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Abstract: Given a dataset P represented by an n×m matrix (where n is the number of data points and m is the number of attributes), we study the effect of applying transformations to P and how this affects the performance of different ensemble algorithms. Specifically, a dataset P can be transformed into a new dataset by a set of transformation operators in the instance dimension, such as sub-sampling, super-sampling, noise injection, and so on, and a corresponding set of transformation operators in the attribute dimension. Based on these conventional transformation operators and , a general form of the transformation operator is proposed to represent different kinds of transformation operators. Then, two new data transformation operators, known respectively as probabilistic based data sampling operator and probabilistic based attribute sampling operator, are designed to generate new datasets in the ensemble. Next, three new random transformation operators are proposed, which include the random combination of transformation operators in the data dimension, in the attribute dimension, and in both dimensions respectively. Finally, a new cluster ensemble approach is proposed, which integrates the random combination of data transformation operators across different dimensions, a hybrid clustering technique, a confidence measure, and the normalized cut algorithm into the ensemble framework. The experiments show that (i) random combination of transformation operators across different dimensions outperforms most of the conventional data transformation operators for different kinds of datasets. (ii) The proposed cluster ensemble framework performs well on different datasets such as gene expression datasets and datasets in the UCI machine learning repository. [Copyright &y& Elsevier]

Abstract: In this paper, a quantization-based clustering algorithm (QBCA) is proposed to cluster a large number of data points efficiently. Unlike previous clustering algorithms, QBCA places more emphasis on the computation time of the algorithm. Specifically, QBCA first assigns the data points to a set of histogram bins by a quantization function. Then, it determines the initial centers of the clusters according to this point distribution. Finally, QBCA performs clustering at the histogram bin level, rather than the data point level. We also propose two approaches to improve the performance of QBCA further: (i) a shrinking process is performed on the histogram bins to reduce the number of distance computations and (ii) a hierarchical structure is constructed to perform efficient indexing on the histogram bins. Finally, we analyze the performance of QBCA theoretically and experimentally and show that the approach: (1) can be easily implemented, (2) identifies the clusters effectively and (3) outperforms most of the current state-of-the-art clustering approaches in terms of efficiency. [Copyright &y& Elsevier]

Classification of 3D head models based on their shape attributes for subsequent indexing and retrieval are important in many applications, as in hierarchical content-based retrieval of these head models for virtual scene composition, and the automatic annotation of these characters in such scenes. While simple feature representations are preferred for more efficient classification operations, these features may not be adequate for distinguishing between the subtly different head model classes. In view of these, we propose an optimization approach based on genetic algorithm (GA) where the original model representation is transformed in such a way that the classification rate is significantly enhanced while retaining the efficiency and simplicity of the original representation. Specifically, based on the Extended Gaussian Image (EGI) representation for 3D models which summarizes the surface normal orientation statistics, we consider these orientations as random variables, and proceed to search for an optimal transformation for these variables based on genetic optimization. The resulting transformed distributions for these random variables are then used as the modified classifier inputs. Experiments have shown that the optimized transformation results in a significant improvement in classification results for a large variety of class structures. More importantly, the transformation can be indirectly realized by bin removal and bin count merging in the original histogram, thus retaining the advantage of the original EGI representation. [Copyright &y& Elsevier]

Abstract: Portfolio selection theory with fuzzy returns has been well developed and widely applied. Within the framework of credibility theory, several fuzzy portfolio selection models have been proposed such as mean–variance model, entropy optimization model, chance constrained programming model and so on. In order to solve these nonlinear optimization models, a hybrid intelligent algorithm is designed by integrating simulated annealing algorithm, neural network and fuzzy simulation techniques, where the neural network is used to approximate the expected value and variance for fuzzy returns and the fuzzy simulation is used to generate the training data for neural network. Since these models are used to be solved by genetic algorithm, some comparisons between the hybrid intelligent algorithm and genetic algorithm are given in terms of numerical examples, which imply that the hybrid intelligent algorithm is robust and more effective. In particular, it reduces the running time significantly for large size problems. [Copyright &y& Elsevier]

Abstract: In this paper, a kernelized version of clustering-based discriminant analysis is proposed that we name KCDA. The main idea is to first map the original data into another high-dimensional space, and then to perform clustering-based discriminant analysis in the feature space. Kernel fuzzy c-means algorithm is used to do clustering for each class. A group of tests on two UCI standard benchmarks have been carried out that prove our proposed method is very promising. [Copyright &y& Elsevier]

Traditional cluster ensemble approaches have several limitations. (1) Few make use of prior knowledge provided by experts. (2) It is difficult to achieve good performance in high-dimensional datasets. (3) All of the weight values of the ensemble members are equal, which ignores different contributions from different ensemble members. (4) Not all pairwise constraints contribute to the final result. In the face of this situation, we propose double weighting semi-supervised ensemble clustering based on selected constraint projection(DCECP) which applies constraint weighting and ensemble member weighting to address these limitations. Specifically, DCECP first adopts the random subspace technique in combination with the constraint projection procedure to handle high-dimensional datasets. Second, it treats prior knowledge of experts as pairwise constraints, and assigns different subsets of pairwise constraints to different ensemble members. An adaptive ensemble member weighting process is designed to associate different weight values with different ensemble members. Third, the weighted normalized cut algorithm is adopted to summarize clustering solutions and generate the final result. Finally, nonparametric statistical tests are used to compare multiple algorithms on real-world datasets. Our experiments on 15 high-dimensional datasets show that DCECP performs better than most clustering algorithms. [ABSTRACT FROM AUTHOR]

• We propose a residual generator (Rg-GAN) served as a better approximation divergence minimization framework for GAN, and prove that residual generator for standard and least-squares GAN are equivalent to the minimization of reverse-KL and a new instance of f-divergence, respectively. • We prove that Rg-GAN can be reduced to IPMs based GAN and bridge the gap between IPMs and f-divergence. • We propose a new loss function for the discriminator of Rg-GAN that manifests a better discriminative property and therefore improved on Rg-GAN generalisation ability. • We conduct experiments on multiple benchmark data sets and demonstrate that our proposed framework can mitigate the mode collapse issue and facilitate GAN to generate higher-quality images with negligible additional computation cost. GAN is a generative modelling framework which has been proven as able to minimise various types of divergence measures under an optimal discriminator. However, there is a gap between the loss function of GAN used in theory and in practice. In theory, the proof of the Jensen divergence minimisation involves the min-max criterion, but in practice the non-saturating criterion is instead used to avoid gradient vanishing. We argue that the formulation of divergence minimization via GAN is biased and may yield a poor convergence of the algorithm. In this paper, we propose the Residual Generator for GAN (Rg-GAN), which is inspired by the closed-loop control theory, to bridge the gap between theory and practice. Rg-GAN minimizes the residual between the loss of the generated data to be real and the loss of the generated data to be fake from the perspective of the discriminator. In this setting, the loss terms of the generator depend only on the generated data and therefore contribute to the optimisation of the model. We formulate the residual generator for standard GAN and least-squares GAN and show that they are equivalent to the minimisation of reverse-KL divergence and a novel instance of f-divergence, respectively. Furthermore, we prove that Rg-GAN can be reduced to Integral Probability Metrics (IPMs) GANs (e.g., Wasserstein GAN) and bridge the gap between IPMs and f-divergence. Additionally, we further improve on Rg-GAN by proposing a loss function for the discriminator that has a better discrimination ability. Experiments on synthetic and natural images data sets show that Rg-GAN is robust to mode collapse, and improves the generation quality of GAN in terms of FID and IS scores. [ABSTRACT FROM AUTHOR]