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Multi-task learning (MTL) is a joint learning paradigm to improve the generalization performance of the tasks. At present, most of MTL methods are all based on one hypothesis that all learning tasks are related and approximate for joint learning. However, this hypothesis may not be held in some scenarios, which may further lead to the problem of negative transfer. Therefore, in this paper, we aim to deal with the negative transfer problem and simultaneously improve the generalization performance in the joint learning. Combining with the subspace learning, we proposed a calibrated multi-task subspace learning method (CMTSL) under the binary group constraint. With the low-rank constraint on subspaces and the binary group indicator, our model can identify "with whom" one task should share and perform the multi-task inference on the high-dimensional parameter space in the meantime. To better approximate the low-rank constraint, we introduce a capped rank function as the tight relaxation term. Last, an iteration based re-weighted algorithm is proposed to solve our model and the convergence analysis is also proved in theory. Experimental results on benchmark datasets demonstrate the superiority of our model. [ABSTRACT FROM AUTHOR]

We develop a parallel primal-dual splitting method to solve large-scale image restoration problems, which involve the sum of several linear-operator-coupled nonsmooth but proximable terms. With the proposed method, the objective function is decomposed into pieces that can be processed individually. No inverse operator is involved in our method and the highly parallel structure makes it preferable in distributed computation. The convergence is proven and the convergence rate is analyzed. Besides, its equivalence to the relaxed parallel linearized alternating direction method of multipliers (PLADMM) is addressed. Applications to image restoration problems with compound l 1 -regularizer and comparisons with state-of-the-art methods are detailed to show the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

As graph technology is widely used in unsupervised dimensionality reduction, many methods automatically construct a full connection graph to learn the structure of data, and then preserve critical information on data in subspace. The construction of a full connection graph with heavy computational complexity, however, is separated from the optimization of transformation matrix. In order to solve significant computational burden, we design anchor-based graph and unify the construction of graph and optimization of transformation matrix into a framework called fast unsupervised embedding learning with anchor-based graph (FUAG) which not only can avoid the impact of noises and redundant features in original space, but also can capture local structure of data in subspace precisely. Our method additionally incorporates the discriminant information of data captured by using trace difference form. Meanwhile, it optimizes the anchor-based graph partitioning problem with Constrained Laplacian Rank in order to ensure that the number of connected components is exactly equal to the number of classes. We also impose ℓ 0 norm constraint on each point to avoid trivial solutions and propose an efficient iterative algorithm. Experimental results on both synthetic and real-world datasets demonstrate the promising performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

• The proposed model is built on Grassmann manifold. • The proposed model can fully mine the subspace information of views. • The proposed model can get clustering results directly without postprocessing. • The proposed model can ensure the inconsistency of different views. • The proposed model with effectiveness and efficiency can be applied to practice. Multi-view clustering plays an important role in a wide spectrum of applications. In this article, we propose a multi-view clustering approach with adaptive Procrustes on Grassmann manifold (MC-APGM) to overcome the three demerits in existing graph-based multi-view clustering methods, namely, insufficient mining of subspace information of views, a requirement for post-processing, and high computational complexity. Specifically, in the proposed model, the indicator matrix is directly learned from multiple orthogonal spectral embeddings, avoiding the random clustering results caused by post-processing; The orthogonal form of the indicator matrix approximates multiple orthogonal spectral embeddings on the Grassmann manifold, fully uncovering subspace information of views and thus improving clustering performance; Both implicitly and explicitly weighted learning mechanisms are established to capture inconsistencies among different views. Moreover, an efficient algorithm with rigorous convergence guarantee is derived to optimize the proposed model. Finally, experimental results on both toy and real-world datasets demonstrate the effectiveness and efficiency of this proposed method. [ABSTRACT FROM AUTHOR]

We derive a parallel alternating direction method of multipliers (PADMM) and apply it to compound l 1 -regularized imaging inverse problems. The proposed method is capable of locating the saddle point of large-scale convex minimization problems with the sum of several nonsmooth but proximable terms. Using an operator splitting strategy, the objective is decomposed into subproblems that are conveniently, individually and simultaneously solved. With the assistance of the Moreau decomposition, our method excludes auxiliary variables that exist in the ADMM and possesses a compacter structure. Thus, the proposed method is preferable in distributed computation. The convergence proof and convergence rate analysis are presented. Application to both image restoration and image compressed sensing demonstrates the effectiveness and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

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]

In this paper, we present a unified representation based on the spatio-temporal steerable pyramid (STSP) for the holistic representation of human actions. A video sequence is viewed as a spatio-temporal volume preserving all the appearance and motion information of an action in it. By decomposing the spatio-temporal volumes into band-passed sub-volumes, the spatio-temporal Laplacian pyramid provides an effective technique for multi-scale analysis of video sequences, and spatio-temporal patterns with different scales could be well localized and captured. To efficiently explore the underlying local spatio-temporal orientation structures at multiple scales, a bank of three-dimensional separable steerable filters are conducted on each of the sub-volume from the Laplacian pyramid. The outputs of the quadrature pair of steerable filters are squared and summed to yield a more robust oriented energy representation. To be further invariant and compact, a spatio-temporal max pooling operation is performed between responses of the filtering at adjacent scales and over spatio-temporal neighbourhoods. In order to capture the appearance, local geometric structure and motion of an action, we apply the STSP on the intensity, 3D gradients and optical flow of video sequences, yielding a unified holistic representation of human actions. Taking advantage of multi-scale, multi-orientation analysis and feature pooling, STSP produces a compact but informative and invariant representation of human actions. We conduct extensive experiments on the KTH, UCF Sports and HMDB51 datasets, which shows the unified STSP achieves comparable results with the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Unsupervised Feature Selection (UFS) methods are known to produce models with excellent ability to select high-quality features. This advantage, however, is challenged when analyzing noisy real-world data, where anomalies are prevalent. For example, there may be a feature (anomalous feature) that is corrupted across many samples or a sample (anomalous sample) that has more corruptions than its peers. Previous literature focused on addressing anomalous samples, and methods that are robust to both types of anomalies have been under-explored. This paper proposes a novel general framework for reconstruction-based UFS methods, which can be embedded into the feature learning process to simultaneously remove anomalous samples and features. Specifically, the framework learns double binary weight vectors to assign 0 weights to samples or features with the highest reconstruction errors and 1 weights to the others when computing reconstruction errors. By discarding the 0-weighted samples and features when updating the model parameters, the anomalies in the data are excluded. This allows the model to focus more on learning from the clean part of the noisy data. Our proposed framework is then integrated with AutoEncoder Feature Selector (AEFS [10]) to develop a new method, which jointly performs anomaly removal and feature selection. The experimental results demonstrate the effectiveness of the proposed framework. Particularly, processing both types of anomalies provides better robustness than processing only one type. Moreover, our proposed method outperforms several state-of-the-art methods on various real-world datasets. [ABSTRACT FROM AUTHOR]

Hashing, a widely-studied tool to the approximate nearest neighbor search, aims to embed samples as compact binary representations. Current approaches to this issue generally seek a low-dimensional Hamming Space where representations are discrete and have smaller intra-class distance and larger inter-class distance. As a result, the performance is often limited by the discrete constraint. In this work, we propose to seek an angularly discriminative Embedding Space where representations are continuous and have smaller intra-class angular margin and larger inter-class angular margin. For our goal is to learn continuous representations rather than discrete hash codes, the problems caused by discrete constraint can be avoided. Besides, in order to further reduce the gap between Embedding Space and Hamming Space, we introduce an additional coordinate-constraint for representations. Our method is simple yet effective. Extensive experiments on the image retrieval task show that it achieves encouraging results on four benchmark datasets. Furthermore, the success of our proposed method demonstrates that leveraging the progress made in representation learning to improve hashing is promising in future. [ABSTRACT FROM AUTHOR]

Linear Discriminant Analysis (LDA) is one of most important methods in dimensionality reduction domain, which is limited with Gaussian assumption. Because of the complexity of real data, data often presents non-Gaussian distribution that points in same class can be divided into several sub-clusters and center point is not enough to describe the distribution of data. In order to solve non-Gaussian data, LDA-based methods consider local structure information through measuring each pairwise distance of full connection graph. However, the strategy of establishing fully-connected graph is at expense of high computational complexity and limits it practical and industrial applications. We propose a Fast Local Representation Learning (FLRL) method which leverages anchor points to establish anchor-based graph and uses similarity matrix to depict the relationships of each pairwise connections. Notably, to avoid the affect of noises and redundant features in original space, anchor points and similarity matrix are updated alternately in subspace that local structure of data will be more precise to learn. Extensive pattern classification and image retrieval experiments on several synthetic datasets, well-known datasets and deep features datasets demonstrate the advantages of our method over the state-of-the-art methods. Our source code available on : https://github.com/superzcy/FLRL. [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]

Fuzzy c-means (FCM) is a classic unsupervised clustering algorithm in machine learning fields. Euclidean distance is a frequently used distance metric in FCM, but it is only suitable for data with spherical clusters. Therefore, Mahalanobis distance was introduced into Gustafson-Kessel Fuzzy C-Means (GK-FCM) to help improve the performance on data with ellipsoidal clusters. However, GK-FCM and existing Mahalanobis distance based algorithms only focus on squared Mahalanobis distance, because squared Mahalanobis distance based problems are usually convex and easily solvable. But squared Mahalanobis distance is not a perfect metric, because it tends to exaggerate the influence of outliers and lead to unsatisfying results. In this paper, we propose a rooted Mahalanobis distance based GK-FCM model, which has better clustering performance and superior robustness than traditional GK-FCM. Moreover, owing to the introduction of rooted Mahalanobis distance, the optimization of the proposed model becomes non-trivial and it is not realistic to obtain a closed-form solution as that of traditional GK-FCM. In this paper, by making reference to the re-weighted method, we develop a novel iterative converging algorithm to optimize the proposed model. Finally, extensive experiments are conducted on both synthetic and real-world data sets to manifest the superiority of the proposed model. [ABSTRACT FROM AUTHOR]

Abstract Given the explosive growth of online videos, it is becoming increasingly important to relieve the tedious work of browsing and managing the video content of interest. Video summarization aims at providing such a technique by transforming one or multiple videos into a compact one. However, conventional multi-video summarization methods often fail to produce satisfying results as they ignore the users' search intents. To this end, this paper proposes a novel query-aware approach by formulating the multi-video summarization in a sparse coding framework, where the web images searched by a query are taken as the important preference information to reveal the query intent. To provide a user-friendly summarization, this paper also develops an event-keyframe presentation structure to present keyframes in groups of specific events related to the query by using an unsupervised multi-graph fusion method. Moreover, we release a new public dataset named MVS1K, which contains about 1000 videos from 10 queries and their video tags, manual annotations, and associated web images. Extensive experiments on the MVS1K and TVSum datasets demonstrate that our approaches produce competitively objective and subjective results. [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]

Breast cancer is one of the most commonly diagnosed cancer types among women. Sonography has been regarded as an important imaging modality for diagnosis of breast lesions. Due to the speckle and the variance in shape and appearance of sonographic lesions, fully automatic segmentation of the breast tumor regions still remains a challenging task. In this paper, we propose an automatic interaction scheme based on an object recognition method to segment the lesions in breast ultrasound images. In this scheme, a 2D ultrasound image is firstly filtered with a total-variation model to reduce the speckle noise. A robust graph-based segmentation method is then used to segment the image into a number of sub-regions. An object recognition method incorporating the procedures of image feature extraction, feature selection and classification is proposed to automatically identify the regions which are associated with breast tumors. Finally, an active contour model is used to refine the contours of the regions that are recognized as tumors. This scheme is validated on a database of 46 breast ultrasound images with diagnosed tumors. The experimental results show that our scheme can segment the breast ultrasound images automatically, indicating its good performance in real applications. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel re-texturing approach using intrinsic video. Our approach first indicates the regions of interest by contour-aware layer segmentation. The intrinsic video including reflectance and illumination components within the segmented region is recovered by our weighted energy optimization. We then compute the texture coordinates in key frames and the normals for the re-textured region using the optimization approach we develop. Meanwhile, the texture coordinates in non-key frames are optimized by our energy function. When the target sample texture is specified, the re-textured video is finally created by multiplying the re-textured reflectance component with the original illumination component within the replaced region. As shown in our experimental results, our method can produce high quality video re-texturing results with a variety of sample textures, and also the lighting and shading effects of the original videos are well preserved after re-texturing. [ABSTRACT FROM AUTHOR]

Feature analysis plays an important role in many multispectral image applications and scale invariant feature transform (SIFT) has been successfully applied for extraction of image features. However, the existing SIFT algorithms cannot extract features from multispectral images directly. This paper puts forward a novel algorithmic framework based on the SIFT for multispectral images. Firstly, with the theory of the geometric algebra (GA), a new representation of multispectral image including spatial and spectral information is put forward and discussed. Secondly, a new method for obtaining the scale space of the multispectral image is proposed. Thirdly, following the procedures of the SIFT, the GA based difference of Gaussian images are computed and the keypoints can be detected in the GA space. Fourthly, the feature points are finally detected and described in the mathematical framework of the GA. Finally, the comparison results show that the GA-SIFT outperforms some previously reported SIFT algorithms in the feature extraction from a multispectral image, and it is comparable with its counterparts in the feature extraction of color images, indicating good performance in various applications of image analysis. [ABSTRACT FROM AUTHOR]