A Study in Pairwise Clustering for Bi-dimensional Irregular Strip Packing Using the Dotted Board Model

There are some problems in the field of text clustering and particle swarm optimization (PSO) technology, for example, the researchers need to determine the appropriate number of clusters before clustering, the clustering results are sensitive to the initial cluster center, and the PSO algorithm has precocious convergence and easy to fall into local optimality defects. We propose a dynamic topology adaptive PSO (DTA-PSO) algorithm that combines the K-means algorithm PSO to realize automatic text clustering. In DTA-PSO, we adopt an improved comprehensive dynamic learning strategy from social group experience the source of the social experience of the particle group is not only the particle with the best performance among all its neighbors, according to the performance of all its neighbors and the relative position with the particle, the target position is calculated in the next iteration. We choose three data sets in the knowledge base of the machine learning open data set and part of the Chinese corpus of Fudan University. Many experiments are carried out on the automatic cluster of DTA-PSO, the text automatic clustering algorithm has a certain improvement on the K value determination and the clustering effect by the contrast analysis.

This paper addresses the Irregular Strip Packing problem, a particular case of Cutting and Packing problems in which a set of polygons has to be packed within a rectangular object. To identify good quality solutions, we propose a hybrid methodology based on a meta-heuristic engine (i.e., Genetic Algorithm) and a well known placement heuristic called Bottom-Left. In addition, differently from several approaches presented in the literature, we investigate the application of the No-fit Polygon as a placement tool for obtaining local optima. The results are further improved by a shrinking algorithm that works within the meta-heuristic component. To assess the potentials of the proposed methodology, computational experiments performed on a set of difficult benchmark instances of the Irregular Strip Packing problem are discussed here for evaluation purposes.

Approximation schemes for Min-Sum [formula omitted]-Clustering

Pair wise clustering methods, including the popular graph cut based approaches such as normalized cut, partition the data space into clusters by the pair wise affinity between data points. The success of pair wise clustering largely depends on the pair wise affinity function defined over data points coming from different clusters. Interpreting the pair wise affinity in a probabilistic framework, we build the relationship between pair wise clustering and unsupervised classification by learning the soft Nearest Neighbor (NN) classifier from unlabeled data, and search for the optimal partition of the data points by minimizing the generalization error of the learned classifier associated with the data partitions. Modeling the underlying distribution of the data by non-parametric kernel density estimation, the asymptotic generalization error of the unsupervised soft NN classification involves only the pair wise affinity between data points. Moreover, such error rate reduces to the well-known kernel form of graph cut in case of uniform data distribution, which provides another understanding of the kernel similarity used in Laplacian Eigenmaps [1] which also assumes uniform distribution. By minimizing the generalization error bound, we propose a new clustering algorithm. Our algorithm efficiently partition the data by inference in a pair wise MRF model. Experimental results demonstrate the effectiveness of our method.

Solving nesting problems involves the waste minimisation in cutting processes, and therefore it is not only economically relevant for many industries but has also an important environmental impact, as the raw materials that are cut are usually a natural resource. However, very few exact approaches have been proposed in the literature for the nesting problem (also known as irregular packing problem), and the majority of the known approaches are heuristic algorithms, leading to suboptimal solutions. The few mathematical programming models known for this problem can be divided into discrete and continuous models, based on how the placement coordinates of the pieces to be cut are dealt with. In this paper, we propose an innovative semi-continuous mixed-integer programming model for two-dimensional cutting and packing problems with irregular shaped pieces. The model aims to exploit the advantages of the two previous classes of approaches and discretises the -axis while keeping the -coordinate continuous. The board can therefore be seen as a set of stripes. Computational results show that the model, when solved by a commercial solver, can deal with large problems and determine the optimal solution for smaller instances, but as it happens with discrete models, the optimal solution value depends on the discretisation step that is used.

Recent works using hyper-heuristics for solving clustering problems have been focusing on Genetic Algorithm. However, to the best of this research knowledge, no work is using hyper-heuristics dedicated for tuning the Genetic algorithm`s chromosome size for automatic clustering problem. The ability to tune the chromosome size is important because it allows the automatic clustering algorithm to be adaptive and dynamic. This paper proposes and evaluates a modified Improvement Selection Rules hyper-heuristic algorithm for tuning automatic genetic clustering chromosome size. The paper reviews related works of Genetic algorithm`s parameters tuning and selective hyper-heuristic algorithms and proposes a modified algorithm. The Iris, Breast Cancer, Wine and E-coli datasets are used for evaluation of the algorithm, based on the fitness, accuracy and robustness. The results indicate that the hyper-heuristic algorithm has produced good performance (fitness) and accuracy but consume considerably higher execution times.

Determination of the appropriate number of clusters is a big challenge for the bi-clustering method of the non-negative matrix factorization (NMF). The conventional determination method may be to test a number of candidates and select the optimal one with the best clustering performance. However, such strategy of repetition test is obviously time-consuming. In this paper, we propose a novel efficient algorithm called the automatic NMF clustering method with competitive sparseness constraints (autoNMF) which can perform the reasonable clustering without pre-assigning the exact number of clusters. It is demonstrated by the experiments that the autoNMF has been significantly improved on both clustering performance and computational efficiency.

Automatic clustering of spectral image data is a common problem with a diverse set of desired and potential solutions. While typical clustering techniques use first order statistics and Gaussian models, the method described in this paper utilizes the spectral data structure to generate a graph representation of the image and then clusters the data by applying the method of optimal modularity for finding communities within the graph. After defining and identifying pixel adjacencies to represent an image as an adjacency matrix, a recursive splitting is performed to group spectrally similar pixels using the method of modularity maximization. The careful selection of pixel adjacencies determines the success of this spectral clustering technique. The modularity maximization process uses the eigenvector of the modularity matrix with the largest positive eigenvalue to split groups of pixels with non-linear decision surfaces and uses the modularity measure to help estimate the optimal number of clusters to best characterize the data. Using information from each recursion, the end result is a variable level of detail cluster map that is more visually useful than previous methods. Additionally, this method outperforms many typical automatic clustering methods such k-means, especially in highly cluttered urban scenes. The optimal modularity technique hierarchically clusters spectral image data and produces results that more reliably characterize the number of clusters in the data than common automatic spectral image clustering techniques.

Context. The problem of clustering (classification without a teacher) is often occures when processing data arrays of various natures, which is quite an interesting and integral part of artificial intelligence. To solve this problem, there are many known methods and algorithms based on the principles of the distribution density of observations in the analyzed data. However, these methods are rather complicated in software implementation and are not without drawbacks, namely: the problem of determining significant clusters in datasets of different densities, multiepoch self-learning, getting stuck in local extrema of goal functions, etc. It should be noted that the methods based on the analysis of the peaks of the data distribution density are clear in nature, therefore, to expand the capabilities of these methods, it is advisable to introduce their fuzzy modification. Objective. The aim of the work is to introduce fast fuzzy data clustering using density peaks distribution of the datasets, that can find the prototypes (centroids) of clusters that overlapping regardless of the amount of incoming data. Method. The problem of fuzzy clustering data arrays based on a hybrid method that based on the simultaneous use of a credibilistic approach to fuzzy clustering and an algorithm for finding the types of distribution density of the initial data is proposed. A feature of the proposed method is computational simplicity and high speed, due to the fact that the entire array is processed only once, that is, eliminates the need for multi-era self-learning, implemented in traditional fuzzy clustering algorithms. Results. A feature of the proposed method of fast fuzzy credibilistic clustering using of density peaks distribution is characterized by computational simplicity and high speed due to the fact that the entire array is processed only once, that is, the need for multiepoch self-learning is eliminated, which is implemented in traditional fuzzy clustering algorithms. The results of the computational experiment confirm the effectiveness of the proposed approach in clustering problems under conditions in the case when the clusters are ovelap. Conclusions. The experimental results allow us to recommend the developed method for solving the problems of automatic clustering and data classification, as quickly as possible to find the centroids of clusters. The proposed method of fast fuzzy credibilistic clustering using of density peaks distribution of dataset is intended for use in computational intelligence systems, neuro-fuzzy systems, in training artificial neural networks and in clustering problems.

Clustering is an very important research topic in knowledge discovery and machine learning. But sometimes the data set for clustering contains vectors missing one or more of the feature values, and is called as incomplete. The incomplete data problem exists in a wide range of field such as computer vision, biological system, and remote sensing. The problem of clustering of incomplete data is considered in this paper. In this paper, we propose a new extended MFA (mean field annealing) algorithm to solve the problem of clustering of incomplete data in the continuous-value state space and show the result of the experiment. The traditional fuzzy clustering methods calculate the centroid vectors of the clusters and then determined the membership probability, and repeat this process until the optimum solution is found. By contrast, the method proposed in this paper perturbs the membership probability, and determines whether to accept the perturbed state or not according to the changes of the energy. The result is compared with the optimal completion strategy fuzzy c-means (FCM) clustering of incomplete data algorithm and shows that the proposed method solves the problem of clustering incomplete data very well and gets a much better result.

Chapter 8 - Bat algorithm–based automatic clustering method and its application in image processing

Every year a huge amount of money is invested by the football clubs in the transfer window period to hire or release players. Estimating players’ value in the transfer market is a crucial task for the managers of the clubs. Also, it is one of the attractive aspects of football for fans. Tranfermarkt.com is a reference website that determines the transfer fee of the players based on its members’ opinions. The limitation of this website has attracted the attention of data scientists in recent years, resulting in creating datasets and data-driven estimating methods. In this paper, a novel method for estimating the value of players in the transfer market, based on the FIFA 20 dataset, is proposed. The proposed method has two phases. In the first phase, the dataset is clustered using an automatic clustering method called APSO-clustering. This automatic clustering method, which can detect the proper number of clusters, has divided the dataset into 4 clusters automatically indicating the position of the players: goalkeepers, midfielders, defenders, and strikers. In the second phase, a hybrid regression method which is a combination of particle swarm optimization (PSO) and support vector regression (SVR), is used to build a prediction model for each clusters’ data points. In this hybrid method, PSO is used for feature selection and parameter tuning of SVR. The achieved results show that the proposed method can estimate the players’ value with an accuracy of 74%. Comparing the performance of PSO with 3 other metaheuristics, the results demonstrated the superiority of PSO over GWO, IPO, and WOA.

An automatic clustering method using multi-objective genetic algorithm with gene rearrangement and cluster merging

Pore space texture and its pore size distribution are critical parameters for displacement efficiency for waterflood, which have been applied in Middle East. For sandstone, pore size is a log-normal distribution usually. However, when it comes to carbonate reservoir, complex sedimentary and diagenesis yield complex pore size distributions including unimodal, bimodal and multimodal distribution. Therefore, it is not reasonable to classify different pore size distribution through statistic parameters such as mean, standard deviation, skewness and kurtosis. It is essential to propose a novel method to classify numerous pore size distribution results accurately and automatically by curve shape. This paper proposes the application of earth mover's distance (EMD) to pore size distribution, which is not mentioned before. The automatic clustering method is efficient and accurate to process massive data. Therefore, this method can prompt to systematic analysis and research of a giant scenario of reservoir injection characteristics in Middle East.

How to extract task-relevant components from spontaneous electroencephalogram background is an open problem in EEG signal analysis. An Independent Component Automatic Clustering (ICAC) method, which combined Independent Component Analysis (ICA) with automatic clustering, is developed in this paper. In ICAC, the ICA decomposed components were grouped into several clusters and sorted automatically. A majority of task-relevant components could be grouped into one cluster and be recognized easily, which can compensate the traditional ICA limitation of component sorting without any task specialized orders. We adopted this method on multi trails EEG signals during imaginary hand movement, results showed that ICAC can automatically extract task-relevant component and increase the Fisher Criterion (FC) separability significantly. Furthermore, we show that the residual mutual information between task-relevant components is not useless as previously regarded but very useful on components recognition.