Distance metric learning (DML) aims to find an appropriate way to reveal the underlying data relationship. It is critical in many machine learning, pattern recognition and data mining algorithms, and usually require large amount of label information (such as class labels or pair triplet constraints) to achieve satisfactory performance. However, the label information may be insufficient in real-world applications due to the high-labeling cost, and DML may fail in this case. Transfer metric learning (TML) is able to mitigate this issue for DML in the domain of interest (target domain) by leveraging knowledge information from other related domains (source domains). Although achieved a certain level of development, TML has limited success in various aspects such as selective transfer, theoretical understanding, handling complex data, big data and extreme cases. In this survey, we present a systematic review of the TML literature. In particular, we group TML into different categories according to different settings and metric transfer strategies, such as direct metric approximation, subspace approximation, distance approximation, and distribution approximation. A summarization and insightful discussion of the various TML approaches and their applications will be presented. Finally, we indicate some challenges and provide possible future directions.
TML is quite related to transfer subspace learning (TSL) @cite_26 @cite_111 or transfer feature learning (TFL) @cite_19 . An early work on TSL is presented in @cite_26 that finds a low-dimensional latent space, where the distribution difference between the source and target domain is minimized. This algorithm is conducted in a transductive manner and not convenient to derive a representation for new samples. This issue is tackled by @cite_41 , where a generic regularization framework is proposed for TSL based on Bregman divergence @cite_60 . A low-rank TSL (LTSL) framework is proposed in @cite_125 @cite_113 , where the subspace is found by reconstructing the projected target data using the projected source data under the low-rank representation @cite_88 @cite_43 theme. The main advantage of the framework is that only relevant source data are utilized to find the subspace and noisy information can be filtered out. That is, it can avoid negative transfer. The framework is further extended in @cite_67 to help recover missing modality in the target domain and improved in @cite_63 by exploiting both low-rank and sparse structures on the reconstruction matrix.
@cite_67 @cite_26 @cite_60 @cite_41 @cite_125 @cite_113 @cite_19 @cite_43 @cite_63 @cite_88 @cite_111
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Subspace learning and reconstruction have been widely explored in recent transfer learning work and generally a specially designed projection and reconstruction transfer matrix are wanted. However, existing subspace reconstruction based algorithms neglect the class prior such that the learned transfer function is biased, especially when data scarcity of some class is encountered. Different from those previous methods, in this paper, we propose a novel reconstruction-based transfer learning method called Class-specific Reconstruction Transfer Learning (CRTL), which optimizes a well-designed transfer loss function without class bias. Using a class-specific reconstruction matrix to align the source domain with the target domain which provides help for classification with class prior modeling. Furthermore, to keep the intrinsic relationship between data and labels after feature augmentation, a projected Hilbert-Schmidt Independence Criterion (pHSIC), that measures the dependency between two sets, is first proposed by mapping the data from original space to RKHS in transfer learning. In addition, combining low-rank and sparse constraints on the class-specific reconstruction coefficient matrix, the global and local data structures can be effectively preserved. Extensive experiments demonstrate that the proposed method outperforms conventional representation-based domain adaptation methods. We propose a novel reconstruction-based transfer learning method called latent sparse domain transfer (LSDT) for domain adaptation and visual categorization of heterogeneous data. For handling cross-domain distribution mismatch, we advocate reconstructing the target domain data with the combined source and target domain data points based on @math -norm sparse coding. Furthermore, we propose a joint learning model for simultaneous optimization of the sparse coding and the optimal subspace representation. In addition, we generalize the proposed LSDT model into a kernel-based linear nonlinear basis transformation learning framework for tackling nonlinear subspace shifts in reproduced kernel Hilbert space. The proposed methods have three advantages: 1) the latent space and the reconstruction are jointly learned for pursuit of an optimal subspace transfer; 2) with the theory of sparse subspace clustering, a few valuable source and target data points are formulated to reconstruct the target data with noise (outliers) from source domain removed during domain adaptation, such that the robustness is guaranteed; and 3) a nonlinear projection of some latent space with kernel is easily generalized for dealing with highly nonlinear domain shift (e.g., face poses). Extensive experiments on several benchmark vision data sets demonstrate that the proposed approaches outperform other state-of-the-art representation-based domain adaptation methods. In this paper, we address the problem of unsupervised domain transfer learning in which no labels are available in the target domain. We use a transformation matrix to transfer both the source and target data to a common subspace, where each target sample can be represented by a combination of source samples such that the samples from different domains can be well interlaced. In this way, the discrepancy of the source and target domains is reduced. By imposing joint low-rank and sparse constraints on the reconstruction coefficient matrix, the global and local structures of data can be preserved. To enlarge the margins between different classes as much as possible and provide more freedom to diminish the discrepancy, a flexible linear classifier (projection) is obtained by learning a non-negative label relaxation matrix that allows the strict binary label matrix to relax into a slack variable matrix. Our method can avoid a potentially negative transfer by using a sparse matrix to model the noise and, thus, is more robust to different types of noise. We formulate our problem as a constrained low-rankness and sparsity minimization problem and solve it by the inexact augmented Lagrange multiplier method. Extensive experiments on various visual domain adaptation tasks show the superiority of the proposed method over the state-of-the art methods. The MATLAB code of our method will be publicly available at http: www.yongxu.org lunwen.html . To uncover an appropriate latent subspace for data representation, in this paper we propose a novel Robust Structured Subspace Learning (RSSL) algorithm by integrating image understanding and feature learning into a joint learning framework. The learned subspace is adopted as an intermediate space to reduce the semantic gap between the low-level visual features and the high-level semantics. To guarantee the subspace to be compact and discriminative, the intrinsic geometric structure of data, and the local and global structural consistencies over labels are exploited simultaneously in the proposed algorithm. Besides, we adopt the @math -norm for the formulations of loss function and regularization respectively to make our algorithm robust to the outliers and noise. An efficient algorithm is designed to solve the proposed optimization problem. It is noted that the proposed framework is a general one which can leverage several well-known algorithms as special cases and elucidate their intrinsic relationships. To validate the effectiveness of the proposed method, extensive experiments are conducted on diversity datasets for different image understanding tasks, i.e., image tagging, clustering, and classification, and the more encouraging results are achieved compared with some state-of-the-art approaches.