Semi-supervised Subspace Learning Research Articles

View-specific subspace learning and re-ranking for semi-supervised person re-identification

Person re-identification (re-ID) focuses on matching the same person across non-overlapping camera views. Most existing methods require tedious manual annotation and can only learn a unitary transformation for images across views, which severely lack of scalability and suffer from view-specific biases. To address these issues, we put forward a View-Specific Semi-supervised Subspace Learning (VS-SSL) approach that can learn specific projections for each view, utilizing limited labeled data to guide the training while leveraging abundant unlabeled data simultaneously. Moreover, a novel re-ranking strategy is proposed to boost the performance further, which re-estimates the similarity between probe and galleries according to the overlap ratio between their expanded neighbors and their position in each other’s ranking list. The effectiveness of the proposed framework is evaluated on several widely-used datasets (VIPeR, PRID450S, PRID2011, CUHK01 and Market-1501), yielding superior performance for both semi-supervised and supervised re-ID.

Semi-Supervised Graph Based Embedding With Non-Convex Sparse Coding Techniques

We consider the problem of semi-supervised graph-based learning upon multimodal and mixmodal data. Since in semi-supervised settings, the labeled information is very limited, we first propose a non-convex sparse-coding based label propagation ( $\alpha$ α -SLP) method to estimate the soft labels, and thereby to enrich the supervised information. By considering the structural properties of multimodal and mixmodal data, we present a semi-supervised graph-based embedding (SGE) approach that incorporates the soft label information with the hierarchical local geometric information of within-class, between-class, and overall-class data. Based on this, subspaces characterizing the multimodal and mixmodal data structure can be derived by maximizing the weighted between-class separability and minimizing the locality-preserved within-class as well as overall-class distances of the training samples. We further extend SGE into semi-supervised sparse subspace learning scenarios and present an $\alpha$ α -structural-regularization-induced SGE ( $\alpha$ α -SSGE) model, which can give better results in extracting discriminative groups of features by utilizing the non-convex structural regularization techniques. Experiments for multimodal and mixmodal digit as well as face recognition verify the validity and effectiveness of the proposed models.

Data induced masking representation learning for face data analysis

Representation learning models, such as the sparse representation and low-rank representation, have shown pleasing efficacy in exploring the intrinsic data structures for patternrecognition tasks. However, conventional methods ignore the local geometric and similarity information among samples, and the performance is restricted. To address this issue, this paper proposes a novel Data Induced Masking Representation (DIMR) learning model by imposing explicit regularization and low-rank constraint. Specifically, DIMR is formulated for shrinking the representations of inter-class and non-neighbor samples. An extra representation regularization term is deployed with a data induced mask matrix, which can incorporate label and locality priors to guide the learning of affinity representation matrix. The affinity graph derived from DIMR is with low-rank, locality preservation (sparsity) and label guiding, such that it can better characterize the adjacent relationship between samples. Extensive experiments on benchmark face datasets demonstrate the superiority of DIMR for both semi-supervised classification and semi-supervised subspace learning tasks.

Low rank representation with adaptive distance penalty for semi-supervised subspace classification

The graph based Semi-supervised Subspace Learning (SSL) methods treat both labeled and unlabeled data as nodes in a graph, and then instantiate edges among these nodes by weighting the affinity between the corresponding pairs of samples. Constructing a good graph to discover the intrinsic structures of the data is critical for these SSL tasks such as subspace clustering and classification. The Low Rank Representation (LRR) is one of powerful subspace clustering methods, based on which a weighted affinity graph can be constructed. Generally, adjacent samples usually belong to a union of subspace and thereby nearby points in the graph should have large edge weights. Motivated by this, in this paper, we proposed a novel LRR with Adaptive Distance Penalty (LRRADP) to construct a good affinity graph. The graph identified by the LRRADP can not only capture the global subspace structure of the whole data but also effectively preserve the neighbor relationship among samples. Furthermore, by projecting the data set into an appropriate subspace, the LRRADP can be further improved to construct a more discriminative affinity graph. Extensive experiments on different types of baseline datasets are carried out to demonstrate the effectiveness of the proposed methods. The improved method, named as LRRADP2, shows impressive performance on real world handwritten and noisy data. The MATLAB codes of the proposed methods will be available at http://www.yongxu.org/lunwen.html.

Semi-supervised subspace learning with L2graph

Subspace learning aims to learn a projection matrix from a given training set so that a transformation of raw data to a low-dimensional representation can be obtained. In practice, the labels of some training samples are available, which can be used to improve the discrimination of low-dimensional representation. In this paper, we propose a semi-supervised learning method which is inspired by the biological observation of similar inputs having similar codes (SISC), i.e., the same collection of cortical columns of the mammal׳s visual cortex is always activated by the similar stimuli. More specifically, we propose a mathematical formulation of SISC which minimizes the distance among the data points with the same label while maximizing the separability between different subjects in the projection space. The proposed method, namely, semi-supervised L2graph (SeL2graph) has two advantages: (1) unlike the classical dimension reduction methods such as principle component analysis, SeL2graph can automatically determine the dimension of feature space. This remarkably reduces the effort to find an optimal feature dimension for a good performance; and (2) it fully exploits the prior knowledge carried by the labeled samples and thus the obtained features are with higher discrimination and compactness. Extensive experiments show that the proposed method outperforms 7 subspace learning algorithms on 15 data sets with respect to classification accuracy, computational efficiency, and robustness to noises and disguises.

Large-scale image recognition based on parallel kernel supervised and semi-supervised subspace learning

Kernel discriminant subspace learning technique is effective to exploit the structure of image dataset in the high-dimensional nonlinear space. However, for large-scale image recognition applications, this technique usually suffers from large computational burden. Although some kernel accelerating methods have been presented, how to greatly reduce computing time and simultaneously keep favorable recognition accuracy is still challenging. In this paper, we introduce the idea of parallel computing into kernel subspace learning and build a parallel kernel discriminant subspace learning framework. In this framework, we firstly design a random non-overlapping equal data division strategy to divide the whole training set into several subsets and assign each computational node a subset. Then, we separately learn kernel discriminant subspaces from these subsets without mutual communications and finally select the most appropriate subspace to classify test samples. Under the built framework, we propose two novel kernel subspace learning approaches, i.e., parallel kernel discriminant analysis (PKDA) and parallel kernel semi-supervised discriminant analysis (PKSDA). We show the superiority of the proposed approaches in terms of time complexity as compared with related methods, and provide the fundamental supports for our framework. For experiment, we establish a parallel computing environment and employ three public large-scale image databases as experiment data. Experimental results demonstrate the efficiency and effectiveness of the proposed approaches.

Greedy approaches to semi-supervised subspace learning

Subspace estimation is of paramount importance in dealing with high-dimensional data with noise. In this paper we consider a semi-supervised learning setup where certain supervised information (e.g., class labels) is available for only a part of data samples. First we formulate a unifying optimization problem that subsumes the well-known principal component analysis in unsupervised scenarios as a special case, while exploiting labeled data effectively. To circumvent difficult matrix rank constraints in the original problem, we propose a nuclear norm based relaxation that ends up with convex optimization. We then provide an infinite-dimensional greedy search algorithm that solves the optimization problem efficiently. An extension to nonlinear dimensionality reduction is also introduced, which is as efficient as the linear model via dual representation with kernel trick. The effectiveness of the proposed approach is demonstrated experimentally on several semi-supervised learning problems.

Boosting Separability in Semisupervised Learning for Object Classification

Boosting algorithms, especially AdaBoost, have attracted great attention in computer vision. In the early version of boosting algorithms, the weak classifier selection and the strong classifier learning are linked together. It has been demonstrated that decoupling of these two processes can provide more flexibility for training a better classifier. In these studies, linear discriminant analysis (LDA) has been adopted to select weak classifiers independently based on class separability rather than a training error that occurs normally in AdaBoost. It is observed that LDA is successful only if a large number of labeled training samples is available. However, a large-scale labeled training set is not always available in many computer vision applications such as object classification. To tackle this problem, this paper proposes semisupervised subspace learning combined with a boosting framework for object classification, through which unlabeled data can participate in the boosting training to compensate for the lack of enough labeled data. With the proposed framework, this paper develops three various approaches that utilize unlabeled data in different ways. According to the experiments on several public image data sets, the proposed methods achieve superior performance over AdaBoost and existing semisupervised algorithms.

Semi-Supervised Hyperspectral Subspace Learning Based on a Generalized Eigenvalue Problem for Regression and Dimensionality Reduction

Manifold learning for the hyperspectral data structure of intra-class variation provides useful information for investigating the intrinsic coordinates corresponding to the quantitative properties inherent in the class. However, in the high-dimensional feature space, it is unfeasible to acquire a statistically sufficient number of labeled data to estimate the coordinates. In this paper, we propose semi-supervised regression and dimensionality reduction methods for hyperspectral subspace learning that utilize abundant unlabeled data and a small number of labeled data. The quantitative target variables for regression and the order constraints for dimensionality reduction are embedded in matrices representing data relations, i.e., a set of between-class scatter matrices, within-class scatter matrices, and supervised local attraction matrices. The optimal projection matrices are estimated by generalized eigenvalue problems based on the matrices. The proposed methods are applied to synthetic linear regression problems and dimensionality reduction problems based on a time-series of hyperspectral data for a deciduous broad-leaved forest to extract local coordinates related to phenological changes. The order consistency of the projections is assessed by evaluating an index based on the Mann-Kendall test statistics. The proposed methods demonstrate much better performances in terms of both regression and dimensionality reduction than the alternative supervised and unsupervised methods.

Semi-Supervised subspace learning for Mumford-Shah model based texture segmentation

We propose a novel image segmentation model which incorporates subspace clustering techniques into a Mumford-Shah model to solve texture segmentation problems. While the natural unsupervised approach to learn a feature subspace can easily be trapped in a local solution, we propose a novel semi-supervised optimization algorithm that makes use of information derived from both the intermediate segmentation results and the regions-of-interest (ROI) selected by the user to determine the optimal subspaces of the target regions. Meanwhile, these subspaces are embedded into a Mumford-Shah objective function so that each segment of the optimal partition is homogeneous in its own subspace. The method outperforms standard Mumford-Shah models since it can separate textures which are less separated in the full feature space. Experimental results are presented to confirm the usefulness of subspace clustering in texture segmentation.

Semi-Supervised Bilinear Subspace Learning

Recent research has demonstrated the success of tensor based subspace learning in both unsupervised and supervised configurations (e.g., 2-D PCA, 2-D LDA, and DATER). In this correspondence, we present a new semi-supervised subspace learning algorithm by integrating the tensor representation and the complementary information conveyed by unlabeled data. Conventional semi-supervised algorithms mostly impose a regularization term based on the data representation in the original feature space. Instead, we utilize graph Laplacian regularization based on the low-dimensional feature space. An iterative algorithm, referred to as adaptive regularization based semi-supervised discriminant analysis with tensor representation (ARSDA/T), is also developed to compute the solution. In addition to handling tensor data, a vector-based variant (ARSDA/V) is also presented, in which the tensor data are converted into vectors before subspace learning. Comprehensive experiments on the CMU PIE and YALE-B databases demonstrate that ARSDA/T brings significant improvement in face recognition accuracy over both conventional supervised and semi-supervised subspace learning algorithms.

Ubiquitously Supervised Subspace Learning

In this paper, our contributions to the subspace learning problem are two-fold. We first justify that most popular subspace learning algorithms, unsupervised or supervised, can be unitedly explained as instances of a ubiquitously supervised prototype. They all essentially minimize the intraclass compactness and at the same time maximize the interclass separability, yet with specialized labeling approaches, such as ground truth, self-labeling, neighborhood propagation, and local subspace approximation. Then, enlightened by this ubiquitously supervised philosophy, we present two categories of novel algorithms for subspace learning, namely, misalignment-robust and semi-supervised subspace learning. The first category is tailored to computer vision applications for improving algorithmic robustness to image misalignments, including image translation, rotation and scaling. The second category naturally integrates the label information from both ground truth and other approaches for unsupervised algorithms. Extensive face recognition experiments on the CMU PIE and FRGC ver1.0 databases demonstrate that the misalignment-robust version algorithms consistently bring encouraging accuracy improvements over the counterparts without considering image misalignments, and also show the advantages of semi-supervised subspace learning over only supervised or unsupervised scheme.

Image retrieval based on incremental subspace learning

Many problems in information processing involve some form of dimensionality reduction, such as face recognition, image/text retrieval, data visualization, etc. The typical linear dimensionality reduction algorithms include principal component analysis (PCA), random projection, locality-preserving projection (LPP), etc. These techniques are generally unsupervised which allows them to model data in the absence of labels or categories. In this paper, we propose a semi-supervised subspace learning algorithm for image retrieval. In relevance feedback-driven image retrieval system, the user-provided information can be used to better describe the intrinsic semantic relationships between images. Our algorithm is fundamentally based on LPP which can incorporate user's relevance feedbacks. As the user's feedbacks are accumulated, we can ultimately obtain a semantic subspace in which different semantic classes can be best separated and the retrieval performance can be enhanced. We compared our proposed algorithm to PCA and the standard LPP. Experimental results on a large collection of images have shown the effectiveness and efficiency of our proposed algorithm.