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Abstract Locality preserving projection (LPP) is a classical tool for dimensionality reduction and feature extraction. It usually makes use of the ℓ 2 -norm criterion for optimization, and is thus sensitive to outliers. In order to achieve robustness, LPP-L1 is proposed by employing the ℓ 1 -norm as distance criterion. However, the edge weights of LPP-L1 measure only the dissimilarity of pairs of vertices and ignore the preservation of the similarity. In this paper, we develop a novel algorithm, termed as ILPP-L1, in which the ℓ 1 -norm is utilized to obtain robustness and the similarities of pairs of vertices are effectively preserved, simultaneously. ILPP-L1 is robust to outliers because of the use of the ℓ 1 -norm. The ℓ 1 -norm minimization problem is directly solved, which ensures the preservation of the similarity of pairs of vertices. The solution is justified to converge to local minimum. In addition, ILPP-L1 avoids small sample size problem. Experiment results on benchmark databases confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract In many real applications of machine learning and data mining, we are often confronted with high-dimensional data represented by heterogeneous features or views, which describe different perspectives of the data. Efficiently clustering such data is a challenge. To address this problem, we propose a unified and embedded framework referred to as multi-view embedded clustering with trace ratio (MECTR), which performs dimensionality reduction and clustering simultaneously, and adaptively controls the interactions among different views at the same time. Within this framework, we are able not only to obtain multiple discriminative subspaces synchronously, but also keep the clustering results consistent among different views. We also develop an alternate iterative optimization strategy to learn the common clustering indicator, multiple discriminative subspaces and weights for heterogeneous features with convergence. Comprehensive experiments on synthesis dataset and three benchmark datasets demonstrate the superiority of the proposed work. [ABSTRACT FROM AUTHOR]

With the development of ultra-high-resolution display devices, the visual perception of fine texture details is becoming increasingly important. Traditional image upsampling methods suffer from either loss of high-frequency texture details or very high time cost. In this paper, we propose an iterative projection reconstruction (IPR) method for fast and efficient image upsampling. The proposed method refines high-frequency texture details with an iterative projection process, and utilizes the pre-computed projection matrix to accelerate the example-based image reconstruction. As a result, the proposed method can reproduce fine texture details with low time cost. Experimental results demonstrate that the proposed method outperforms some state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In this paper, an efficient local operator, namely the Local Quantization Code (LQC), is proposed for texture classification. The conventional local binary pattern can be regarded as a special local quantization method with two levels, 0 and 1. Some variants of the LBP demonstrate that increasing the local quantization level can enhance the local discriminative capability. Hence, we present a simple and unified framework to validate the performance of different local quantization levels. In the proposed LQC, pixels located in different quantization levels are separately counted and the average local gray value difference is adopted to set a series of quantization thresholds. Extensive experiments are carried out on several challenging texture databases. The experimental results demonstrate the LQC with appropriate local quantization level can effectively characterize the local gray-level distribution. [ABSTRACT FROM AUTHOR]

Diagonal principal component analysis (DiaPCA) is an important method for dimensionality reduction and feature extraction. It usually makes use of the ℓ 2 -norm criterion for optimization, and is thus sensitive to outliers. In this paper, we present a DiaPCA with non-greedy ℓ 1 -norm maximization (DiaPCA-L1 non-greedy), which is more robust to outliers. Experimental results on two benchmark datasets show the effectiveness and advantages of our proposed method. [ABSTRACT FROM AUTHOR]

Abstract: An efficient parallel algorithm for the minimum crossing number problem is presented. The algorithm, which is designed to embed the edges of a graph such that the total number of crossings is minimized, is based on an improved Hopfield neural network in which the internal dynamics is modified to permit temporary increases of the energy function so that the network can escape from local minima. The proposed algorithm is tested on several complete graphs and the simulation results show that the proposed algorithm provides a high probability of finding optimal solutions. [Copyright &y& Elsevier]

This paper presents an improved genetic algorithm (GA) for solving the subset sum problem (SSP). Unlike a conventional GA, the proposed algorithm performs conditional (and not probable) crossover and mutation. Simulation results show that the proposed GA is capable of finding an optimal solution for the SSP. [Copyright &y& Elsevier]

In this letter, we utilize the Hopfield network learning method to adjust the balance between constraint term and cost term of the energy function so that the local minimum that the network once falls into vanishes and the network can continue updating in a gradient descent direction of energy. We applied the proposed learning method to the traveling salesman problem to show that the method is capable of finding an optimal solution or a near-optimal solution in a shorter time. [Copyright &y& Elsevier]

Classification plays a significant role in production activities and lives. In this era of big data, it is especially important to design efficient classifiers with high classification accuracy for large scale datasets. In this paper, we propose a randomly partitioned and a Principal Component Analysis (PCA)-partitioned multivariate decision tree classifiers, of which the training time is quite short and the classification accuracy is quite high. Approximately balanced trees are created in the form of a full binary tree based on two simple ways of generating multivariate combination weights and a median-based method to select the divide value having ensured the efficiency and effectiveness of the proposed algorithms. Extensive experiments conducted on a series of large datasets have demonstrated that the proposed methods are superior to other classifiers in most cases. [ABSTRACT FROM AUTHOR]