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Heterogeneous domain adaptation (HDA) addresses the task of associating data not only across dissimilar domains but also described by different types of features. Inspired by the recent advances of neural networks and deep learning, we propose a deep leaning model of transfer neural trees (TNT), which jointly solves cross-domain feature mapping, adaptation, and classification in a unified architecture. As the prediction layer in TNT, we introduce transfer neural decision forest (transfer-NDF), which is able to learn the neurons in TNT for adaptation by stochastic pruning. In order to handle semi-supervised HDA, a unique embedding loss term is introduced to TNT for preserving prediction and structural consistency between labeled and unlabeled target-domain data. Furthermore, we show that our TNT can be extended to zero shot learning for associating image and attribute data with promising performance. Finally, experiments on different classification tasks across features, datasets, and modalities would verify the effectiveness of our TNT.

Late fusion is one of the most effective approaches to enhance recognition accuracy through combining prediction scores of multiple classifiers, each of which is trained by a specific feature or model. The existing methods generally use a fixed fusion weight for one classifier over all samples, and ignore the fact that each classifier may perform better or worse for different subsets of samples. In order to address this issue, we propose a novel sample specific late fusion (SSLF) method. Specifically, we cast late fusion into an information propagation process that diffuses the fusion weights of labeled samples to the individual unlabeled samples, and enforce positive samples to have higher fusion scores than negative samples. Upon this process, the optimal fusion weight for each sample is identified, while positive samples are pushed toward the top at the fusion score rank list to achieve better accuracy. In this paper, two SSLF methods are presented. The first method is ranking SSLF (R-SSLF), which is based on graph Laplacian with RankSVM style constraints. We formulate and solve the problem with a fast gradient projection algorithm; the second method is infinite push SSLF (I-SSLF), which combines graph Laplacian with infinite push constraints. I-SSLF is a $l_{\infty }$ norm constrained optimization problem and can be solved by an efficient alternating direction method of multipliers method. Extensive experiments on both large-scale image and video data sets demonstrate the effectiveness of our methods. In addition, in order to make our method scalable to support large data sets, the AnchorGraph model is employed to propagate information on a subset of samples (anchor points) and then reconstruct the entire graph to get the weights of all samples. To the best of our knowledge, this is the first method that supports learning of sample specific fusion weights for late fusion.

The two-dimensional (2-D) fractional Brownian motion (fBm) model is useful in describing natural scenes and textures. Most fractal estimation algorithms for 2-D isotropic fBm images are simple extensions of the one-dimensional (1-D) fBm estimation method. This method does not perform well when the image size is small (say, 32/spl times/32). We propose a new algorithm that estimates the fractal parameter from the decay of the variance of the wavelet coefficients across scales. Our method places no restriction on the wavelets. Also, it provides a robust parameter estimation for small noisy fractal images. For image denoising, a Wiener filter is constructed by our algorithm using the estimated parameters and is then applied to the noisy wavelet coefficients at each scale. We show that the averaged power spectrum of the denoised image is isotropic and is a nearly 1/f process. The performance of our algorithm is shown by numerical simulation for both the fractal parameter and the image estimation. Applications to coastline detection and texture segmentation in a noisy environment are also demonstrated.