Classification Error Term Research Articles

Discriminative Spectral–Spatial Feature Extraction-Based Band Selection for Hyperspectral Image Classification

Recently, some spectral–spatial band selection (BS) strategies have become hugely popular as they fuse the spectral information of the pixels and the spatial relationship with the neighboring pixels to enhance the performance of classification methods. However, being unsupervised in nature, these methods do not utilize the class information of the training samples which could substantially empower the capabilities of such spectral–spatial BS methods. To circumvent this limitation, a supervised spectral–spatial BS method based on component loadings obtained from the principal components of spectral–spatial principal component analysis (PCA) and using a novel super-pixel based graph Laplacian embedding is proposed. The methodology attempts to unify the two strategies of dimensionality reduction, i.e., BS and feature extraction (FE), so that the benefits from both of them can be combined. The importance of each band is estimated in terms of its component loadings along the principal components which are estimated from a unified objective function consisting of three terms: data fidelity, classification error term, and spatial prior. Additionally, the spatial relationship among the neighboring samples is characterized using a novel superpixel-based graph model. An objective comparison of the proposed approach with several widely used, state-of-the-art BS methods demonstrates a significant improvement in the classification accuracy.

Structured discriminant analysis dictionary learning for pattern classification

Dictionary learning has been widely used in the field of pattern recognition. Although the existing synthesis dictionary learning methods have achieved impressive results, they need compute sparse codes using a time-consuming sparse coding procedure. As a dual viewpoint of synthesis dictionary learning, analysis dictionary learning (ADL) has attracted much attention due to its high efficiency and intuitive meaning in recent years. However, how to associate analysis dictionary atoms with class labels and learn a structured discriminant analysis dictionary, is still a challenging problem. In this paper, we propose a structured discriminant analysis dictionary learning (SDADL) method to learn a structured discriminant analysis dictionary that consists of the class-specific analysis sub-dictionaries associated with the corresponding classes. Specifically, we introduce a classification error term into SDADL model to learn an optimal linear classifier for classification. To obtain the discriminant analysis sparse codes, we introduce a discriminant analysis sparse code error term into SDADL model, which forces the samples from the same class to have similar analysis sparse codes. Moreover, we also introduce a structured discriminant term into SDADL model to improve the discrimination capability of both each class-specific analysis sub-dictionary and analysis sparse codes. An efficient iterative algorithm is also developed to solve the optimization problem of SDADL. In addition, we design a novel scheme for classification. Extensive experiments on five image datasets verify the effectiveness of SDADL for pattern classification.

Multiscale Supervised Kernel Dictionary Learning for SAR Target Recognition

In this article, a supervised nonlinear dictionary learning (DL) method, called multiscale supervised kernel DL (MSK-DL), is proposed for target recognition in synthetic aperture radar (SAR) images. We use Frost filters with different parameters to extract an SAR image’s multiscale features for data augmentation and noise suppression. In order to reduce the computation cost, the dimension of each scale feature is reduced by principal component analysis (PCA). Instead of the widely used linear DL, we learn multiple nonlinear dictionaries to capture the nonlinear structure of data by introducing the dimension-reduced features into the nonlinear reconstruction error terms. A classification model, which is defined as a discriminative classification error term, is learned simultaneously. Hence, the objective function contains the nonlinear reconstruction error terms and a classification error term. Two optimization algorithms, called multiscale supervised kernel K-singular value decomposition (MSK-KSVD) and multiscale supervised incremental kernel DL (MSIK-DL), are proposed to compute the multidictionary and the classifier. Experiments on the moving and stationary target automatic recognition (MSTAR) data set are performed to evaluate the effectiveness of the two proposed algorithms. And the experimental results demonstrate that the proposed scheme outperforms some representative common machine learning strategies, state-of-the-art convolutional neural network (CNN) models and some representative DL methods, especially in terms of its robustness against training set size and noise.

Graph-structure constraint and Schatten p-norm-based unsupervised domain adaptation for image classification

Unsupervised domain adaptation, which aims to classify a target domain correctly only using a labeled source domain, has achieved promising performance yet remains a challenging problem. Most traditional methods focus on exploiting either geometric or statistical characteristics to reduce domain shifts. To take advantage of both sides, in this paper, we propose a unified framework incorporating both the geometric and statistical characteristics by adopting the non-convex Schatten p-norm and graph Laplacian constraints to preserve global and local structure information and constructing marginal and conditional distribution minimization terms to reduce the distribution shifts. Moreover, a classification error term on the source domain is embedded into the objective function to increase the discriminability. The proposed method has been evaluated on six datasets and the experimental results demonstrate the superiority of the proposed method over several state-of-the-art methods. The MATLAB code of our method will be publicly available at https://github.com/HeyouChang/unsupervised-domain-adaptation .

Cross-view hashing via supervised deep discrete matrix factorization

Matrix factorization has been utilized for the task of cross-view hashing, where basis functions are learned to map data from different views to the same hamming embedding. It is possible that the basis functions between the hamming embedding and the original data matrix contain rather complex hierarchical information, which existing work can not capture. In addition, previous work employs relaxation technique in the matrix factorization based hashing which may lead to large quantization error. To address these issues, this paper presents a novel Supervised Discrete Deep Matrix Factorization (SDDMF) for cross-view hashing. We introduce deep matrix factorization so that SDDMF is able to learn a set of hierarchical basis functions and unified binary codes from different views. In addition, a classification error term is incorporated into the objective to learn discriminative binary codes. We then employ a linearization technique to directly optimize the discrete constraints which can significantly reduce the quantization error. Experimental results on three standard datasets with image-text modalities verify that SDDMF significantly outperforms several state-of-the-art methods.

Class-aware tensor factorization for multi-relational classification

In this paper, we propose a tensor factorization method, called CLASS-RESCAL, which associates the class labels of data samples with their latent representations. Specifically, we extend RESCAL to produce a semi-supervised factorization method that combines a classification error term with the standard factor optimization process. CLASS-RESCAL assimilates information from all the relations of the tensor, while also taking into account classification performance. This procedure forces the data samples within the same class to have similar latent representations. Experimental results on several real-world social network data indicate this is a promising approach for multi-relational classification tasks.

Multiscale Incremental Dictionary Learning With Label Constraint for SAR Object Recognition

In this letter, a novel nonlinear supervised dictionary learning (DL) scheme called multiscale incremental DL, whose objective function contains reconstruction error terms and a classification error term, is proposed for synthetic aperture radar (SAR) object recognition. In the reconstruction error terms, considering the local and global features of SAR images, Gaussian functions with different blurring parameters are exploited to extract SAR images' multiscale features, and all features can be reconstructed according to the weights assigned to these features at different scales. In the classification error term, a linear combination of classification vectors close to the labels of samples restricts sparse codes from different classes to be almost independent. Furthermore, an incremental method is utilized to address the memory consumption problem, and the optimal solution is obtained. Experiments on the moving and stationary target automatic recognition database demonstrate that the proposed algorithm outperforms several representative DL, support vector machine, and k-nearest neighbor methods in the case of a small training sample set size and exhibits strong antinoise performance.

Duplex Metric Learning for Image Set Classification.

Image set classification has attracted much attention because of its broad applications. Despite the success made so far, the problems of intra-class diversity and inter-class similarity still remain two major challenges. To explore a possible solution to these challenges, this paper proposes a novel approach, termed duplex metric learning (DML), for image set classification. The proposed DML consists of two progressive metric learning stages with different objectives used for feature learning and image classification, respectively. The metric learning regularization is not only used to learn powerful feature representations but also well explored to train an effective classifier. At the first stage, we first train a discriminative stacked autoencoder (DSAE) by layer-wisely imposing a metric learning regularization term on the neurons in the hidden layers and meanwhile minimizing the reconstruction error to obtain new feature mappings in which similar samples are mapped closely to each other and dissimilar samples are mapped farther apart. At the second stage, we discriminatively train a classifier and simultaneously fine-tune the DSAE by optimizing a new objective function, which consists of a classification error term and a metric learning regularization term. Finally, two simple voting strategies are devised for image set classification based on the learnt classifier. In the experiments, we extensively evaluate the proposed framework for the tasks of face recognition, object recognition, and face verification on several commonly-used data sets and state-of-the-art results are achieved in comparison with existing methods.

Discriminative Histogram Intersection Metric Learning and Its Applications

In this paper, a novel method called discriminative histogram intersection metric learning (DHIML) is proposed for pair matching and classification. Specifically, we introduce a discrimination term for learning a metric from binary information such as same/not-same or similar/dissimilar, and then combine it with the classification error for the discrimination in classifier construction. Compared with conventional approaches, the proposed method has several advantages. 1) The histogram intersection strategy is adopted into metric learning to deal with the widely used histogram features effectively. 2) By introducing discriminative term and classification error term into metric learning, a more discriminative distance metric and a classifier can be learned together. 3) The objective function is robust to outliers and noises for both features and labels in the training. The performance of the proposed method is tested on four applications: face verification, face-track identification, face-track clustering, and image classification. Evaluations on the challenging restricted protocol of Labeled Faces in the Wild (LFW) benchmark, a dataset with more than 7 000 face-tracks, and Caltech-101 dataset validate the robustness and discriminability of the proposed metric learning, compared with the recent state-of-the-art approaches.

Online structured sparse learning with labeled information for robust object tracking

We formulate object tracking under the particle filter framework as a collaborative tracking problem. The priori information from training data is exploited effectively to online learn a discriminative and reconstructive dictionary, simultaneously without losing structural information. Specifically, the class label and the semantic structure information are incorporated into the dictionary learning process as the classification error term and ideal coding regularization term, respectively. Combined with the traditional reconstruction error, a unified dictionary learning framework for robust object tracking is constructed. By minimizing the unified objective function with different mixed norm constraints on sparse coefficients, two robust optimizing methods are developed to learn the high-quality dictionary and optimal classifier simultaneously. The best candidate is selected by minimizing the reconstructive error and classification error jointly. As the tracking continues, the proposed algorithms alternate between the robust sparse coding and the dictionary updating. The proposed trackers are empirically compared with 14 state-of-the-art trackers on some challenging video sequences. Both quantitative and qualitative comparisons demonstrate that the proposed algorithms perform well in terms of accuracy and robustness.

Supervised within-class-similar discriminative dictionary learning for face recognition

The current study puts forward a supervised within-class-similar discriminative dictionary learning (SCDDL) algorithm for face recognition. Some popular discriminative dictionary learning schemes for recognition tasks always incorporate the linear classification error term into the objective function or make some discriminative restrictions on representation coefficients. In the presented SCDDL algorithm, we propose to directly restrict the representation coefficients to be similar within the same class and simultaneously include the linear classification error term in the supervised dictionary learning scheme to derive a more discriminative dictionary for face recognition. The experimental results on three large well-known face databases suggest that our approach can enhance the fisher ratio of representation coefficients when compared with several dictionary learning algorithms that incorporate linear classifiers. In addition, the learned discriminative dictionary, the large fisher ratio of representation coefficients and the simultaneously learned classifier can improve the recognition rate compared with some state-of-the-art dictionary learning algorithms.

Supervised multiview learning based on simultaneous learning of multiview intact and single view classifier

Multiview learning problem refers to the problem of learning a classifier from multiple view data. In this data set, each data points is presented by multiple different views. In this paper, we propose a novel method for this problem. This method is based on two assumptions. The first assumption is that each data point has an intact feature vector, and each view is obtained by a linear transformation from the intact vector. The second assumption is that the intact vectors are discriminative, and in the intact space, we have a linear classifier to separate the positive class from the negative class. We define an intact vector for each data point, and a view-conditional transformation matrix for each view, and propose to reconstruct the multiple view feature vectors by the product of the corresponding intact vectors and transformation matrices. Moreover, we also propose a linear classifier in the intact space, and learn it jointly with the intact vectors. The learning problem is modeled by a minimization problem, and the objective function is composed of a Cauchy error estimator-based view-conditional reconstruction term over all data points and views, and a classification error term measured by hinge loss over all the intact vectors of all the data points. Some regularization terms are also imposed to different variables in the objective function. The minimization problem is solve by an iterative algorithm using alternate optimization strategy and gradient descent algorithm. The proposed algorithm shows it advantage in the compression to other multiview learning algorithms on benchmark data sets.

A Locality-Constrained and Label Embedding Dictionary Learning Algorithm for Image Classification.

Locality and label information of training samples play an important role in image classification. However, previous dictionary learning algorithms do not take the locality and label information of atoms into account together in the learning process, and thus their performance is limited. In this paper, a discriminative dictionary learning algorithm, called the locality-constrained and label embedding dictionary learning (LCLE-DL) algorithm, was proposed for image classification. First, the locality information was preserved using the graph Laplacian matrix of the learned dictionary instead of the conventional one derived from the training samples. Then, the label embedding term was constructed using the label information of atoms instead of the classification error term, which contained discriminating information of the learned dictionary. The optimal coding coefficients derived by the locality-based and label-based reconstruction were effective for image classification. Experimental results demonstrated that the LCLE-DL algorithm can achieve better performance than some state-of-the-art algorithms.

Online Learning a High-Quality Dictionary and Classifier Jointly for Multitask Object Tracking

This article formulates object tracking in a particle filter framework as a binary classification problem. The method effectively exploits a priori information from training data to learn online a compact and discriminative dictionary. The method incorporates the class label information into the dictionary learning process as the classification error term and idea coding regularization term, respectively. Combined with the traditional reconstruction error, a total objective function for dictionary learning is constructed. By minimizing the total object function, the approach jointly obtains a high-quality dictionary and optimal linear classifier. Combined with multitask sparse coding, the best candidate is selected by jointly evaluating the reconstructive error and classification error. As the tracking continues, the proposed algorithm alternates between multitask sparse coding and dictionary updating. Experimental evaluations on challenging video sequences show that the proposed algorithm performs favorably against state-of-the-art methods in terms of effectiveness, accuracy, and robustness.

Online Learning Discriminative Dictionary with Label Information for Robust Object Tracking

A supervised approach to online-learn a structured sparse and discriminative representation for object tracking is presented. Label information from training data is incorporated into the dictionary learning process to construct a robust and discriminative dictionary. This is accomplished by adding an ideal-code regularization term and classification error term to the total objective function. By minimizing the total objective function, we learn the high quality dictionary and optimal linear multiclassifier jointly using iterative reweighed least squares algorithm. Combined with robust sparse coding, the learned classifier is employed directly to separate the object from background. As the tracking continues, the proposed algorithm alternates between robust sparse coding and dictionary updating. Experimental evaluations on the challenging sequences show that the proposed algorithm performs favorably against state-of-the-art methods in terms of effectiveness, accuracy, and robustness.