Sparse coding, which represents a data point as a sparse reconstruction code with regard to a dictionary, has been a popular data representation method. Meanwhile, in database retrieval problems, learning the ranking scores from data points plays an important role. Up to now, these two problems have always been considered separately, assuming that data coding and ranking are two independent and irrelevant problems. However, is there any internal relationship between sparse coding and ranking score learning? If yes, how to explore and make use of this internal relationship? In this paper, we try to answer these questions by developing the first joint sparse coding and ranking score learning algorithm. To explore the local distribution in the sparse code space, and also to bridge coding and ranking problems, we assume that in the neighborhood of each data point, the ranking scores can be approximated from the corresponding sparse codes by a local linear function. By considering the local approximation error of ranking scores, the reconstruction error and sparsity of sparse coding, and the query information provided by the user, we construct a unified objective function for learning of sparse codes, the dictionary and ranking scores. We further develop an iterative algorithm to solve this optimization problem.

In this paper, we propose a novel learning framework for the problem of domain transfer learning. We map the data of two domains to one single common space, and learn a classifier in this common space. Then we adapt the common classifier to the two domains by adding two adaptive functions to it respectively. In the common space, the target domain data points are weighted and matched to the target domain in term of distributions. The weighting terms of source domain data points and the target domain classification responses are also regularized by the local reconstruction coefficients. The novel transfer learning framework is evaluated over some benchmark cross-domain data sets, and it outperforms the existing state-of-the-art transfer learning methods.

To date, many machine learning applications have multiple views of features, and different applications require specific multivariate performance measures, such as the F-score for retrieval. However, existing multivariate performance measure optimization methods are limited to single-view data, while traditional multi-view learning methods cannot optimize multivariate performance measures directly. To fill this gap, in this paper, we propose the problem of optimizing multivariate performance measures from multi-view data, and an effective method to solve it. We propose to learn linear discriminant functions for different views, and combine them to construct an overall multivariate mapping function for multi-view data. To learn the parameters of the linear discriminant functions of different views to optimize a given multivariate performance measure, we formulate an optimization problem. In this problem, we propose to minimize the complexity of the linear discriminant function of each view, promote the consistency of the responses of different views over the same data points, and minimize the upper boundary of the corresponding loss of a given multivariate performance measure. To optimize this problem, we develop an iterative cutting-plane algorithm. Experiments on four benchmark data sets show that it not only outperforms traditional single-view based multivariate performance optimization methods, but also achieves better results than ordinary multi-view learning methods.

Sparse coding (Sc) has been studied very well as a powerful data representation method. It attempts to represent the feature vector of a data sample by reconstructing it as the sparse linear combination of some basic elements, and a $L_2$ norm distance function is usually used as the loss function for the reconstruction error. In this paper, we investigate using Sc as the representation method within multi-instance learning framework, where a sample is given as a bag of instances, and further represented as a histogram of the quantized instances. We argue that for the data type of histogram, using $L_2$ norm distance is not suitable, and propose to use the earth mover's distance (EMD) instead of $L_2$ norm distance as a measure of the reconstruction error. By minimizing the EMD between the histogram of a sample and the its reconstruction from some basic histograms, a novel sparse coding method is developed, which is refereed as SC-EMD. We evaluate its performances as a histogram representation method in tow multi-instance learning problems --- abnormal image detection in wireless capsule endoscopy videos, and protein binding site retrieval. The encouraging results demonstrate the advantages of the new method over the traditional method using $L_2$ norm distance.

Sparse coding approximates the data sample as a sparse linear combination of some basic codewords and uses the sparse codes as new presentations. In this paper, we investigate learning discriminative sparse codes by sparse coding in a semi-supervised manner, where only a few training samples are labeled. By using the manifold structure spanned by the data set of both labeled and unlabeled samples and the constraints provided by the labels of the labeled samples, we learn the variable class labels for all the samples. Furthermore, to improve the discriminative ability of the learned sparse codes, we assume that the class labels could be predicted from the sparse codes directly using a linear classifier. By solving the codebook, sparse codes, class labels and classifier parameters simultaneously in a unified objective function, we develop a semi-supervised sparse coding algorithm. Experiments on two real-world pattern recognition problems demonstrate the advantage of the proposed methods over supervised sparse coding methods on partially labeled data sets.

A combination of the sparse coding and transfer learning techniques was shown to be accurate and robust in classification tasks where training and testing objects have a shared feature space but are sampled from different underlying distributions, i.e., belong to different domains. The key assumption in such case is that in spite of the domain disparity, samples from different domains share some common hidden factors. Previous methods often assumed that all the objects in the target domain are unlabeled, and thus the training set solely comprised objects from the source domain. However, in real world applications, the target domain often has some labeled objects, or one can always manually label a small number of them. In this paper, we explore such possibility and show how a small number of labeled data in the target domain can significantly leverage classification accuracy of the state-of-the-art transfer sparse coding methods. We further propose a unified framework named supervised transfer sparse coding (STSC) which simultaneously optimizes sparse representation, domain transfer and classification. Experimental results on three applications demonstrate that a little manual labeling and then learning the model in a supervised fashion can significantly improve classification accuracy.

Nonnegative Matrix Factorization (NMF) has been a popular representation method for pattern classification problem. It tries to decompose a nonnegative matrix of data samples as the product of a nonnegative basic matrix and a nonnegative coefficient matrix, and the coefficient matrix is used as the new representation. However, traditional NMF methods ignore the class labels of the data samples. In this paper, we proposed a supervised novel NMF algorithm to improve the discriminative ability of the new representation. Using the class labels, we separate all the data sample pairs into within-class pairs and between-class pairs. To improve the discriminate ability of the new NMF representations, we hope that the maximum distance of the within-class pairs in the new NMF space could be minimized, while the minimum distance of the between-class pairs pairs could be maximized. With this criterion, we construct an objective function and optimize it with regard to basic and coefficient matrices and slack variables alternatively, resulting in a iterative algorithm.

Sparse coding has shown its power as an effective data representation method. However, up to now, all the sparse coding approaches are limited within the single domain learning problem. In this paper, we extend the sparse coding to cross domain learning problem, which tries to learn from a source domain to a target domain with significant different distribution. We impose the Maximum Mean Discrepancy (MMD) criterion to reduce the cross-domain distribution difference of sparse codes, and also regularize the sparse codes by the class labels of the samples from both domains to increase the discriminative ability. The encouraging experiment results of the proposed cross-domain sparse coding algorithm on two challenging tasks --- image classification of photograph and oil painting domains, and multiple user spam detection --- show the advantage of the proposed method over other cross-domain data representation methods.