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Effective dimensionality reduction is a classical research area for many large-scale analysis tasks in computer vision. Several recent methods attempt to learn either graph embedding or binary hashing for fast and accurate applications. In this paper, we propose a novel framework to automatically learn the task-specific compact coding, called evolutionary compact embedding (ECE), which can be regarded as an optimization algorithm combining genetic programming (GP) and a boosting trick. As an evolutionary computation methodology, GP can solve problems inspired by natural evolution without any prior knowledge of the solutions. In our evolutionary architecture, each bit of ECE is iteratively computed using a binary classification function, which is generated through GP evolving by jointly minimizing its empirical risk with the AdaBoost strategy on a training set. We address this as greedy optimization leading to small Hamming distances for similar samples and large distances for dissimilar samples. We then evaluate ECE on four image datasets: USPS digital hand-writing, CMU PIE face, CIFAR-10 tiny image and SUN397 scene, showing the accurate and robust performance of our method for large-scale image classification. [ABSTRACT FROM AUTHOR]

Matrix completion from very limited information is an important machine learning topic, and has received extensive attention in various scientific applications. Matrix completion aims at finding a low-rank matrix to approximate the incomplete data matrix. However, noise in the data matrix may degrade the performance of the existing matrix completion algorithms, especially if there are different types of noise. In this paper, we proposed a robust matrix completion method with column outliers and sparse noise. The incomplete matrix is iteratively divided into low-rank and sparse parts. The ℓ 2 , 1 -norm based objective function makes the recovered matrix keeps a low-rank structure and lets the algorithm robust to column outliers, while the regularization term based on ℓ 1 -norm can alleviate the influence of sparse noise. Besides, a vector completion algorithm has been proposed to help us estimate the missing entries of the out-of-sample vectors. Moreover, the proposed model can be optimized by an efficient iterative re-weighted method, without introducing any additional parameters, while the adaptive weights obtained in the optimization process can help us detect column outliers. Both theoretical analysis and experiments based on synthetic datasets and real world datasets are implemented to validate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

The Steiner travelling salesman problem (STSP) is an important issue in intelligent transportation systems and has various practical applications, such as travelling and parcel delivery. In this study, we consider the STSP in real-world road maps, i.e., given a road map with a set of service points or intersections, selection of the representative vertices of a graph G to determine a closed route so a vehicle can visit each service point at least once with the minimum cost. It has been theoretically proved that the STSP and its ancestor, travelling salesman problem, are NP-hard. However, it has been empirically demonstrated that they can be solved efficiently on planar graphs with small branchwidths. Therefore, we propose a branch decomposition-based extraction algorithm for the STSP in planar graphs. Our algorithm can solve the STSP in a planar graph G with a time complexity of 2 O ( bw ( G )) n O (1) , where bw ( G ) is the branchwidth of G . In the case of planar graphs with a small branchwidth, our algorithm performs efficiently. We evaluated our algorithm by applying it to real-world urban road maps, which demonstrated the suitability of our method for real-world applications. [ABSTRACT FROM AUTHOR]

Nonnegative matrix factorization (NMF) has been successfully used in many fields as a low-dimensional representation method. Projective nonnegative matrix factorization (PNMF) is a variant of NMF that was proposed to learn a subspace for feature extraction. However, both original NMF and PNMF are sensitive to noise and are unsuitable for feature extraction if data is grossly corrupted. In order to improve the robustness of NMF, a framework named Projective Robust Nonnegative Factorization (PRNF) is proposed in this paper for robust image feature extraction and classification. Since learned projections can weaken noise disturbances, PRNF is more suitable for classification and feature extraction. In order to preserve the geometrical structure of original data, PRNF introduces a graph regularization term which encodes geometrical structure. In the PRNF framework, three algorithms are proposed that add a sparsity constraint on the noise matrix based on L 1/2 norm, L 1 norm, and L 2, 1 norm, respectively. Robustness and classification performance of the three proposed algorithms are verified with experiments on four face image databases and results are compared with state-of-the-art robust NMF-based algorithms. Experimental results demonstrate the robustness and effectiveness of the algorithms for image classification and feature extraction. [ABSTRACT FROM AUTHOR]