This paper introduces a learning scheme to construct a Hilbert space (i.e., a vector space along its inner product) to address both unsupervised and semi-supervised domain adaptation problems. This is achieved by learning projections from each domain to a latent space along the Mahalanobis metric of the latent space to simultaneously minimizing a notion of domain variance while maximizing a measure of discriminatory power. In particular, we make use of the Riemannian optimization techniques to match statistical properties (e.g., first and second order statistics) between samples projected into the latent space from different domains. Upon availability of class labels, we further deem samples sharing the same label to form more compact clusters while pulling away samples coming from different classes.We extensively evaluate and contrast our proposal against state-of-the-art methods for the task of visual domain adaptation using both handcrafted and deep-net features. Our experiments show that even with a simple nearest neighbor classifier, the proposed method can outperform several state-of-the-art methods benefitting from more involved classification schemes.
One notable example of constructing a latent space is the work of @cite_18 . In particular, the authors propose to use two fixed and predefined transformations to project source and target data to a common and higher-dimensional space. As a requirement, the method only accepts domains with the same dimensionality and hence cannot be directly used to adapt heterogeneous domains.
@cite_18
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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. Given data, deep generative models, such as variational autoencoders (VAE) and generative adversarial networks (GAN), train a lower dimensional latent representation of the data space. The linear Euclidean geometry of data space pulls back to a nonlinear Riemannian geometry on the latent space. The latent space thus provides a low-dimensional nonlinear representation of data and classical linear statistical techniques are no longer applicable. In this paper we show how statistics of data in their latent space representation can be performed using techniques from the field of nonlinear manifold statistics. Nonlinear manifold statistics provide generalizations of Euclidean statistical notions including means, principal component analysis, and maximum likelihood fits of parametric probability distributions. We develop new techniques for maximum likelihood inference in latent space, and adress the computational complexity of using geometric algorithms with high-dimensional data by training a separate neural network to approximate the Riemannian metric and cometric tensor capturing the shape of the learned data manifold. Transfer learning addresses the problem of how to utilize plenty of labeled data in a source domain to solve related but different problems in a target domain, even when the training and testing problems have different distributions or features. In this paper, we consider transfer learning via dimensionality reduction. To solve this problem, we learn a low-dimensional latent feature space where the distributions between the source domain data and the target domain data are the same or close to each other. Onto this latent feature space, we project the data in related domains where we can apply standard learning algorithms to train classification or regression models. Thus, the latent feature space can be treated as a bridge of transferring knowledge from the source domain to the target domain. The main contribution of our work is that we propose a new dimensionality reduction method to find a latent space, which minimizes the distance between distributions of the data in different domains in a latent space. The effectiveness of our approach to transfer learning is verified by experiments in two real world applications: indoor WiFi localization and binary text classification. In this paper we present a fully Bayesian latent variable model which exploits conditional nonlinear(in)-dependence structures to learn an efficient latent representation. The latent space is factorized to represent shared and private information from multiple views of the data. In contrast to previous approaches, we introduce a relaxation to the discrete segmentation and allow for a "softly" shared latent space. Further, Bayesian techniques allow us to automatically estimate the dimensionality of the latent spaces. The model is capable of capturing structure underlying extremely high dimensional spaces. This is illustrated by modelling unprocessed images with tenths of thousands of pixels. This also allows us to directly generate novel images from the trained model by sampling from the discovered latent spaces. We also demonstrate the model by prediction of human pose in an ambiguous setting. Our Bayesian framework allows us to perform disambiguation in a principled manner by including latent space priors which incorporate the dynamic nature of the data.