Out-of-sample generalizations for supervised manifold learning for classification

Supervised manifold learning methods for data classification map data samples residing in a high-dimensional ambient space to a lower-dimensional domain in a structure-preserving way, while enhancing the separation between different classes in the learned embedding. Most nonlinear supervised manifold learning methods compute the embedding of the manifolds only at the initially available training points, while the generalization of the embedding to novel points, known as the out-of-sample extension problem in manifold learning, becomes especially important in classification applications. In this work, we propose a semi-supervised method for building an interpolation function that provides an out-of-sample extension for general supervised manifold learning algorithms studied in the context of classification. The proposed algorithm computes a radial basis function (RBF) interpolator that minimizes an objective function consisting of the total embedding error of unlabeled test samples, defined as their distance to the embeddings of the manifolds of their own class, as well as a regularization term that controls the smoothness of the interpolation function in a direction-dependent way. The class labels of test data and the interpolation function parameters are estimated jointly with a progressive procedure. Experimental results on face and object images demonstrate the potential of the proposed out-of-sample extension algorithm for the classification of manifold-modeled data sets

A study of the classification of low-dimensional data with supervised manifold learning

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of supervised manifold learning for classification. We consider nonlinear dimensionality reduction algorithms that yield linearly separable embeddings of training data and present generalization bounds for this type of algorithms. A necessary condition for satisfactory generalization performance is that the embedding allow the construction of a sufficiently regular interpolation function in relation with the separation margin of the embedding. We show that for supervised embeddings satisfying this condition, the classification error decays at an exponential rate with the number of training samples. Finally, we examine the separability of supervised nonlinear embeddings that aim to preserve the low-dimensional geometric structure of data based on graph representations. The proposed analysis is supported by experiments on several real data sets

Synchronization recovery and state model reduction for soft decoding of variable length codes

Variable length codes exhibit de-synchronization problems when transmitted over noisy channels. Trellis decoding techniques based on Maximum A Posteriori (MAP) estimators are often used to minimize the error rate on the estimated sequence. If the number of symbols and/or bits transmitted are known by the decoder, termination constraints can be incorporated in the decoding process. All the paths in the trellis which do not lead to a valid sequence length are suppressed. This paper presents an analytic method to assess the expected error resilience of a VLC when trellis decoding with a sequence length constraint is used. The approach is based on the computation, for a given code, of the amount of information brought by the constraint. It is then shown that this quantity as well as the probability that the VLC decoder does not re-synchronize in a strict sense, are not significantly altered by appropriate trellis states aggregation. This proves that the performance obtained by running a length-constrained Viterbi decoder on aggregated state models approaches the one obtained with the bit/symbol trellis, with a significantly reduced complexity. It is then shown that the complexity can be further decreased by projecting the state model on two state models of reduced size

Geometry-Aware Neighborhood Search for Learning Local Models for Image Reconstruction

Local learning of sparse image models has proven to be very effective to solve inverse problems in many computer vision applications. To learn such models, the data samples are often clustered using the K-means algorithm with the Euclidean distance as a dissimilarity metric. However, the Euclidean distance may not always be a good dissimilarity measure for comparing data samples lying on a manifold. In this paper, we propose two algorithms for determining a local subset of training samples from which a good local model can be computed for reconstructing a given input test sample, where we take into account the underlying geometry of the data. The first algorithm, called Adaptive Geometry-driven Nearest Neighbor search (AGNN), is an adaptive scheme which can be seen as an out-of-sample extension of the replicator graph clustering method for local model learning. The second method, called Geometry-driven Overlapping Clusters (GOC), is a less complex nonadaptive alternative for training subset selection. The proposed AGNN and GOC methods are evaluated in image super-resolution, deblurring and denoising applications and shown to outperform spectral clustering, soft clustering, and geodesic distance based subset selection in most settings.Comment: 15 pages, 10 figures and 5 table

Light field image processing : overview and research issues

Light field (LF) imaging first appeared in the computer graphics community with the goal of photorealistic 3D rendering [1]. Motivated by a variety of potential applications in various domains (e.g., computational photography, augmented reality, light field microscopy, medical imaging, 3D robotic, particle image velocimetry), imaging from real light fields has recently gained in popularity, both at the research and industrial level.peer-reviewe

Incremental-LDI for Multi-View Coding

International audienceThis paper describes an Incremental algorithm for Layer Depth Image construction (I-LDI) from multi-view plus depth data sets. A solution to sampling artifacts is proposed, based on pixel interpolation (inpainting) restricted to isolated unknown pixels. A solution to ghosting artifacts is also proposed, based on a depth discontinuity detection, followed by a local foreground / background classification. We propose a formulation of warping equations which reduces time consumption, specifically for LDI warping. Tests on Breakdancers and Ballet MVD data sets show that extra layers in I-LDI contain only 10% of first layer pixels, compared to 50% for LDI. I-LDI Layers are also more compact, with a less spread pixel distribution, and thus easier to compress than LDI Visual rendering is of similar quality with I-LDI and LDI

Learning-based Spatial and Angular Information Separation for Light Field Compression

Light fields are a type of image data that capture both spatial and angular scene information by recording light rays emitted by a scene from different orientations. In this context, spatial information is defined as features that remain static regardless of perspectives, while angular information refers to features that vary between viewpoints. We propose a novel neural network that, by design, can separate angular and spatial information of a light field. The network represents spatial information using spatial kernels shared among all Sub-Aperture Images (SAIs), and angular information using sets of angular kernels for each SAI. To further improve the representation capability of the network without increasing parameter number, we also introduce angular kernel allocation and kernel tensor decomposition mechanisms. Extensive experiments demonstrate the benefits of information separation: when applied to the compression task, our network outperforms other state-of-the-art methods by a large margin. And angular information can be easily transferred to other scenes for rendering dense views, showing the successful separation and the potential use case for the view synthesis task. We plan to release the code upon acceptance of the paper to encourage further research on this topic