Cluster dependent Kernels (FLeCK) learns the scaling parameters by optimizing both the intra-cluster and the inter-cluster dissimilarities. Consequently, the learned scale parameters reflect the relative density, size, and position of each cluster with respect to the other clusters. We also introduce semi-supervised versions of LSL and FLeCK. These algorithms generate a fuzzy partition of the data and learn the optimal kernel resolution of each cluster simultaneously. We show that the incorporation of a small set of constraints can guide the clustering process to better learn the scaling parameters and the fuzzy memberships in order to obtain a better partition of the data. In particular, we show that the partial supervision is even more useful on real high dimensional data sets where the algorithms are more susceptible to local minima. All of the proposed algorithms are optimized iteratively by dynamically updating the partition and the scaling parameter in each iteration. This makes these algorithms simple and fast. Moreover, our algorithms are formulated to work on relational data. This makes them applicable to data where objects cannot be represented by vectors or when clusters of similar objects cannot be represented efficiently by a single prototype. Our extensive experiments show that FLeCK and SS-FLeCK outperform existing algorithms. In particular, we show that when data include clusters with various inter-cluster and intra-cluster distances, learning cluster dependent kernel is crucial in obtaining a good partition

Unsupervised and semi-supervised fuzzy clustering with multiple kernels.

For real-world clustering tasks, the input data is typically not easily separable due to the highly complex data structure or when clusters vary in size, density and shape. Recently, kernel-based clustering has been proposed to perform clustering in a higher-dimensional feature space spanned by embedding maps and corresponding kernel functions. Although good results were obtained using the Gaussian kernel function, its performance depends on the selection of the scaling parameter among an extensive range of possibilities. This step is often heavily influenced by prior knowledge about the data and by the patterns we expect to discover. Unfortunately, it is often unclear which kernels are more suitable for a particular task. The problem is aggravated for many real-world clustering applications, in which the distributions of the different clusters in the feature space exhibit large variations. Thus, in the absence of a priori knowledge, a single kernel selected from a predefined group is sometimes insufficient to represent the data. One way to learn optimal scaling parameters is through an exhaustive search of one optimal scaling parameter for each cluster. However, this approach is not practical since it is computationally expensive, especially when the data includes a large number of clusters and when the dynamic range of possible values of the scaling parameters is large. Moreover, the evaluation of the resulting partition in order to select the optimal parameters is not an easy task. To overcome the above drawbacks, we introduce two novel fuzzy clustering techniques that use Multiple Kernel Learning to provide an elegant solution for parameter selection. The Fuzzy C-Means with Multiple Kernels algorithm (FCMK) simultaneously finds the optimal partition and the cluster-dependent kernel combination weights that reflect the intrinsic structure of the data. The Relational Fuzzy Clustering with Multiple Kernels (RFCMK) learns the kernel combination weights by optimizing the relational dissimilarities. Consequently, the learned kernel combination weights reflect the relative density, size, and position of each cluster with respect to the other clusters. We also extended FCMK and RFCMK to the semi-supervised paradigms. We show that the incorporation of prior knowledge in the unsupervised clustering task in the form of a small set of constraints on which instances should or should not reside in the same cluster, guides the unsupervised approaches to a better partitioning of the data and avoid local minima, especially for high dimensional real world data. All of the proposed algorithms are optimized iteratively by dynamically updating the partition and the kernel combination weights in each iteration. This makes these algorithms simple and fast. Moreover, our algorithms are formulated to work on both vector and relational data. This makes them applicable to data where objects cannot be represented by vectors or when clusters of similar objects cannot be represented efficiently by a single prototype. We also introduced two relational fuzzy clustering with multiple kernel algorithms for large data to deal with the scalability issue of RFCMK. The random sample and extend RFCMK (rseRFCMK) computes cluster prototypes from a smaller sample of randomly selected objects, and then extends the partition to the remainder of the data. The single pass RFCMK (spRFCMK) sequentially loads manageable sized chunks, clustering the chunks in a single pass, and then combining the results from each chunk. Our extensive experiments show that RFCMK and SS-RFCMK outperform existing algorithms. In particular, we show that when data include clusters with various intrinsic structures and densities, learning kernel weights that vary over clusters is crucial in obtaining a good partition

Robust fuzzyclustering for object recognition and classification of relational data

Prototype based fuzzy clustering algorithms have unique ability to partition the data while detecting multiple clusters simultaneously. However since real data is often contaminated with noise, the clustering methods need to be made robust to be useful in practice. This dissertation focuses on robust detection of multiple clusters from noisy range images for object recognition. Dave\u27s noise clustering (NC) method has been shown to make prototype-based fuzzy clustering techniques robust. In this work, NC is generalized and the new NC membership is shown to be a product of fuzzy c-means (FCM) membership and robust M-estimator weight (or possibilistic membership). Thus the generalized NC approach is shown to have the partitioning ability of FCM and robustness of M-estimators. Since the NC (or FCM) algorithms are based on fixed-point iteration technique, they suffer from the problem of initializations. To overcome this problem, the sampling based robust LMS algorithm is considered by extending it to fuzzy c-LMS algorithm for detecting multiple clusters. The concept of repeated evidence has been incorporated to increase the speed of the new approach. The main problem with the LMS approach is the need for ordering the distance data. To eliminate this problem, a novel sampling based robust algorithm is proposed following the NC principle, called the NLS method, that directly searches for clusters in the maximum density region of the range data without requiring the specification of number of clusters. The NC concept is also introduced to several fuzzy methods for robust classification of relational data for pattern recognition. This is also extended to non-Euclidean relational data. The resulting algorithms are used for object recognition from range images as well as for identification of bottleneck parts while creating desegregated cells of machine/ components in cellular manufacturing and group technology (GT) applications

Fuzzy clustering with spatial-temporal information

Clustering geographical units based on a set of quantitative features observed at several time occasions requires to deal with the complexity of both space and time information. In particular, one should consider (1) the spatial nature of the units to be clustered, (2) the characteristics of the space of multivariate time trajectories, and (3) the uncertainty related to the assignment of a geographical unit to a given cluster on the basis of the above com- plex features. This paper discusses a novel spatially constrained multivariate time series clustering for units characterised by different levels of spatial proximity. In particular, the Fuzzy Partitioning Around Medoids algorithm with Dynamic Time Warping dissimilarity measure and spatial penalization terms is applied to classify multivariate Spatial-Temporal series. The clustering method has been theoretically presented and discussed using both simulated and real data, highlighting its main features. In particular, the capability of embedding different levels of proximity among units, and the ability of considering time series with different length

Clustering-Based Pre-Processing Approaches To Improve Similarity Join Techniques

Research on similarity join techniques is becoming one of the growing practical areas for study, especially with the increasing E-availability of vast amounts of digital data from more and more source systems. This research is focused on pre-processing clustering-based techniques to improve existing similarity join approaches. Identifying and extracting the same real-world entities from different data sources is still a big challenge and a significant task in the digital information era. Dissimilar extracts may indeed represent the same real-world entity because of inconsistent values and naming conventions, incorrect or missing data values, or incomplete information. Therefore discovering efficient and accurate approaches to determine the similarity of data objects or values is of theoretical as well as practical significance. Semantic problems are raised even on the concept of similarity regarding its usage and foundation. Existing similarity join approaches often have a very specific view of similarity measures and pre-defined predicates that represent a narrow focus on the context of similarity for a given scenario. The predicates have been assumed to be a group of clustering [MSW 72] related attributes on the join. To identify those entities for data integration purposes requires a broader view of similarity; for instance a number of generic similarity measures are useful in a given data integration systems. This study focused on string similarity join, namely based on the Levenshtein or edit distance and Q-gram. Proposed effective and efficient pre-processing clustering-based techniques were the focus of this study to identify clustering related predicates based on either attribute value or data value that improve existing similarity join techniques in enterprise data integration scenarios

Clustering of Multiple Dissimilarity Data Tables for Documents Categorization

ISBN 978-3-7908-2603-6 e-ISBN 978-3-7908-2604-3International audienceThis paper introduces a clustering algorithm that is able to partition objects taking into account simultaneously their relational descriptions given by multiple dissimilarity matrices. These matrices could have been generated using different sets of variables and a fixed dissimilarity function, using a fixed set of variables and different dissimilarity functions or using different sets of variables and dissimilarity functions. This method, which is based on the dynamic hard clustering algorithm for relational data, is designed to provided a partition and a prototype for each cluster as well as to learn a relevance weight for each dissimilarity matrix by optimizing an adequacy criterion that measures the fit between clusters and their representatives. These relevance weights change at each algorithm iteration and are different from one cluster to another. Experiments aiming at obtaining a categorization of a document data base demonstrate the usefulness of this partitional clustering method

A study of distributed clustering of vector time series on the grid by task farming

Traditional data mining methods were limited by availability of computing resources like network bandwidth, storage space and processing power. These algorithms were developed to work around this problem by looking at a small cross-section of the whole data available. However since a major chunk of the data is kept out, the predictions were generally inaccurate and missed out on significant features that was part of the data. Today with resources growing at almost the same pace as data, it is possible to rethink mining algorithms to work on distributed resources and essentially distributed data. Distributed data mining thus holds great promise. Using grid technologies, data mining can be extended to areas which were not previously looked at because of the volume of data being generated, like climate modeling, web usage, etc. An important characteristic of data today is that it is highly decentralized and mostly redundant. Data mining algorithms which can make efficient use of distributed data has to be thought of. Though it is possible to bring all the data together and run traditional algorithms, this has a high overhead, in terms of bandwidth usage for transmission, preprocessing steps which have to be to handle every format the received data. By processing the data locally, the preprocessing stage can be made less bulky and also the traditional data mining techniques would be able to work on the data efficiently. The focus of this project is to use an existing data mining technique, fuzzy c-means clustering to work on distributed data in a simulated grid environment and to review the performance of this approach viz., the traditional approach

An initial state of design and development of intelligent knowledge discovery system for stock exchange database

Data mining is a challenging matter in research field for the last few years.Researchers are using different techniques in data mining.This paper discussed the initial state of Design and Development Intelligent Knowledge Discovery System for Stock Exchange (SE) Databases. We divide our problem in two modules.In first module we define Fuzzy Rule Base System to determined vague information in stock exchange databases.After normalizing massive amount of data we will apply our proposed approach, Mining Frequent Patterns with Neural Networks.Future prediction (e.g., political condition, corporation factors, macro economy factors, and psychological factors of investors) perform an important rule in Stock Exchange, so in our prediction model we will be able to predict results more precisely.In second module we will generate clustering algorithm. Generally our clustering algorithm consists of two steps including training and running steps.The training step is conducted for generating the neural network knowledge based on clustering.In running step, neural network knowledge based is used for supporting the Module in order to generate learned complete data, transformed data and interesting clusters that will help to generate interesting rules

Robust techniques and applications in fuzzy clustering

This dissertation addresses issues central to frizzy classification. The issue of sensitivity to noise and outliers of least squares minimization based clustering techniques, such as Fuzzy c-Means (FCM) and its variants is addressed. In this work, two novel and robust clustering schemes are presented and analyzed in detail. They approach the problem of robustness from different perspectives. The first scheme scales down the FCM memberships of data points based on the distance of the points from the cluster centers. Scaling done on outliers reduces their membership in true clusters. This scheme, known as the Mega-clustering, defines a conceptual mega-cluster which is a collective cluster of all data points but views outliers and good points differently (as opposed to the concept of Dave\u27s Noise cluster). The scheme is presented and validated with experiments and similarities with Noise Clustering (NC) are also presented. The other scheme is based on the feasible solution algorithm that implements the Least Trimmed Squares (LTS) estimator. The LTS estimator is known to be resistant to noise and has a high breakdown point. The feasible solution approach also guarantees convergence of the solution set to a global optima. Experiments show the practicability of the proposed schemes in terms of computational requirements and in the attractiveness of their simplistic frameworks. The issue of validation of clustering results has often received less attention than clustering itself. Fuzzy and non-fuzzy cluster validation schemes are reviewed and a novel methodology for cluster validity using a test for random position hypothesis is developed. The random position hypothesis is tested against an alternative clustered hypothesis on every cluster produced by the partitioning algorithm. The Hopkins statistic is used as a basis to accept or reject the random position hypothesis, which is also the null hypothesis in this case. The Hopkins statistic is known to be a fair estimator of randomness in a data set. The concept is borrowed from the clustering tendency domain and its applicability to validating clusters is shown here. A unique feature selection procedure for use with large molecular conformational datasets with high dimensionality is also developed. The intelligent feature extraction scheme not only helps in reducing dimensionality of the feature space but also helps in eliminating contentious issues such as the ones associated with labeling of symmetric atoms in the molecule. The feature vector is converted to a proximity matrix, and is used as an input to the relational fuzzy clustering (FRC) algorithm with very promising results. Results are also validated using several cluster validity measures from literature. Another application of fuzzy clustering considered here is image segmentation. Image analysis on extremely noisy images is carried out as a precursor to the development of an automated real time condition state monitoring system for underground pipelines. A two-stage FCM with intelligent feature selection is implemented as the segmentation procedure and results on a test image are presented. A conceptual framework for automated condition state assessment is also developed

Ligand-based design of dopamine reuptake inhibitors : fuzzy relational clustering and 2-D and 3-D QSAR modleing

As the three-dimensional structure of the dopamine transporter (DAT) remains undiscovered, any attempt to model the binding of drug-like ligands to this protein must necessarily include strategies that use ligand information. For flexible ligands that bind to the DAT, the identification of the binding conformation becomes an important but challenging task. In the first part of this work, the selection of a few representative structures as putative binding conformations from a large collection of conformations of a flexible GBR 12909 analogue was demonstrated by cluster analysis. Novel structurebased features that can be easily generalized to other molecules were developed and used for clustering. Since the feature space may or may not be Euclidean, a recently-developed fuzzy relational clustering algorithm capable of handling such data was used. Both superposition-dependent and superposition-independent features were used along with region-specific clustering that focused on separate pharmacophore elements in the molecule. Separate sets of representative structures were identified for the superpositiondependent and superposition-independent analyses. In the second part of this work, several QSAR models were developed for a series of analogues of methylphenidate (MP), another potent dopamine reuptake inhibitor. In a novel method, the Electrotopological-state (B-state) indices for atoms of the scaffold common to all 80 compounds were used to develop an effective test set spanning both the structure space as well as the activity space. The utility of B-state indices in modeling a series of analogues with a common scaffold was demonstrated. Several models were developed using various combinations of 2-D and 3-D descriptors in the Molconn-Z and MOE descriptor sets. The models derived from CoMFA descriptors were found to be the most predictive and explanatory. Progressive scrambling of all models indicated several stable models. The best models were used to predict the activity of the test set analogues and were found to produce reasonable residuals. Substitutions in the phenyl ring of MP, especially at the 3- and 4-positions, were found to be the most important for DATbinding. It was predicted that for better DAT-binding the substituents at these positions should be relatively bulky, electron-rich atoms or groups