Automatic Subspace Learning via Principal Coefficients Embedding

A supervised discriminant data representation: application to pattern classification

The performance of machine learning and pattern recognition algorithms generally depends on data representation. That is why, much of the current effort in performing machine learning algorithms goes into the design of preprocessing frameworks and data transformations able to support effective machine learning. The method proposed in this work consists of a hybrid linear feature extraction scheme to be used in supervised multi-class classification problems. Inspired by two recent linear discriminant methods: robust sparse linear discriminant analysis (RSLDA) and inter-class sparsity-based discriminative least square regression (ICS_DLSR), we propose a unifying criterion that is able to retain the advantages of these two powerful methods. The resulting transformation relies on sparsity-promoting techniques both to select the features that most accurately represent the data and to preserve the row-sparsity consistency property of samples from the same class. The linear transformation and the orthogonal matrix are estimated using an iterative alternating minimization scheme based on steepest descent gradient method and different initialization schemes. The proposed framework is generic in the sense that it allows the combination and tuning of other linear discriminant embedding methods. According to the experiments conducted on several datasets including faces, objects, and digits, the proposed method was able to outperform competing methods in most cases.

An enhanced approach to the robust discriminant analysis and class sparsity based embedding

In recent times, feature extraction attracted much attention in machine learning and pattern recognition fields. This paper extends and improves a scheme for linear feature extraction that can be used in supervised multi-class classification problems. Inspired by recent frameworks for robust sparse LDA and Inter-class sparsity, we propose a unifying criterion able to retain the advantages of these two powerful linear discriminant methods. We introduce an iterative alternating minimization scheme in order to estimate the linear transformation and the orthogonal matrix. The linear transformation is efficiently updated via the steepest descent gradient technique. The proposed framework is generic in the sense that it allows the combination and tuning of other linear discriminant embedding methods. We used our proposed method to fine tune the linear solutions delivered by two recent linear methods: RSLDA and RDA_FSIS. Experiments have been conducted on public image datasets of different types including objects, faces, and digits. The proposed framework compared favorably with several competing methods.

Discriminative Label Relaxed Regression with Adaptive Graph Learning

The traditional label relaxation regression (LRR) algorithm directly fits the original data without considering the local structure information of the data. While the label relaxation regression algorithm of graph regularization takes into account the local geometric information, the performance of the algorithm depends largely on the construction of graph. However, the traditional graph structures have two defects. First of all, it is largely influenced by the parameter values. Second, it relies on the original data when constructing the weight matrix, which usually contains a lot of noise. This makes the constructed graph to be often not optimal, which affects the subsequent work. Therefore, a discriminative label relaxation regression algorithm based on adaptive graph (DLRR_AG) is proposed for feature extraction. DLRR_AG combines manifold learning with label relaxation regression by constructing adaptive weight graph, which can well overcome the problem of label overfitting. Based on a large number of experiments, it can be proved that the proposed method is effective and feasible.

Deep Spectral Representation Learning From Multi-View Data

Multi-view representation learning (MvRL) aims to learn a consensus representation from diverse sources or domains to facilitate downstream tasks such as clustering, retrieval, and classification. Due to the limited representative capacity of the adopted shallow models, most existing MvRL methods may yield unsatisfactory results, especially when the labels of data are unavailable. To enjoy the representative capacity of deep learning, this paper proposes a novel multi-view unsupervised representation learning method, termed as Multi-view Laplacian Network (MvLNet), which could be the first deep version of the multi-view spectral representation learning method. Note that, such an attempt is nontrivial because simply combining Laplacian embedding (i.e., spectral representation) with neural networks will lead to trivial solutions. To solve this problem, MvLNet enforces an orthogonal constraint and reformulates it as a layer with the help of Cholesky decomposition. The orthogonal layer is stacked on the embedding network so that a common space could be learned for consensus representation. Compared with numerous recent-proposed approaches, extensive experiments on seven challenging datasets demonstrate the effectiveness of our method in three multi-view tasks including clustering, recognition, and retrieval. The source code could be found at www.pengxi.me.

Dual Shared-Specific Multiview Subspace Clustering

Multiview subspace clustering has received significant attention as the availability of diverse of multidomain and multiview real-world data has rapidly increased in the recent years. Boosting the performance of multiview clustering algorithms is challenged by two major factors. First, since original features from multiview data are highly redundant, reconstruction based on these attributes inevitably results in inferior performance. Second, since each view of such multiview data may contain unique knowledge as against the others, it remains a challenge to exploit complimentary information across multiple views while simultaneously investigating the uniqueness of each view. In this paper, we present a novel dual shared-specific multiview subspace clustering (DSS-MSC) approach that simultaneously learns the correlations between shared information across multiple views and also utilizes view-specific information to depict specific property for each independent view. Further, we formulate a dual learning framework to capture shared-specific information into the dimensional reduction and self-representation processes, which strengthens the ability of our approach to exploit shared information while preserving view-specific property effectively. The experimental results on several benchmark datasets have demonstrated the effectiveness of the proposed approach against other state-of-the-art techniques.

Linear embedding by joint Robust Discriminant Analysis and Inter-class Sparsity

Linear Discriminant Analysis (LDA) and its variants are widely used as feature extraction methods. They have been used for different classification tasks. However, these methods have some limitations that need to be overcome. The main limitation is that the projection obtained by LDA does not provide a good interpretability for the features. In this paper, we propose a novel supervised method used for multi-class classification that simultaneously performs feature selection and extraction. The targeted projection transformation focuses on the most discriminant original features, and at the same time, makes sure that the transformed features (extracted features) belonging to each class have common sparsity. Our proposed method is called Robust Discriminant Analysis with Feature Selection and Inter-class Sparsity (RDA_FSIS). The corresponding model integrates two types of sparsity. The first type is obtained by imposing the ℓ_2,1 constraint on the projection matrix in order to perform feature selection. The second type of sparsity is obtained by imposing the inter-class sparsity constraint used for ensuring a common sparsity structure in each class. An orthogonal matrix is also introduced in our model in order to guarantee that the extracted features can retain the main variance of the original data and thus improve the robustness to noise. The proposed method retrieves the LDA transformation by taking into account the two types of sparsity. Various experiments are conducted on several image datasets including faces, objects and digits. The projected features are used for multi-class classification. Obtained results show that the proposed method outperforms other competing methods by learning a more compact and discriminative transformation.

Dynamic Collaborative Tracking

Correlation filter has been demonstrated remarkable success for visual tracking recently. However, most existing methods often face model drift caused by several factors, such as unlimited boundary effect, heavy occlusion, fast motion, and distracter perturbation. To address the issue, this paper proposes a unified dynamic collaborative tracking framework that can perform more flexible and robust position prediction. Specifically, the framework learns the object appearance model by jointly training the objective function with three components: target regression submodule, distracter suppression submodule, and maximum margin relation submodule. The first submodule mainly takes advantage of the circulant structure of training samples to obtain the distinguishing ability between the target and its surrounding background. The second submodule optimizes the label response of the possible distracting region close to zero for reducing the peak value of the confidence map in the distracting region. Inspired by the structure output support vector machines, the third submodule is introduced to utilize the differences between target appearance representation and distracter appearance representation in the discriminative mapping space for alleviating the disturbance of the most possible hard negative samples. In addition, a CUR filter as an assistant detector is embedded to provide effective object candidates for alleviating the model drift problem. Comprehensive experimental results show that the proposed approach achieves the state-of-the-art performance in several public benchmark data sets.

Robust Kronecker Component Analysis

Dictionary learning and component analysis models are fundamental for learning compact representations that are relevant to a given task (feature extraction, dimensionality reduction, denoising, etc.). The model complexity is encoded by means of specific structure, such as sparsity, low-rankness, or nonnegativity. Unfortunately, approaches like K-SVD - that learn dictionaries for sparse coding via Singular Value Decomposition (SVD) - are hard to scale to high-volume and high-dimensional visual data, and fragile in the presence of outliers. Conversely, robust component analysis methods such as the Robust Principal Component Analysis (RPCA) are able to recover low-complexity (e.g., low-rank) representations from data corrupted with noise of unknown magnitude and support, but do not provide a dictionary that respects the structure of the data (e.g., images), and also involve expensive computations. In this paper, we propose a novel Kronecker-decomposable component analysis model, coined as Robust Kronecker Component Analysis (RKCA), that combines ideas from sparse dictionary learning and robust component analysis. RKCA has several appealing properties, including robustness to gross corruption; it can be used for low-rank modeling, and leverages separability to solve significantly smaller problems. We design an efficient learning algorithm by drawing links with a restricted form of tensor factorization, and analyze its optimality and low-rankness properties. The effectiveness of the proposed approach is demonstrated on real-world applications, namely background subtraction and image denoising and completion, by performing a thorough comparison with the current state of the art.

Feature Extraction for Incomplete Data Via Low-Rank Tensor Decomposition With Feature Regularization

Multidimensional data (i.e., tensors) with missing entries are common in practice. Extracting features from incomplete tensors is an important yet challenging problem in many fields such as machine learning, pattern recognition, and computer vision. Although the missing entries can be recovered by tensor completion techniques, these completion methods focus only on missing data estimation instead of effective feature extraction. To the best of our knowledge, the problem of feature extraction from incomplete tensors has yet to be well explored in the literature. In this paper, we therefore tackle this problem within the unsupervised learning environment. Specifically, we incorporate low-rank tensor decomposition with feature variance maximization (TDVM) in a unified framework. Based on orthogonal Tucker and CP decompositions, we design two TDVM methods, TDVM-Tucker and TDVM-CP, to learn low-dimensional features viewing the core tensors of the Tucker model as features and viewing the weight vectors of the CP model as features. TDVM explores the relationship among data samples via maximizing feature variance and simultaneously estimates the missing entries via low-rank Tucker/CP approximation, leading to informative features extracted directly from observed entries. Furthermore, we generalize the proposed methods by formulating a general model that incorporates feature regularization into low-rank tensor approximation. In addition, we develop a joint optimization scheme to solve the proposed methods by integrating the alternating direction method of multipliers with the block coordinate descent method. Finally, we evaluate our methods on six real-world image and video data sets under a newly designed multiblock missing setting. The extracted features are evaluated in face recognition, object/action classification, and face/gait clustering. Experimental results demonstrate the superior performance of the proposed methods compared with the state-of-the-art approaches.

Robust Subspace Clustering with Compressed Data

Dimension reduction is widely regarded as an effective way for decreasing the computation, storage and communication loads of data-driven intelligent systems, leading to a growing demand for statistical methods that allow analysis (e.g., clustering) of compressed data. We therefore study in this paper a novel problem called compressive robust subspace clustering, which is to perform robust subspace clustering with the compressed data, and which is generated by projecting the original high-dimensional data onto a lower-dimensional subspace chosen at random. Given only the compressed data and sensing matrix, the proposed method, row space pursuit (RSP), recovers the authentic row space that gives correct clustering results under certain conditions. Extensive experiments show that RSP is distinctly better than the competing methods, in terms of both clustering accuracy and computational efficiency.

Ship Detection for Optical Remote Sensing Images Based on Visual Attention Enhanced Network

Ship detection plays a significant role in military and civil fields. Although some state-of-the-art detection methods, based on convolutional neural networks (CNN) have certain advantages, they still cannot solve the challenge well, including the large size of images, complex scene structure, a large amount of false alarm interference, and inshore ships. This paper proposes a ship detection method from optical remote sensing images, based on visual attention enhanced network. To effectively reduce false alarm in non-ship area and improve the detection efficiency from remote sensing images, we developed a light-weight local candidate scene network(L2CSN) to extract the local candidate scenes with ships. Then, for the selected local candidate scenes, we propose a ship detection method, based on the visual attention DSOD(VA-DSOD). Here, to enhance the detection performance and positioning accuracy of inshore ships, we both extract semantic features, based on DSOD and embed a visual attention enhanced network in DSOD to extract the visual features. We test the detection method on a large number of typical remote sensing datasets, which consist of Google Earth images and GaoFen-2 images. We regard the state-of-the-art method [sliding window DSOD (SW+DSOD)] as a baseline, which achieves the average precision (AP) of 82.33%. The AP of the proposed method increases by 7.53%. The detection and location performance of our proposed method outperforms the baseline in complex remote sensing scenes.

Cost-Effective Object Detection: Active Sample Mining With Switchable Selection Criteria

Though quite challenging, leveraging large-scale unlabeled or partially labeled data in learning systems (e.g., model/classifier training) has attracted increasing attentions due to its fundamental importance. To address this problem, many active learning (AL) methods have been proposed that employ up-to-date detectors to retrieve representative minority samples according to predefined confidence or uncertainty thresholds. However, these AL methods cause the detectors to ignore the remaining majority samples (i.e., those with low uncertainty or high prediction confidence). In this paper, by developing a principled active sample mining (ASM) framework, we demonstrate that cost-effective mining samples from these unlabeled majority data are a key to train more powerful object detectors while minimizing user effort. Specifically, our ASM framework involves a switchable sample selection mechanism for determining whether an unlabeled sample should be manually annotated via AL or automatically pseudolabeled via a novel self-learning process. The proposed process can be compatible with mini-batch-based training (i.e., using a batch of unlabeled or partially labeled data as a one-time input) for object detection. In this process, the detector, such as a deep neural network, is first applied to the unlabeled samples (i.e., object proposals) to estimate their labels and output the corresponding prediction confidences. Then, our ASM framework is used to select a number of samples and assign pseudolabels to them. These labels are specific to each learning batch based on the confidence levels and additional constraints introduced by the AL process and will be discarded afterward. Then, these temporarily labeled samples are employed for network fine-tuning. In addition, a few samples with low-confidence predictions are selected and annotated via AL. Notably, our method is suitable for object categories that are not seen in the unlabeled data during the learning process. Extensive experiments on two public benchmarks (i.e., the PASCAL VOC 2007/2012 data sets) clearly demonstrate that our ASM framework can achieve performance comparable to that of the alternative methods but with significantly fewer annotations.

Marginal Representation Learning With Graph Structure Self-Adaptation

Learning discriminative feature representations has shown remarkable importance due to its promising performance for machine learning problems. This paper presents a discriminative data representation learning framework by employing a simple yet powerful marginal regression function with probabilistic graphical structure adaptation. A marginally structured representation learning (MSRL) method is proposed by seamlessly incorporating distinguishable regression targets analysis, graph structure adaptation, and robust linear structural learning into a joint framework. Specifically, MSRL learns marginal regression targets from data rather than exploiting the conventional zero-one matrix that greatly hinders the freedom of regression fitness and degrades the performance of regression results. Meanwhile, an optimized graph regularization term with self-improving adaptation is constructed based on probabilistic connection knowledge to improve the compactness of the learned representation. Additionally, the regression targets are further predicted by utilizing the explanatory factors from the latent subspace of data, which can uncover the underlying feature correlations to enhance the reliability. The resulting optimization problem can be elegantly solved by an efficient iterative algorithm. Finally, the proposed method is evaluated by eight diverse but related tasks, including object, face, texture, and scene, categorization data sets. The encouraging experimental results and the explicit theoretical analysis demonstrate the efficacy of the proposed representation learning method in comparison with state-of-the-art algorithms.

Structured AutoEncoders for Subspace Clustering

Existing subspace clustering methods typically employ shallow models to estimate underlying subspaces of unlabeled data points and cluster them into corresponding groups. However, due to the limited representative capacity of the employed shallow models, those methods may fail in handling realistic data without the linear subspace structure. To address this issue, we propose a novel subspace clustering approach by introducing a new deep model-Structured AutoEncoder (StructAE). The StructAE learns a set of explicit transformations to progressively map input data points into nonlinear latent spaces while preserving the local and global subspace structure. In particular, to preserve local structure, the StructAE learns representations for each data point by minimizing reconstruction error w.r.t. itself. To preserve global structure, the StructAE incorporates a prior structured information by encouraging the learned representation to preserve specified reconstruction patterns over the entire data set. To the best of our knowledge, StructAE is one of first deep subspace clustering approaches. Extensive experiments show that the proposed StructAE significantly outperforms 15 state-of-the-art subspace clustering approaches in terms of five evaluation metrics.

Angle 2DPCA: A New Formulation for 2DPCA

2-D principal component analysis (2DPCA), which employs squared -norm as the distance metric, has been widely used in dimensionality reduction for data representation and classification. It, however, is commonly known that squared -norm is very sensitivity to outliers. To handle this problem, we present a novel formulation for 2DPCA, namely Angle-2DPCA. It employs -norm as the distance metric and takes into consideration the relationship between reconstruction error and variance in the objective function. We present a fast iterative algorithm to solve the solution of Angle-2DPCA. Experimental results on the Extended Yale B, AR, and PIE face image databases illustrate the effectiveness of our proposed approach.

Robust Face Hallucination via Locality-Constrained Bi-Layer Representation

Recently, locality-constrained linear coding (LLC) has been drawn great attentions and been widely used in image processing and computer vision tasks. However, the conventional LLC model is always fragile to outliers. In this paper, we present a robust locality-constrained bi-layer representation model to simultaneously hallucinate the face images and suppress noise and outliers with the assistant of a group of training samples. The proposed scheme is not only able to capture the nonlinear manifold structure but also robust to outliers by incorporating a weight vector into the objective function to subtly tune the contribution of each pixel offered in the objective. Furthermore, a high-resolution (HR) layer is employed to compensate the missed information in the low-resolution (LR) space for coding. The use of two layers (the LR layer and the HR layer) is expected to expose the complicated correlation between the LR and HR patch spaces, which helps to obtain the desirable coefficients to reconstruct the final HR face. The experimental results demonstrate that the proposed method outperforms the state-of-the-art image super-resolution methods in terms of both quantitative measurements and visual effects.

LRR for Subspace Segmentation via Tractable Schatten-$p$ Norm Minimization and Factorization

Recently, nuclear norm-based low rank representation (LRR) methods have been popular in several applications, such as subspace segmentation. However, there exist two limitations: one is that nuclear norm as the relaxation of rank function will lead to the suboptimal solution since nuclear norm-based minimization subproblem tends to the over-relaxations of singular value elements and treats each of them equally; the other is that solving LRR problems may cause more time consumption due to involving singular value decomposition of the large scale matrix at each iteration. To overcome both disadvantages, this paper mainly considers two tractable variants of LRR: one is Schatten-p norm minimization-based LRR (i.e., SpNM_LRR) and the other is Schatten-p norm factorization-based LRR (i.e., SpNFLRR) for p=1, 2/3 and 1/2. By introducing two or more auxiliary variables in the constraints, the alternating direction method of multiplier (ADMM) with multiple updating variables can be devised to solve these variants of LRR. Furthermore, both computational complexity and convergence property are given to evaluate nonconvex multiblocks ADMM algorithms. Several experiments finally validate the efficacy and efficiency of our methods on both synthetic data and real world data.

Connections Between Nuclear-Norm and Frobenius-Norm-Based Representations

A lot of works have shown that frobenius-norm-based representation (FNR) is competitive to sparse representation and nuclear-norm-based representation (NNR) in numerous tasks such as subspace clustering. Despite the success of FNR in experimental studies, less theoretical analysis is provided to understand its working mechanism. In this brief, we fill this gap by building the theoretical connections between FNR and NNR. More specially, we prove that: 1) when the dictionary can provide enough representative capacity, FNR is exactly NNR even though the data set contains the Gaussian noise, Laplacian noise, or sample-specified corruption and 2) otherwise, FNR and NNR are two solutions on the column space of the dictionary.

Class-Specific Kernel Discriminant Analysis Revisited: Further Analysis and Extensions

In this paper, we revisit class-specific kernel discriminant analysis (KDA) formulation, which has been applied in various problems, such as human face verification and human action recognition. We show that the original optimization problem solved for the determination of class-specific discriminant projections is equivalent to a low-rank kernel regression (LRKR) problem using training data-independent target vectors. In addition, we show that the regularized version of class-specific KDA is equivalent to a regularized LRKR problem, exploiting the same targets. This analysis allows us to devise a novel fast solution. Furthermore, we devise novel incremental, approximate and deep (hierarchical) variants. The proposed methods are tested in human facial image and action video verification problems, where their effectiveness and efficiency is shown.

Sparse Weighted Constrained Energy Minimization for Accurate Remote Sensing Image Target Detection

Target detection is an important task for remote sensing images, while it is still difficult to obtain satisfied performance when some images possess complex and confusion spectrum information, for example, the high similarity between target and background spectrum under some circumstance. Traditional detectors always detect target without any preprocessing procedure, which can increase the difference between target spectrum and background spectrum. Therefore, these methods could not discriminate the target from complex or similar background effectively. In this paper, sparse representation was introduced to weight each pixel for further increasing the difference between target and background spectrum. According to sparse reconstruction error matrix of pixels on images, adaptive weights will be assigned to each pixel for improving the difference between target and background spectrum. Furthermore, the sparse weighted-based constrained energy minimization method only needs to construct target dictionary, which is easier to acquire. Then, according to more distinct spectrum characteristic, the detectors can distinguish target from background more effectively and efficiency. Comparing with state-of-the-arts of target detection on remote sensing images, the proposed method can obtain more sensitive and accurate detection performance. In addition, the method is more robust to complex background than the other methods.

Parallel N-Path Quantification Hierarchical K-Means Clustering Algorithm for Video Retrieval

Using clustering method to detect useful patterns in large datasets has attracted considerable interest recently. The HKM clustering algorithm (Hierarchical K-means) is very efficient in large-scale data analysis. It has been widely used to build visual vocabulary for large scale video/image retrieval system. However, the speed and even the accuracy of hierarchical K-means clustering algorithm still have room to be improved. In this paper, we propose a Parallel N-path quantification hierarchical K-means clustering algorithm which improves on the hierarchical K-means clustering algorithm in the following ways. Firstly, we replace the Euclidean kernel with the Hellinger kernel to improve the accuracy. Secondly, the Greedy N-best Paths Labeling method is adopted to improve the clustering accuracy. Thirdly, the multi-core processors-based parallel clustering algorithm is proposed. Our results confirm that the proposed clustering algorithm is much faster and more effective.

Non-Convex Sparse and Low-Rank Based Robust Subspace Segmentation for Data Mining

Parsimony, including sparsity and low-rank, has shown great importance for data mining in social networks, particularly in tasks such as segmentation and recognition. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an objective function with convex l₁-norm or nuclear norm constraints. However, the obtained results by convex optimization are usually suboptimal to solutions of original sparse or low-rank problems. In this paper, a novel robust subspace segmentation algorithm has been proposed by integrating l_p-norm and Schatten p-norm constraints. Our so-obtained affinity graph can better capture local geometrical structure and the global information of the data. As a consequence, our algorithm is more generative, discriminative and robust. An efficient linearized alternating direction method is derived to realize our model. Extensive segmentation experiments are conducted on public datasets. The proposed algorithm is revealed to be more effective and robust compared to five existing algorithms.