text: The problem of data augmentation in feature space is considered. A new architecture, denoted the FeATure TransfEr Network (FATTEN), is proposed for the modeling of feature trajectories induced by variations of object pose. This architecture exploits a parametrization of the pose manifold in terms of pose and appearance. This leads to a deep encoder decoder network architecture, where the encoder factors into an appearance and a pose predictor. Unlike previous attempts at trajectory transfer, FATTEN can be efficiently trained end-to-end, with no need to train separate feature transfer functions. This is realized by supplying the decoder with information about a target pose and the use of a multi-task loss that penalizes category- and pose-mismatches. In result, FATTEN discourages discontinuous or non-smooth trajectories that fail to capture the structure of the pose manifold, and generalizes well on object recognition tasks involving large pose variation. Experimental results on the artificial ModelNet database show that it can successfully learn to map source features to target features of a desired pose, while preserving class identity. Most notably, by using feature space transfer for data augmentation (w.r.t. pose and depth) on SUN-RGBD objects, we demonstrate considerable performance improvements on one few-shot object recognition in a transfer learning setup, compared to current state-of-the-art methods.
  @cite_8: 
  @cite_33: Many areas of science depend on exploratory data analysis and visualization. The need to analyze large amounts of multivariate data raises the fundamental problem of dimensionality reduction: how to discover compact representations of high-dimensional data. Here, we introduce locally linear embedding (LLE), an unsupervised learning algorithm that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs. Unlike clustering methods for local dimensionality reduction, LLE maps its inputs into a single global coordinate system of lower dimensionality, and its optimizations do not involve local minima. By exploiting the local symmetries of linear reconstructions, LLE is able to learn the global structure of nonlinear manifolds, such as those generated by images of faces or documents of text. How do we judge similarity? Our mental representations of the world are formed by processing large numbers of sensory in
  @cite_39: One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a low-dimensional manifold embedded in a high-dimensional space. Drawing on the correspondence between the graph Laplacian, the Laplace Beltrami operator on the manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for representing the high-dimensional data. The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality-preserving properties and a natural connection to clustering. Some potential applications and illustrative examples are discussed.
summary: Since objects describe smooth trajectories in image space, as a function of viewing angle, it has long been known that such trajectories span a 3D manifold in image space, parameterized by the viewing angle. Hence, many of the manifold modeling methods proposed in the literature @cite_33 @cite_39 @cite_8 could, in principle, be used to develop trajectory transfer algorithms. However, many of these methods are transductive, , they do not produce a function that can make predictions for images outside of the training set, and do not leverage recent advances in deep learning. While deep learning could be used to explicitly model pose manifolds, it is difficult to rely on CNNs pre-trained on ImageNet for this purpose. This is because these networks attempt to collapse the manifold into a space where class discrimination is linear. On the other hand, the feature trajectories in response to pose variability are readily available. These trajectories are also much easier to model. For example, if the CNN is successful in mapping the pose manifold of a given object into a single point, , exhibits total pose invariance for that object, the problem is already solved and trajectory leaning is trivial for that object.