Robust Visual Domain Adaptation with LowRank Reconstruction 




IHong Jhuo^{†},
Dong Liu^{‡}, D.T. Lee^{†} and ShihFu Chang^{‡} National Taiwan University^{†} Columbia University^{‡} AbstractVisual domain adaptation addresses the problem of adapting the sample distribution of the source domain to the target domain, where the recognition task is intended but the data distributions are different. In this paper, we present a lowrank reconstruction method to reduce the domain distribution disparity. Specifically, we transform the visual samples in the source domain into an intermediate representation such that each transformed source sample can be linearly reconstructed by the samples of the target domain. Unlike the existing work, our method captures the intrinsic relatedness of the source samples during the adaptation process while uncovering the noises and outliers in the source domain that cannot be adapted, making it more robust than previous methods. We formulate our problem as a constrained nuclear norm and l_{2,1} norm minimization objective and then adopt the Augmented Lagrange Multiplier (ALM) method for the optimization. Extensive experiments on various visual adaptation tasks show that the proposed method consistently and significantly beats the stateoftheart domain adaptation methods. Motivationl To effectively adapt the sample distribution of the source domain to match that of the target domain. l The common issues with prior works are: n Dealing with source samples separately: The adapted distributions may be inconsistent among different source domains. n Outliers problem: Not every source sample is useful. There are possibly outliers. Blindly translating outlier samples will hurt performance. Approachl Visual Domain Adaptation with Low Rank Reconstruction Ø We transform the visual samples in the source domain into an intermediate representation. Ø Each transformed source sample can be linearly reconstructed by the samples of the target domain. Ø We enforce the reconstruction coefficient matrix corresponding to all source samples to be low rank while removing the noisy features that cannot be adapted through group sparsity. l The problem is solved with a constrained nuclear norm and l_{2,1} norm optimization by Augmented Lagrange Multiplier (ALM) algorithm.
Fig. Illustration of our proposed method. Each source domain S_{i} contains two classes of samples (marked as purple ellipses and blue triangles) as well as some noisy samples (marked as black diamonds). The samples in the target domain are marked with letter `t'. Our method transforms each source domain S_{i} into an intermediate representation W_{i}S_{i} such that each transformed sample can be linearly reconstructed by the target samples. Within each source domain S_{i}, we enforce the reconstruction of source samples to be related to each other under a lowrank structure while allowing the existence of a sparse set of noisy samples. Furthermore, by enforcing different source domains W_{1}S_{1},...,W_{M}S_{M} to be jointly low rank, we form a compact source sample set whose distribution is close to the target domain. The whole procedure is unsupervised without utilizing any label information. Problem Definitionl Our goal is to find a transformation matrix to transform the source domain S into an intermediate representation matrix, given a set of n samples in a source domain, and in the target domain, where d is the dimension of the feature vector. l The relation between samples in source and target domains is the following: , where is the reconstruction coefficient matrix. Ø Single Source Domain Adaptation Adapt one source domain to the target domain. Capturing intrinsic structure information and handle the outliers/ noises in the source domain.
, where denotes the nuclear norm of a matrix and encourages the error columns of E to be zero.
Ø Multiple Source Domain Adaptation The multitask low rank domain adaptation can be formulated as:
² are two tradeoff parameters. ² Q is a matrix formed by and represents the ith transformed source domain. Experiments and ResultsWe evaluate the effectiveness of our proposed method, referred to as Robust Domain Adaptation with Lowrank Reconstruction (RDALR), on various challenging visual domain adaptation tasks including threedomain object, Caltech256, and TRECVID. In each task, the performance of the following domain adaptation methods will be compared. (1) Naive Combination (NC). We directly augment the target domain with samples from the source domain without any transformation. (2) Adaptive SVM (ASVM). In this method, a SVM classifier is first trained in the source domain, and then adjusted to fit the training samples in the target domain. (3) Noisy Domain Adaptive Reconstruction (NDAR). In this case, we do not consider to remove the noise and outlier information in the source domain. (4) Our proposed RDALR method.
Threedomain object
Fig. Performance of
different methods on Caltech 256 dataset, where the per category
number of training images
in the target domain
varies from 5 to 50. The per
category number of images from the
Bing source domain is fixed at 10. TRECVID
MED 2011
Fig. Perevent performance comparison on the TRECVID MED 2011 dataset Poster Publications IHong Jhuo, Dong Liu, D.T. Lee, ShihFu Chang. Robust Visual Domain Adaptation with LowRank Reconstruction. In IEEE International Conference on Computer Vision and Pattern Recognition (CVPR), 2012. [pdf] 