Domain adaptation solves a learning problem in a target domain by utilizing the training data in a different but related source domain. Intuitively, discovering a good feature representation across domains is crucial. In this paper, we propose to find such a representation through a new learning method, transfer component analysis (TCA), for domain adaptation. TCA tries to learn some transfer components across domains in a Reproducing Kernel Hilbert Space (RKHS) using Maximum Mean Discrepancy (MMD). In the subspace spanned by these transfer components, data distributions in different domains are close to each other. As a result, with the new representations in this subspace, we can apply standard machine learning methods to train classifiers or regression models in the source domain for use in the target domain. The main contribution of our work is that we propose a novel feature representation in which to perform domain adaptation via a new parametric kernel using feature extraction methods, which can dramatically minimize the distance between domain distributions by projecting data onto the learned transfer components. Furthermore, our approach can handle large datsets and naturally lead to out-of-sample generalization. The effectiveness and efficiency of our approach in are verified by experiments on two real-world applications: cross-domain indoor WiFi localization and cross-domain text classification.

In this paper, we address the problem of finding the pre-image of a feature vector in the feature space induced by a kernel. This is of central importance in some kernel applications, such as on using kernel principal component analysis (PCA) for image denoising. Unlike the traditional method in (Mika et al., 1998) which relies on nonlinear optimization, our proposed method directly finds the location of the pre-image based on distance constraints in the feature space. It is non-iterative, involves only linear algebra and does not suffer from numerical instability or local minimum problems. Performance of this method is evaluated on performing kernel PCA and kernel clustering on the USPS data set.

Sparse coding which encodes the original signal in a sparse signal space, has shown its state-of-the-art performance in the visual codebook generation and feature quantization process of BoW based image representation. However, in the feature quantization process of sparse coding, some similar local features may be quantized into different visual words of the codebook due to the sensitiveness of quantization. In this paper, to alleviate the impact of this problem, we propose a Laplacian sparse coding method, which will exploit the dependence among the local features. Specifically, we propose to use histogram intersection based kNN method to construct a Laplacian matrix, which can well characterize the similarity of local features. In addition, we incorporate this Laplacian matrix into the objective function of sparse coding to preserve the consistence in sparse representation of similar local features. Comprehensive experimental results show that our method achieves or outperforms existing state-of-the-art results, and exhibits excellent performance on Scene 15 data set.

In this paper, we study the heterogeneous domain adaptation (HDA) problem, in which the data from the source domain and the target domain are represented by heterogeneous features with different dimensions. By introducing two different projection matrices, we first transform the data from two domains into a common subspace such that the similarity between samples across different domains can be measured. We then propose a new feature mapping function for each domain, which augments the transformed samples with their original features and zeros. Existing supervised learning methods (e.g., SVM and SVR) can be readily employed by incorporating our newly proposed augmented feature representations for supervised HDA. As a showcase, we propose a novel method called Heterogeneous Feature Augmentation (HFA) based on SVM. We show that the proposed formulation can be equivalently derived as a standard Multiple Kernel Learning (MKL) problem, which is convex and thus the global solution can be guaranteed. To additionally utilize the unlabeled data in the target domain, we further propose the semi-supervised HFA (SHFA) which can simultaneously learn the target classifier as well as infer the labels of unlabeled target samples. Comprehensive experiments on three different applications clearly demonstrate that our SHFA and HFA outperform the existing HDA methods.

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Sparse coding exhibits good performance in many computer vision applications. However, due to the overcomplete codebook and the independent coding process, the locality and the similarity among the instances to be encoded are lost. To preserve such locality and similarity information, we propose a Laplacian sparse coding (LSc) framework. By incorporating the similarity preserving term into the objective of sparse coding, our proposed Laplacian sparse coding can alleviate the instability of sparse codes. Furthermore, we propose a Hypergraph Laplacian sparse coding (HLSc), which extends our Laplacian sparse coding to the case where the similarity among the instances defined by a hypergraph. Specifically, this HLSc captures the similarity among the instances within the same hyperedge simultaneously, and also makes the sparse codes of them be similar to each other. Both Laplacian sparse coding and Hypergraph Laplacian sparse coding enhance the robustness of sparse coding. We apply the Laplacian sparse coding to feature quantization in Bag-of-Words image representation, and it outperforms sparse coding and achieves good performance in solving the image classification problem. The Hypergraph Laplacian sparse coding is also successfully used to solve the semi-auto image tagging problem. The good performance of these applications demonstrates the effectiveness of our proposed formulations in locality and similarity preservation.