Hard Clustering Method Research Articles

Gaussian Mixture Regression Model with Sparsity for Clustering of Territory Risk in Auto Insurance

Abstract Insurance rating territory design and accurate estimation of territory risk relativities are fundamental aspects of auto insurance rate regulation. It is crucial to develop methodologies that can facilitate the effective design of rating territories and their risk relativities estimate, as they directly impact the rate filing and the decision support of the rate change review process. This article proposes a Gaussian Mixture Regression model clustering approach for territory design. The proposed method incorporates a linear regression model, taking spatial location as model covariates, which helps estimate the cluster mean more accurately. Also, to further enhance the estimation of territory risk relativities, we impose sparsity through sparse matrix decomposition of the membership coefficient matrix obtained from the Gaussian Mixture Regression model. By transitioning from the current hard clustering method to a soft approach, our methodology could improve the evaluation of territory risk for rate-making purposes. Moreover, using non-negative sparse matrix approximation ensures that the estimation of risk relativities for basic rating units remains smooth, effectively eliminating data noise from the territory risk relativity estimate. Overall, our novel methodology aims to significantly enhance the accuracy and reliability of risk analysis in auto insurance. Furthermore, the proposed method exhibits potential for extension to various other domains that involve spatial clustering of data, thereby broadening its applicability and expanding its usefulness beyond auto insurance rate regulation.

Research on multi-view clustering algorithm based on sequential three-way decision

Multi-view clustering has achieved many applications in recent years. But the existing multi-view clustering methods face two problems, firstly, the traditional multi-view clustering uses a hard clustering method, which cannot describe the uncertainty between the samples and the clusters, and secondly how to perform effective incremental learning on multi-view data when the number of views increases. Therefore to address the above two problems, we firstly propose a three-way fuzzy spectral clustering algorithm based on fuzzy clustering, which can perform three-way clustering on multi-views and get soft clustering results, thus describing the uncertainty between samples and clusters. Then based on the sequential decision making approach, an incremental learning mechanism is designed for multi-view clustering when the number of views increases. Finally, these two works are combined to propose a multi-view clustering algorithm based on sequential three-way decision making. The experimental results demonstrate that the method proposed in this paper has better clustering accuracy and efficiency compared to the traditional multi-view clustering algorithm.

Designing a New Shuttle Service to Meet Large-Scale Instantaneous Peak Demands for Passenger Transportation in a Metropolitan Context: A Green, Low-Cost Mass Transport Option

Currently, the green, sustainable development of metropolises is hindered by problems caused by Large-scale Instantaneous Peak-demands for Passenger-transportation (LIPP), such as traffic congestion and air pollution. To mitigate these problems, we propose a new type of demand-responsive service as an alternative to inefficient “door-to-door” service. The proposed service is based on service units designed to aggregate passengers for shuttle service. To guarantee service quality and efficiency, a maximum passenger walking time constraint, a request rejection mechanism and a scheme for ensuring solution feasibility are considered. Through numerical experiments, we prove the following: (i) the proposed transport option exhibits better performance (by 40.37% for passengers and by 35.79% for operators) than the door-to-door transport option for solving real cases. (ii) By testing different datasets, we prove that the proposed service is more suitable for the request distributions that are spatiotemporally concentrated. (iii) Regarding the individual components of the proposed clustering-first, routing-second solution framework, the proposed soft clustering algorithm exhibits better performance than the classical hard clustering method (by 8%), and the proposed routing algorithm is 1.5 times more efficient than the commercial solution software GAMS.

CE3: A three-way clustering method based on mathematical morphology

Many existing clustering methods produce clusters with clear and sharp boundaries, which does not truly reflect the fact that a cluster may not necessarily have a well-defined boundary in many real world situations. In this paper, by combining ideas of erosion and dilation from mathematical morphology and principles of three-way decision, we propose a framework of a contraction-and-expansion based three-way clustering called CE3. A three-way cluster is defined by a nested pair of sets called the core and the support of the cluster, respectively. A stronger relationship holds between objects in the core and a weaker relationship holds between objects in the support. Given a cluster obtained from a hard clustering method, CE3 uses a contraction operation to shrink the cluster into the core of a three-way cluster and uses an expansion operation to enlarge the cluster into the support. The difference between the support and the core is called the fringe region, representing an unsharp boundary of a cluster. Within the CE3 framework, we can define different types of contraction and expansion operations. We can apply the CE3 framework on the top of any existing clustering method. As examples for demonstration, we introduce a pair of neighbor-based contraction and expansion operations and apply the CE3 framework on the top of k-means and spectral clustering, respectively. We use one synthetic data set, five UCI data sets, and three USPS data sets to evaluate experimentally the performance of CE3. The results show that CE3 is in fact effective in revealing cluster structures.

Fuzzy-Decision-based Segmentation Approach for Detecting Region of Interest

Many clustering strategies have been used, such as the hard clustering scheme and the fuzzy clustering scheme, each of which has its own special characteristics. The conventional hard clustering method restricts each point of the data set to exclusively just one cluster. As a consequence, with this approach the segmentation results are often very crisp, i.e., each pixel of the image belongs to exactly just one class. In this paper we have considered the fuzzy decision based clustering approach for finding the objects of interest. The methodology is basically the parameter based clustering where the regions are divided based on the parameter value which develops the regions of interest. The proposed methodology is test on the benchmark datasets and evaluated with different measures for performance analysis.

Unsupervised language model adaptation using LDA-based mixture models and latent semantic marginals

In this paper, we present unsupervised language model (LM) adaptation approaches using latent Dirichlet allocation (LDA) and latent semantic marginals (LSM). The LSM is the unigram probability distribution over words that are calculated using LDA-adapted unigram models. The LDA model is used to extract topic information from a training corpus in an unsupervised manner. The LDA model yields a document–topic matrix that describes the number of words assigned to topics for the documents. A hard-clustering method is applied on the document–topic matrix of the LDA model to form topics. An adapted model is created by using a weighted combination of the n-gram topic models. The stand-alone adapted model outperforms the background model. The interpolation of the background model and the adapted model gives further improvement. We modify the above models using the LSM. The LSM is used to form a new adapted model by using the minimum discriminant information (MDI) adaptation approach called unigram scaling, which minimizes the distance between the new adapted model and the other model. The unigram scaling of the adapted model using LSM yields better results over a conventional unigram scaling approach. The unigram scaling of the interpolation of the background and the adapted model using the LSM outperform the background model, the unigram scaling of the background model, the unigram scaling of the adapted model, and the interpolation of the background and the adapted models respectively. We perform experiments using the '87–89 Wall Street Journal (WSJ) corpus incorporating a multi-pass continuous speech recognition (CSR) system. In the first pass, we used the background n-gram language model for lattice generation and then we apply the LM adaptation approaches for lattice rescoring in the second pass.

A New Clustering Method with Fuzzy Approach Based on Takagi-Sugeno Model in Queuing Systems

In this paper, the authors propose a new hard clustering method to provide objective knowledge on field of fuzzy queuing system. In this method, locally linear controllers are extracted and translated into the first-order Takagi-Sugeno rule base fuzzy model. In this extraction process, the region of fuzzy subspaces of available inputs corresponding to different implications is used to obtain the clusters of outputs of the queuing system. Then, the multiple regression functions associated with these separate clusters are used to interpret the performance of queuing systems. An application of the method also is presented and the performance of the queuing system is discussed.

SOFT CLUSTERING BASED EXPOSITION TO MULTIPLE DICTIONARY BAG OF WORDS

Object classification is a highly important area of computer vision and has many applications including robotics, searching images, face recognition, aiding visually impaired people, censoring images and many more. A new common method of classification that uses features is the Bag of Words approach. In this method a codebook of visual words is created using various clustering methods. For increasing the performance Multiple Dictionaries BoW (MDBoW) method that uses more visual words from different independent dictionaries instead of adding more words to the same dictionary was implemented using hard clustering method. Nearest-neighbor assignments are used in hard clustering of features. A given feature may be nearly the same distance from two cluster centers. For a typical hard clustering method, only the slightly nearer neighbor is selected to represent that feature. Thus, the ambiguous features are not well-represented by the visual vocabulary. To address this problem, soft clustering model based Multiple Dictionary Bag of Visual words for image classification is implemented with dictionary generated using modified Fuzzy C-means algorithm using R1 norm. A performance evaluation on images has been done by varying the dictionary size. The proposed method works better when the number of topics and the number of images per topics are more. The results obtained indicate that multiple dictionary bag of words model using fuzzy clustering increases the recognition performance than the baseline method.

Multilevel Functional Clustering Analysis

In this article, we investigate clustering methods for multilevel functional data, which consist of repeated random functions observed for a large number of units (e.g., genes) at multiple subunits (e.g., bacteria types). To describe the within- and between variability induced by the hierarchical structure in the data, we take a multilevel functional principal component analysis (MFPCA) approach. We develop and compare a hard clustering method applied to the scores derived from the MFPCA and a soft clustering method using an MFPCA decomposition. In a simulation study, we assess the estimation accuracy of the clustering membership and the cluster patterns under a series of settings: small versus moderate number of time points; various noise levels; and varying number of subunits per unit. We demonstrate the applicability of the clustering analysis to a real data set consisting of expression profiles from genes activated by immunity system cells. Prevalent response patterns are identified by clustering the expression profiles using our multilevel clustering analysis.

Improvement of the PFCM(Possibilistic Fuzzy C-Means) Clustering Method

Cluster analysis or clustering is a kind of unsupervised learning method in which a set of data points is divided into a given number of homogeneous groups. Fuzzy clustering method, one of the most popular clustering method, allows a point to belong to all the clusters with different degrees, so produces more intuitive and natural clusters than hard clustering method does. Even more some of fuzzy clustering variants have noise-immunity. In this paper, we improved the Possibilistic Fuzzy C-Means (PFCM), which generates a membership matrix as well as a typicality matrix, using Gath-Geva (GG) method. The proposed method has a focus on the boundaries of clusters, which is different from most of the other methods having a focus on the centers of clusters. The generated membership values are suitable for the classification-type applications. As the typicality values generated from the algorithm have a similar distribution with the values of density function of Gaussian distribution, it is useful for Gaussian-type density estimation. Even more GG method can handle the clusters having different numbers of data points, which the other well-known method by Gustafson and Kessel can not. All of these points are obvious in the experimental results.