Manifold learning Research Papers - Academia.edu (original) (raw)

MR image data can provide many features or measures although any single measure is unlikely to comprehensively characterize the underlying morphology. We present a framework in which multiple measures are used in manifold learning steps... more

MR image data can provide many features or measures although any single measure is unlikely to comprehensively characterize the underlying morphology. We present a framework in which multiple measures are used in manifold learning steps to generate coordinate embeddings which are then combined to give an improved single representation of the population. An application to neonatal brain MRI data shows that the use of shape and appearance measures in particular leads to biologically plausible and consistent representations correlating well with clinical data. Orthogonality among the correlations suggests the embedding components relate to comparatively independent morphological features. The rapid changes that occur in brain shape and in MR image appearance during neonatal brain development justify the use of shape measures (obtained from a deformation metric) and appearance measures (obtained from image similarity). The benefit of combining separate embeddings is demonstrated by improved correlations with clinical data and we illustrate the potential of the proposed framework in characterizing trajectories of brain development.

Manifold learning has been successfully used for finding dominant factors (low-dimensional manifold) in a high-dimensional data set. However, most existing manifold learning algorithms only consider one manifold based on one dissimilarity... more

Manifold learning has been successfully used for finding dominant factors (low-dimensional manifold) in a high-dimensional data set. However, most existing manifold learning algorithms only consider one manifold based on one dissimilarity matrix. For utilizing multiple manifolds, a key question is how different pieces of information can be integrated when multiple measurements are available. Amari proposed α-integration for stochastic model integration, which is a generalized averaging method that includes as a special case arithmetic, geometric, and harmonic averages. In this paper, we propose a new generalized manifold integration algorithm equipped with α-integration, manifold α -integration (MAI). Interestingly, MAI can be shown to be a generalization of other integration methods (that may or may not use manifolds) like kernel fusion or mixture of random walk. Our experimental results also confirm that integration of multiple sources of information on individual manifolds is superior to the use of individual manifolds separately, in tasks including classification and sensorimotor integration.

The visualization and exploration of multivariate data is still a challenging task. Methods either try to visualize all variables simultaneously at each position using glyph-based approaches or use linked views for the interaction between... more

The visualization and exploration of multivariate data is still a challenging task. Methods either try to visualize all variables simultaneously at each position using glyph-based approaches or use linked views for the interaction between attribute space and physical domain such as brushing of scatterplots. Most visualizations of the attribute space are either difficult to understand or suffer from visual clutter. We propose a transformation of the high-dimensional data in attribute space to 2D that results in a point cloud, called attribute cloud, such that points with similar multivariate attributes are located close to each other. The transformation is based on ideas from multivariate density estimation and manifold learning. The resulting attribute cloud is an easy to understand visualization of multivariate data in two dimensions. We explain several techniques to incorporate additional information into the attribute cloud, that help the user get a better understanding of multivariate data. Using different examples from fluid dynamics and climate simulation, we show how brushing can be used to explore the attribute cloud and find interesting structures in physical space.

Large medical image datasets form a rich source of anatomical descriptions for research into pathology and clinical biomarkers. Many features may be extracted from data such as MR images to provide, through manifold learning methods, new... more

Large medical image datasets form a rich source of anatomical descriptions for research into pathology and clinical biomarkers. Many features may be extracted from data such as MR images to provide, through manifold learning methods, new representations of the population's anatomy. However, the ability of any individual feature to fully capture all aspects morphology is limited. We propose a framework for deriving a representation from multiple features or measures which can be chosen to suit the application and are processed using separate manifold-learning steps. The results are then combined to give a single set of embedding coordinates for the data. We illustrate the framework in a population study of neonatal brain MR images and show how consistent representations, correlating well with clinical data, are given by measures of shape and of appearance. These particular measures were chosen as the developing neonatal brain undergoes rapid changes in shape and MR appearance and were derived from extracted cortical surfaces, non-rigid deformations and image similarities. Combined single embeddings show improved correlations demonstrating their benefit for further studies such as identifying patterns in the trajectories of brain development. The results also suggest a lasting effect of age at birth on brain morphology, coinciding with previous clinical studies.

We find the minimax rate of convergence in Hausdorff distance for estimating a manifold M of dimension d embedded in R^D given a noisy sample from the manifold. We assume that the manifold satisfies a smoothness condition and that the... more

We find the minimax rate of convergence in Hausdorff distance for estimating a manifold M of dimension d embedded in R^D given a noisy sample from the manifold. We assume that the manifold satisfies a smoothness condition and that the noise distribution has compact support. We show that the optimal rate of convergence is n^{-2/(2+d)}. Thus, the minimax rate depends only on the dimension of the manifold, not on the dimension of the space in which M is embedded.

In this work, we present a nonrigid approach to jointly solving the tasks of 2D-3D pose estimation and 2D image segmentation. In general, most frameworks that couple both pose estimation and segmentation assume that one has exact... more

In this work, we present a nonrigid approach to jointly solving the tasks of 2D-3D pose estimation and 2D image segmentation. In general, most frameworks that couple both pose estimation and segmentation assume that one has exact knowledge of the 3D object. However, under nonideal conditions, this assumption may be violated if only a general class to which a given shape belongs is given (e.g., cars, boats, or planes). Thus, we propose to solve the 2D-3D pose estimation and 2D image segmentation via nonlinear manifold learning of 3D embedded shapes for a general class of objects or deformations for which one may not be able to associate a skeleton model. Thus, the novelty of our method is threefold: First, we present and derive a gradient flow for the task of nonrigid pose estimation and segmentation. Second, due to the possible nonlinear structures of one's training set, we evolve the preimage obtained through kernel PCA for the task of shape analysis. Third, we show that the derivation for shape weights is general. This allows us to use various kernels, as well as other statistical learning methodologies, with only minimal changes needing to be made to the overall shape evolution scheme. In contrast with other techniques, we approach the nonrigid problem, which is an infinitedimensional task, with a finite-dimensional optimization scheme. More importantly, we do not explicitly need to know the interaction between various shapes such as that needed for skeleton models as this is done implicitly through shape learning. We provide experimental results on several challenging pose estimation and segmentation scenarios.

The creation of concepts requires integrating information coming from different sensory modal- ities. In real world learning scenarios explicit labels are often not provided, and modelling the mechanisms underlying the formation of... more

The creation of concepts requires integrating information coming from different sensory modal- ities. In real world learning scenarios explicit labels are often not provided, and modelling the mechanisms underlying the formation of complex categories by aligning multi-sensory information without explicit supervision is a challenging task. Numerous methods have been proposed to model this alignment process. The vast majority of these methods are designed for information in the form of manifolds embedded in Euclidean space. However, knowledge networks, e.g. Wikipedia, and complex symbolic datasets often exhibit a latent tree-like hierarchical structure, which is not optimally embedded in Euclidean space as it does not allow to optimally capture hierarchy and similarity relations between the embedded elements. Moreover, tree-like hierarchical datasets ex- hibit a type of invariance named branch permutation, or node order invariance, given by a lack of consistent ordering of branches in the embeddings of a dataset obtained from different runs of the same algorithm. It has recently been proven that hyperbolic space represents a much more efficient metric when embedding hierarchical data. For this reason, we propose an algorithm for semi-supervised manifold alignment in hyperbolic space with the aim of leveraging the properties of hyperbolic metric for a more efficient conceptual systems alignment. We believe we opened the way for a class of graph alignment methods in hyperbolic space which have the potential to drastically improve state-of-the-art manifold alignment methods. This could in turn provide an alternative method for tackling tasks such as transfer learning, cross-lingual information re- trieval and more. Additionally, it could provide a better understanding of how the alignment of conceptual systems is performed in the brain.

In this paper, we provide a framework based upon diffusion processes for finding meaningful geometric descriptions of data sets. We show that eigenfunctions of Markov matrices can be used to construct coordinates called diffusion maps... more

In this paper, we provide a framework based upon diffusion processes for finding meaningful geometric descriptions of data sets. We show that eigenfunctions of Markov matrices can be used to construct coordinates called diffusion maps that generate efficient representations of complex geometric structures. The associated family of diffusion distances, obtained by iterating the Markov matrix, defines multiscale geometries that prove to be useful in the context of data parametrization and dimensionality reduction. The proposed framework relates the spectral properties of Markov processes to their geometric counterparts and it unifies ideas arising in a variety of contexts such as machine learning, spectral graph theory and eigenmap methods.

In this thesis we examine linear transformations and matrices in connection to signal processing. These two concepts are very interrelated in that it is the matrix that carry out a linear transformation. We will discuss some transforms,... more

In this thesis we examine linear transformations and matrices in connection to signal processing. These two concepts are very interrelated in that it is the matrix that carry out a linear transformation. We will discuss some transforms, which are widely used in signal processing, and examine how they perform in denoising and prediction. These properties are related to how well the signal is represented using the respective transforms and their statistical properties.
The linear transformation we are going to investigate in detail is the independent component analysis (ICA) transform. The ICA transform has several interesting properties. In the visual cortex of the human brain, some features have been encountered, which is referred to as sparse coding. This is one of the ICA transform's main properties. The transformed data becomes sparser than the original data.

Abstract. We link nonlinear manifold learning techniques for data analysis/compression with model reduction techniques for evolution equations with time scale separation. In particular, we demonstrate a “nonlinear extension” of the... more

Abstract. We link nonlinear manifold learning techniques for data analysis/compression with model reduction techniques for evolution equations with time scale separation. In particular, we demonstrate a “nonlinear extension” of the POD-Galerkin approach to obtaining ...

Over the past few decades, a large family of algorithms-supervised or unsupervised; stemming from statistics or geometry theory-has been designed to provide different solutions to the problem of dimensionality reduction. Despite the... more

Over the past few decades, a large family of algorithms-supervised or unsupervised; stemming from statistics or geometry theory-has been designed to provide different solutions to the problem of dimensionality reduction. Despite the different motivations of these algorithms, we present in this paper a general formulation known as graph embedding to unify them within a common framework. In graph embedding, each algorithm can be considered as the direct graph embedding or its linear/kernel/tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set, with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided. Furthermore, the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms. By utilizing this framework as a tool, we propose a new supervised dimensionality reduction algorithm called Marginal Fisher Analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class, while the penalty graph connects the marginal points and characterizes the interclass separability. We show that MFA effectively overcomes the limitations of the traditional Linear Discriminant Analysis algorithm due to data distribution assumptions and available projection directions. Real face recognition experiments show the superiority of our proposed MFA in comparison to LDA, also for corresponding kernel and tensor extensions.

The isometric feature mapping (Isomap) method has demonstrated promising results in finding low-dimensional manifolds from data points in high-dimensional input space. Isomap has one free parameter (number of nearest neighbours K or... more

The isometric feature mapping (Isomap) method has demonstrated promising results in finding low-dimensional manifolds from data points in high-dimensional input space. Isomap has one free parameter (number of nearest neighbours K or neighbourhood radius), which has to be specified manually. In this paper we present a new method for selecting the optimal parameter value for Isomap automatically. Numerous experiments on synthetic and real data sets show the effectiveness of our method.

In this paper, we propose a novel method called dynamic transition embedding (DTE) for linear dimensionality reduction. Differing from the recently proposed manifold learning-based methods, DTE introduces the dynamic transition... more

In this paper, we propose a novel method called dynamic transition embedding (DTE) for linear dimensionality reduction. Differing from the recently proposed manifold learning-based methods, DTE introduces the dynamic transition information into the objective function by characterizing the Markov transition processes of the data set in time t(t > 0). In the DTE framework, running the Markov chain forward in time, or equivalently, taking the larger powers of Markov transition matrices integrates the local geometry and, therefore, reveals relevant geometric structures of the data set at different timescales. Since the Markov transition matrices defined by the connectivity on a graph contain the intrinsic geometry information of the data points, the elements of the Markov transition matrices can be viewed as the probabilities or the similarities between two points. Thus, minimizing the errors of the probability reconstruction or similarity reconstruction instead of the least-square reconstruction in the well-known manifold learning algorithms will obtain the optimal linear projections with respect to preserving the intrinsic Markov processes of the data set. Comprehensive comparisons and extensive experiments show that DTE achieves higher recognition rates than some well-known linear dimensionality reduction techniques.

In this paper, we examine the accuracy of manifold coordinate representations as a reduced representation of a hyperspectral imagery (HSI) lookup table (LUT) for bathymetry retrieval. We also explore on a more limited basis the potential... more

In this paper, we examine the accuracy of manifold coordinate representations as a reduced representation of a hyperspectral imagery (HSI) lookup table (LUT) for bathymetry retrieval. We also explore on a more limited basis the potential for using these coordinates for modeling other in water properties. Manifold coordinates are chosen because they are a datadriven intrinsic set of coordinates, which naturally parameterize nonlinearities that are present in HSI of water scenes. The approach is based on the extraction of a reduced dimensionality representation in manifold coordinates of a sufficiently large representative set of HSI. The manifold coordinates are derived from a scalable version of the isometric mapping algorithm. In the present and in our earlier works, these coordinates were used to establish an interpolating LUT for bathymetric retrieval by associating the representative data with ground truth data, in this case from a Light Detection and Ranging (LIDAR) estimate in the representative area. While not the focus of the present paper, the compression of LUTs could also be applied, in principle, to LUTs generated by forward radiative transfer models, and some preliminary work in this regard confirms the potential utility for this application. In this paper, we analyze the approach using data acquired by the Portable Hyperspectral Imager for Low-Light Spectroscopy (PHILLS) hyperspectral camera over the Indian River Lagoon, Florida, in 2004. Within a few months of the PHILLS overflights, Scanning Hydrographic Operational Airborne LIDAR Survey, LIDAR data were obtained for a portion of this study area, principally covering the beach zone and, in some instances, portions of contiguous river channels. Results demonstrate that significant compression of the LUTs is possible with little loss in retrieval accuracy.

We describe a semisupervised regression algorithm that learns to transform one time series into another time series given examples of the transformation. This algorithm is applied to tracking, where a time series of observations from... more

We describe a semisupervised regression algorithm that learns to transform one time series into another time series given examples of the transformation. This algorithm is applied to tracking, where a time series of observations from sensors is transformed to a time series describing the pose of a target. Instead of defining and implementing such transformations for each tracking task separately, our algorithm learns a memoryless transformation of time series from a few example input-output mappings. The algorithm searches for a smooth function that fits the training examples and, when applied to the input time series, produces a time series that evolves according to assumed dynamics. The learning procedure is fast and lends itself to a closed-form solution. It is closely related to nonlinear system identification and manifold learning techniques. We demonstrate our algorithm on the tasks of tracking RFID tags from signal strength measurements, recovering the pose of rigid objects, deformable bodies, and articulated bodies from video sequences. For these tasks, this algorithm requires significantly fewer examples compared to fully supervised regression algorithms or semisupervised learning algorithms that do not take the dynamics of the output time series into account.

The problem of dimensionality reduction arises in many fields of information processing, including machine learning, data compression, scientific visualization, pattern recognition, and neural computation. Here we describe locally linear... more

The problem of dimensionality reduction arises in many fields of information processing, including machine learning, data compression, scientific visualization, pattern recognition, and neural computation. Here we describe locally linear embedding (LLE), an unsupervised learning algorithm that computes low dimensional, neighborhood preserving embeddings of high dimensional data. The data, assumed to be sampled from an underlying manifold, are mapped into a single global coordinate system of lower dimensionality. The mapping is derived from the symmetries of locally linear reconstructions, and the actual computation of the embedding reduces to a sparse eigenvalue problem. Notably, the optimizations in LLE--though capable of generating highly nonlinear embeddings--are simple to implement, and they do not involve local minima. In this paper, we describe the implementation of the algorithm in detail and discuss several extensions that enhance its performance. We present results of the algorithm applied to data sampled from known manifolds, as well as to collections of images of faces, lips, and handwritten digits. These examples are used to provide extensive illustrations of the algorithm's performance--both successes and failures--and to relate the algorithm to previous and ongoing work in nonlinear dimensionality reduction.

Face images under uncontrolled environments suffer from the changes of multiple factors such as camera view, illumination, expression, etc. Tensor analysis provides a way of analyzing the influence of different factors on facial... more

Face images under uncontrolled environments suffer from the changes of multiple factors such as camera view, illumination, expression, etc. Tensor analysis provides a way of analyzing the influence of different factors on facial variation. However, the TensorFace model creates a difficulty in representing the nonlinearity of view subspace. In this paper, to break this limitation, we present a view-manifold-based TensorFace (V-TensorFace), in which the latent view manifold preserves the local distances in the multiview face space. Moreover, a kernelized TensorFace (K-TensorFace) for multiview face recognition is proposed to preserve the structure of the latent manifold in the image space. Both methods provide a generative model that involves a continuous view manifold for unseen view representation. Most importantly, we propose a unified framework to generalize Tensor-Face, V-TensorFace, and K-TensorFace. Finally, an expectationmaximization like algorithm is developed to estimate the identity and view parameters iteratively for a face image of an unknown/unseen view. The experiment on the PIE database shows the effectiveness of the manifold construction method. Extensive comparison experiments on Weizmann and Oriental Face databases for multiview face recognition demonstrate the superiority of the proposed V-and K-TensorFace methods over the view-based principal component analysis and other state-of-theart approaches for such purpose.

Correlation filters are special classifiers designed for shift-invariant object recognition, which are robust to pattern distortions. The recent literature shows that combining a set of sub-filters trained based on a single or a small... more

Correlation filters are special classifiers designed for shift-invariant object recognition, which are robust to pattern distortions. The recent literature shows that combining a set of sub-filters trained based on a single or a small group of images obtains the best performance. The idea is equivalent to estimating variable distribution based on the data sampling (bagging), which can be interpreted as finding solutions (variable distribution approximation) directly from sampled data space. However, this methodology fails to account for the variations existed in the data. In this paper, we introduce an intermediate step – solution sampling – after the data sampling step to form a subspace, in which an optimal solution can be estimated. More specifically, we propose a new method, named latent constrained correlation filters (LCCF), by mapping the correlation filters to a given latent subspace, and develop a new learning framework in the latent subspace that embeds distribution-related constraints into the original problem. To solve the optimization problem, we introduce a subspace based alternating direction method of multipliers (SADMM), which is proven to converge at the saddle point. Our approach is successfully applied to three different tasks, including eye localization, car detection and object tracking. Extensive experiments demonstrate that LCCF outperforms the state-of-the-art methods. 1

We introduce vector diffusion maps (VDM), a new mathematical framework for organizing and analyzing massive high dimensional data sets, images and shapes. VDM is a mathematical and algorithmic generalization of diffusion maps and other... more

We introduce vector diffusion maps (VDM), a new mathematical framework for organizing and analyzing massive high dimensional data sets, images and shapes. VDM is a mathematical and algorithmic generalization of diffusion maps and other non-linear dimensionality reduction methods, such as LLE, ISOMAP and Laplacian eigenmaps. While existing methods are either directly or indirectly related to the heat kernel for functions over the data, VDM is based on the heat kernel for vector fields. VDM provides tools for organizing complex data sets, embedding them in a low dimensional space, and interpolating and regressing vector fields over the data. In particular, it equips the data with a metric, which we refer to as the vector diffusion distance. In the manifold learning setup, where the data set is distributed on (or near) a low dimensional manifold M d embedded in R p , we prove the relation between VDM and the connection-Laplacian operator for vector fields over the manifold.

Semi-supervised learning (SSL) is the problem of learning a function with only a partially labeled training set. It has considerable practical interest in applications where labeled data is costly to obtain, while unlabeled data is... more

Semi-supervised learning (SSL) is the problem of learning a function with only a partially labeled training set. It has considerable practical interest in applications where labeled data is costly to obtain, while unlabeled data is abundant. One approach to SSL in the case of binary classification is inspired by work on transductive learning (TL) by V. Vapnik. It has been applied prevalently using support vector machines (SVM) as the base learning algorithm, giving rise to the so-called transductive SVM (TR-SVM). The resulting optimization problem, however, is highly non-convex and complex to solve. In this paper, we propose an alternative semi-supervised training algorithm based on the TL theory, namely semi-supervised random vector functional-link (RVFL) network, which is able to obtain state-of-the-art performance, while resulting in a standard convex optimization problem. In particular we show that, thanks to the characteristics of RVFLs networks, the resulting optimization problem can be safely approximated with a standard quadratic programming problem solvable in polynomial time. A wide range of experiments validate our proposal. As a comparison, we also propose a semi-supervised algorithm for RVFLs based on the theory of manifold regularization.

We propose a novel regularizer when training an auto-encoder for unsupervised feature extraction. We explicitly encourage the latent representation to contract the input space by regularizing the norm of the Jacobian (analytically) and... more

We propose a novel regularizer when training an auto-encoder for unsupervised feature extraction. We explicitly encourage the latent representation to contract the input space by regularizing the norm of the Jacobian (analytically) and the Hessian (stochastically) of the encoder’s output with respect to its input, at the training points. While the penalty on the Jacobian’s norm ensures robustness to tiny corruption of samples in the input space, constraining the norm of the Hessian extends this robustness when moving further away from the sample. From a manifold learning perspective, balancing this regularization with the auto-encoder’s reconstruction objective yields a representation that varies most when moving along the data manifold in input space, and is most insensitive in directions orthogonal to the manifold. The second order regularization, using the Hessian, penalizes curvature, and thus favors smooth manifold. We show that our proposed technique, while remaining computationally efficient, yields representations that are significantly better suited for initializing deep architectures than previously proposed approaches, beating state-of-the-art performance on a number of datasets.

Recent years have witnessed great success of manifold learning methods in understanding the structure of multidimensional patterns. However, most of these methods operate in a batch mode and cannot be effectively applied when data are... more

Recent years have witnessed great success of manifold learning methods in understanding the structure of multidimensional patterns. However, most of these methods operate in a batch mode and cannot be effectively applied when data are collected sequentially. In this paper, we propose a general incremental learning framework, capable of dealing with one or more new samples each time, for the so-called spectral embedding methods. In the proposed framework, the incremental dimensionality reduction problem reduces to an incremental eigen-problem of matrices. Furthermore, we present, using this framework as a tool, an incremental version of Hessian eigenmaps, the IHLLE method. Finally, we show several experimental results on both synthetic and real world datasets, demonstrating the efficiency and accuracy of the proposed algorithm.

Dimensionality Reduction (DR) is attracting more attention these days as a result of the increasing need to handle huge amounts of data effectively. DR methods allow the number of initial features to be reduced considerably until a set of... more

Dimensionality Reduction (DR) is attracting more attention these days as a result of the increasing need to handle huge amounts of data effectively. DR methods allow the number of initial features to be reduced considerably until a set of them is found that allows the original properties of the data to be kept. However, their use entails an inherent loss of quality that is likely to affect the understanding of the data, in terms of data analysis. This loss of quality could be determinant when selecting a DR method, because of the nature of each method. In this paper, we propose a methodology that allows different DR methods to be analyzed and compared as regards the loss of quality produced by them. This methodology makes use of the concept of preservation of geometry (quality assessment criteria) to assess the loss of quality. Experiments have been carried out by using the most well-known DR algorithms and quality assessment criteria, based on the literature. These experiments have been applied on 12 real-world datasets. Results obtained so far show that it is possible to establish a method to select the most appropriate DR method, in terms of minimum loss of quality. Experiments have also highlighted some interesting relationships between the quality assessment criteria. Finally, the methodology allows the appropriate choice of dimensionality for reducing data to be established, whilst giving rise to a minimum loss of quality.

This paper develops a manifold-oriented stochastic neighbor projection (MSNP) technique for feature extraction. MSNP is designed to find a linear projection for the purpose of capturing the underlying pattern structure of observations... more

This paper develops a manifold-oriented stochastic neighbor projection (MSNP) technique for feature extraction. MSNP is designed to find a linear projection for the purpose of capturing the underlying pattern structure of observations that actually lie on a nonlinear manifold. In MSNP, the similarity information of observations is encoded with stochastic neighbor distribution based on geodesic distance metric, then the same distribution is required to be hold in feature space. This learning criterion not only empowers MSNP to extract nonlinear feature through a linear projection, but makes MSNP competitive as well by reason that distribution preservation is more workable and flexible than rigid distance preservation. MSNP is evaluated in three applications: data visualization for faces image, face recognition and palmprint recognition. Experimental results on several benchmark databases suggest that the proposed MSNP provides a unsupervised feature extraction approach with powerful pattern revealing capability for complex manifold data.

Stochastic neighbor embedding (SNE) and its variants are methods of dimensionality reduction (DR) that involve normalized softmax similarities derived from pairwise distances. These methods try to reproduce in the low-dimensional... more

Stochastic neighbor embedding (SNE) and its variants are methods of dimensionality reduction (DR) that involve normalized softmax similarities derived from pairwise distances. These methods try to reproduce in the low-dimensional embedding space the similarities observed in the high-dimensional data space. Their outstanding experimental results, compared to previous state-of-the-art methods, originate from their capability to foil the curse of dimensionality. Previous work has shown that this immunity stems partly from a property of shift invariance that allows appropriately normalized softmax similarities to mitigate the phenomenon of norm concentration. This paper investigates a complementary aspect, namely, the cost function that quantifies the mismatch between similarities computed in the high-and low-dimensional spaces. Stochastic neighbor embedding and its variant t-SNE rely on a single Kullback-Leibler divergence, whereas a weighted mixture of two dual KL divergences is used in neighborhood retrieval and visualization (NeRV). We propose in this paper a different mixture of KL divergences, which is a scaled version of the generalized Jensen-Shannon divergence. We show experimentally that this divergence produces embeddings that better preserve small K-ary neighborhoods, as compared to both the single KL divergence used in SNE and t-SNE and the mixture used in NeRV. These results allow us to conclude that future improvements in similaritybased DR will likely emerge from better definitions of the cost function.

The low-dimensional representation of high-dimensional data and the concise description of its intrinsic structures are central problems in data analysis. In this paper, an unsupervised learning algorithm called weighted locally linear... more

The low-dimensional representation of high-dimensional data and the concise description of its intrinsic structures are central problems in data analysis. In this paper, an unsupervised learning algorithm called weighted locally linear embedding (WLLE) is presented to discover the intrinsic structures of data, such as neighborhood relationships, global distributions and clustering. The WLLE algorithm is motivated by locally linear embedding (LLE) algorithm and cam weighted distance, a novel distance measure which usually gives a deflective cam contours for equal-distance contour in classification for an improved classification. It is a major advantage of the WLLE to optimize the process of intrinsic structure discovery by avoiding unreasonable neighbor searching, and at the same time, allow the discovery adapt to the characteristics of input data set. Furthermore, the algorithm discovers intrinsic structures which can be used to compute manipulative embedding for potential classification and recognition purposes, thus can work as a feature extraction algorithm. Simulation studies demonstrate that the WLLE can give better results in manifold learning and dimension reduction than LLE and neighborhood linear embedding (NLE), and is more robust to parameter changes. Experiments on face images data sets and comparison to other famous face recognition methods such as kernel-PCA (KPCA) and kernel direct discriminant analysis (KDDA) are done to show the potential of WLLE for real world problem.

In this article, we review recent mathematical models and computational methods for the processing of diffusion Magnetic Resonance Images, including state-of-the-art reconstruction of diffusion models, cerebral white matter connectivity... more

In this article, we review recent mathematical models and computational methods for the processing of diffusion Magnetic Resonance Images, including state-of-the-art reconstruction of diffusion models, cerebral white matter connectivity analysis, and segmentation techniques. We focus on Diffusion Tensor Images (DTI) and Q-Ball Images (QBI).

In the data-based approach to structural health monitoring (SHM) when novelty detection is utilised as a means of diagnosis, benign operational and environmental variations of the structure can lead to false alarms and mask the presence... more

In the data-based approach to structural health monitoring (SHM) when novelty detection is utilised as a means of diagnosis,
benign operational and environmental variations of the structure can lead to false alarms and mask the presence of damage. The key element
of this paper is to demonstrate a series of pattern recognition approaches which investigate complex correlations between the variables and
thus potentially shed light on the variations within the data that are of interest for SHM.
The non-linear manifold learning techniques discussed here, like locally linear embedding combined with robust discordance measures like
the minimum covariance determinant and regression techniques like Gaussian processes offer a strategy that includes reliable novelty detection
analysis but also a method of investigating the space where structural data clusters are lying.

We present new multi-layer joint gait-pose manifolds (multi-layer JGPMs) for complex human gait motion modeling, where three latent variables are defined jointly in a lowdimensional manifold to represent a variety of body configurations.... more

We present new multi-layer joint gait-pose manifolds (multi-layer JGPMs) for complex human gait motion modeling, where three latent variables are defined jointly in a lowdimensional manifold to represent a variety of body configurations. Specifically, the pose variable (along the pose manifold) denotes a specific stage in a walking cycle; the gait variable (along the gait manifold) represents different walking styles; and the linear scale variable characterizes the maximum stride in a walking cycle. We discuss two kinds of topological priors for coupling the pose and gait manifolds, i.e., cylindrical and toroidal, to examine their effectiveness and suitability for motion modeling. We resort to a topologically-constrained Gaussian Process latent variable model to learn the multi-layer JGPMs where two new techniques are introduced to facilitate model learning under limited training data. First is training data diversification that creates a set of simulated motion data with different strides. Second is the topology-aware local learning to speed up model learning by taking advantage of the local topological structure. The experimental results on the CMU Mocap data demonstrate the advantages of our proposed multi-layer models over several existing Gaussian Process-based motion models in terms of the overall performance of human gait motion modeling.

Image matting refers to the problem of accurately extracting foreground objects in images and video. The most recent work [1] and [2] in natural image matting relies on the local and manifold smoothness assumptions on foreground and... more

Image matting refers to the problem of accurately extracting foreground objects in images and video. The most recent work [1] and [2] in natural image matting relies on the local and manifold smoothness assumptions on foreground and background colors on which a cost function is established. In this paper, we present a framework of formulating new regularization for robust solutions and illustrate new algorithms using the standard benchmark images.

Machine learning methods are often applied to the problem of learning a map from a robot's sensor data, but they are rarely applied to the problem of learning a robot's motion model. The motion model, which can be influenced by robot... more

Machine learning methods are often applied to the problem of learning a map from a robot's sensor data, but they are rarely applied to the problem of learning a robot's motion model. The motion model, which can be influenced by robot idiosyncrasies and terrain properties, is a crucial aspect of current algorithms for Simultaneous Localization and Mapping (SLAM). In this paper we concentrate on generating the correct motion model for a robot by applying EM methods in conjunction with a current SLAM algorithm. In contrast to previous calibration approaches, we not only estimate the mean of the motion, but also the interdependencies between motion terms, and the variances in these terms. This can be used to provide a more focused proposal distribution to a particle filter used in a SLAM algorithm, which can reduce the resources needed for localization while decreasing the chance of losing track of the robot's position. We validate this approach by recovering a good motion model despite initialization with a poor one. Further experiments validate the generality of the learned model in similar circumstances.

It has been proposed that molecular changes in breast cancer (BC) may be accompanied by corresponding changes in phenotype. One such phenotype is the presence of lymphocytic infiltration (LI), a form of immune response seen often in high... more

It has been proposed that molecular changes in breast cancer (BC) may be accompanied by corresponding changes in phenotype. One such phenotype is the presence of lymphocytic infiltration (LI), a form of immune response seen often in high grade BC. The presence of LI in BC histology has been shown to correlate with prognosis and course of treatment. The advent of digitized histopathology has made tissue slides amenable to computer aided diagnosis (CAD). While texture-based features have recently been shown to successfully distinguish between tissue classes in histopathology, the similarity in appearance of BC nuclei and LI suggests that texture features alone may be insufficient. In this paper, we present a methodology that integrates manifold learning with graph-based features to distinguish high grade BC histology specimens based on the presence or absence of LI. Lymphocytes are first automatically detected via a segmentation scheme comprising a Bayesian classifier and template matching. For a total of 41 samples, the graphbased features, in conjunction with a Support Vector Machine classifier, achieve a classification accuracy of 89.50%. Our method is also compared against the popular Varma-Zisserman (VZ) texton-based classifier, which achieves a maximum accuracy of 62.50%. Visualization of the low dimensional manifold of the LI complex via Graph Embedding shows the presence of three distinct stages of LI.

We propose motion manifold learning and motion primitive segmentation framework for human motion synthesis from motion-captured data. High dimensional motion capture date are represented using a low dimensional representation by topology... more

We propose motion manifold learning and motion primitive segmentation framework for human motion synthesis from motion-captured data. High dimensional motion capture date are represented using a low dimensional representation by topology preserving network, which maps similar motion instances to the neighborhood points on the low dimensional motion manifold. Nonlinear manifold learning between a low dimensional manifold representation and high dimensional motion data provides a generative model to synthesize new motion sequence by controlling trajectory on the low dimensional motion manifold. We segment motion primitives by analyzing low dimensional representation of body poses through motion from motion captured data. Clustering techniques like k-means algorithms are used to find motion primitives after dimensionality reduction. Motion dynamics in training sequences can be described by transition characteristics of motion primitives. The transition matrix represents the temporal dynamics of the motion with Markovian assumption. We can generate new motion sequences by perturbing the temporal dynamics.

For improving the nonlinear alignment performance of Active Appearance Models (AAM), we apply a variant of the nonlinear manifold learning algorithm, Local Linear Embedded, to model shapetexture manifold. Experiments show that our method... more

For improving the nonlinear alignment performance of Active Appearance Models (AAM), we apply a variant of the nonlinear manifold learning algorithm, Local Linear Embedded, to model shapetexture manifold. Experiments show that our method maintains a lower alignment residual to some small scale movements compared with traditional AAM based on Principal Component Analysis (PCA) and makes a successful alignment to large scale motions when PCA-AAM failed.

Least square regression (LSR) is popular in pattern classification. Compared against other matrix factorization based methods, it is simple yet efficient. However, LSR ignores unlabeled samples in the training stage, so the regression... more

Least square regression (LSR) is popular in pattern classification. Compared against other matrix factorization based methods, it is simple yet efficient. However, LSR ignores unlabeled samples in the training stage, so the regression error could be large when the labeled samples are insufficient. To solve this problem, the Laplacian regularization can be used to penalize LSR. Extensive theoretical and experimental results have confirmed the validity of Laplacian regularized least square (LapRLS). However, multiple hyper-parameters have been introduced to estimate the intrinsic manifold induced by the regularization, and thus the time consuming cross-validation should be applied to tune these parameters. To alleviate this problem, we assume the intrinsic manifold is a linear combination of a given set of known manifolds. By further assuming the priors of the given manifolds are equivalent, we introduce the entropy maximization penalty to automatically learn the linear combination coefficients. The entropy maximization trades the smoothness off the complexity.

The emergence of low-cost sensor architectures for diverse modalities has made it possible to deploy sensor arrays that capture a single event from a large number of vantage points and using multiple modalities. In many scenarios, these... more

The emergence of low-cost sensor architectures for diverse modalities has made it possible to deploy sensor arrays that capture a single event from a large number of vantage points and using multiple modalities. In many scenarios, these sensors acquire very high-dimensional data such as audio signals, images, and video. To cope with such high-dimensional data, we typically rely on low-dimensional models. Manifold models provide a particularly powerful model that captures the structure of high-dimensional data when it is governed by a low-dimensional set of parameters. However, these models do not typically take into account dependencies among multiple sensors. We thus propose a new joint manifold framework for data ensembles that exploits such dependencies. We show that simple algorithms can exploit the joint manifold structure to improve their performance on standard signal processing applications. Additionally, recent results concerning dimensionality reduction for manifolds enable us to formulate a network-scalable data compression scheme that uses random projections of the sensed data. This scheme efficiently fuses the data from all sensors through the addition of such projections, regardless of the data modalities and dimensions.

Monte Carlo planning has been proven successful in many sequential decision-making settings, but it suffers from poor exploration when the rewards are sparse. In this paper, we improve exploration in UCT by generalizing across similar... more

Monte Carlo planning has been proven successful in many sequential decision-making settings, but it suffers from poor exploration when the rewards are sparse. In this paper, we improve exploration in UCT by generalizing across similar states using a given distance metric. When the state space does not have a natural distance metric, we show how we can learn a local manifold from the transition graph of states in the near future. to obtain a distance metric. On domains inspired by video games, empirical evidence shows that our algorithm is more sample efficient than UCT, particularly when rewards are sparse.

Conventional appearance-based face recognition methods usually assume there are multiple samples per person (MSPP) available during the training phase for discriminative feature extraction. In many practical face recognition applications... more

Conventional appearance-based face recognition methods usually assume there are multiple samples per person (MSPP) available during the training phase for discriminative feature extraction. In many practical face recognition applications such as law enhancement, e-passport and ID card identification, this assumption, however, may not hold as there is only a single sample per person (SSPP) enrolled or recorded in these systems. Many popular face recognition methods fail to work well in this scenario because there are not enough samples for discriminant learning. To address this problem, we propose in this paper a novel discriminative multi manifold analysis (DMMA) method by learning discriminative features from image patches. First, we partition each enrolled image into several nonoverlapping patches to form an image set for each sample per person. Then, we formulate the SSPP face recognition as a manifold-manifold matching problem and learn multiple DMMA feature spaces to maximize the manifold margins of different persons. Lastly, we propose are construction-based manifoldmanifold distance to identify the unlabeled subjects. Experimental results on three widely used face databases are presented to demonstrate the efficacy of the proposed approach.

Diffusion Maps (DiffMaps) has recently provided a general framework that unites many other spectral manifold learning algorithms, including Laplacian Eigenmaps, and it has become one of the most successful and popular frameworks for... more

Diffusion Maps (DiffMaps) has recently provided a general framework that unites many other spectral manifold learning algorithms, including Laplacian Eigenmaps, and it has become one of the most successful and popular frameworks for manifold learning to date. However, Diffusion Maps still often creates unnecessary distortions, and its performance varies widely in response to parameter value changes. In this paper, we draw a previously unnoticed connection between DiffMaps and spring-motivated methods. We show that DiffMaps has a physical interpretation: it finds the arrangement of high-dimensional objects in low-dimensional space that minimizes the elastic energy of a particular spring network. Within this interpretation, we recognize the root cause of a variety of problems that are commonly observed in the Diffusion Maps output, including sensitivity to user-specified parameters, sensitivity to sampling density, and distortion of boundaries. We then show how to exploit the connection between Diffusion Map and spring criteria to create a method that can be efficiently applied post hoc to alleviate these commonly observed deficiencies in the Diffusion Maps output.

Present days, cloud computing has developed as a significant worldview for IT industry with diminished cost, pay as you use, adaptability, simple availability and improved adaptability. In a cloud situation customer information can live... more

Present days, cloud computing has developed as a significant worldview for IT industry with diminished cost, pay as you use, adaptability, simple availability and improved adaptability. In a cloud situation customer information can live in any side of the world as can be security and protection issue with the customer information. To guarantee the security of information over cloud it is a great idea to redistribute the information in a scrambled works very really great with single information proprietor. Be that as it may, single proprietor plan confine the adaptability of framework which isn't helpful. So various information proprietors can re the information safely with encryption. While recovering such encoded information accessible symmetric Encryption procedure is utilized this will be inspected profoundly in this paper. To expand ease of use of framework, it is a great idea to pe positioned query item gives orderly view to the got outcome over scrambled information. Note that, recovering the information security safeguarding is principle issue. To accomplis in this review paper. Keywords: Multi-Keyword ranked investigate preserving; Introduction: Cloud is a capacity point where different information sources for example proprietors store information for accessibility and security. For protection safeguarding information proprietor permit approved information client to see their information. For inst foundation direct the examination for study. For that reason some volunteer patients would consent to share their wellbeing information on the cloud. For protection concern, i with discharge key. By this lone approved association can play out a protected inquiry over encoded information. Considering above situation creating multi proprietor framework. In a solitary proprietor framework, information produce trapdoors (encoded key

Recently developed feature extraction methods proposed in the explosive hazard detection community have yielded many features that potentially provide complementary information for explosive detection. Finding the right combination of... more

Recently developed feature extraction methods proposed in the explosive hazard detection community have yielded many features that potentially provide complementary information for explosive detection. Finding the right combination of features that is most effective in distinguishing targets from clutter, on the other hand, is extremely challenging due to a large number of potential features to explore. Furthermore, sensors employed for mine and buried explosive hazard detection are typically sensitive to environmental conditions such as soil properties and weather as well as other operating parameters. In this work, we applied Bayesian cross-categorization (CrossCat) to a heterogeneous set of features derived from EMI sensor time-series for purposes of buried explosive hazard detection. The set of features used here includes simple, point-wise measurements such as the overall magnitude of the EMI response, contextual information such as soil type, and a new feature consisting of spatially aggregated Discrete Spectra of Relaxation Frequencies (DSRFs). Previous work showed that the DSRF characterizes target properties with some invariance to orientation and position. We have developed a novel approach to aggregate point-wise DSRF estimates. The spatial aggregation is based on the Bag-of-Words (BoW) model found in the machine learning and computer vision literatures and aims to enhance the invariance properties of point-wise DSRF estimates. We considered various refinements to the BoW model for purpose of buried explosive hazard detection and tested their usefulness as part of a Bayesian cross-categorization framework on data collected from two different sites. The results show improved performance over classifiers using only point-wise features.

In the present study, we propose a novel local regression algorithm based on manifold-ranking and k-nearest neighbors (MRKNN for short). Under the framework of kernel methods, the group relationship shared among multiple molecules is... more

In the present study, we propose a novel local regression algorithm based on manifold-ranking and k-nearest neighbors (MRKNN for short). Under the framework of kernel methods, the group relationship shared among multiple molecules is firstly captured by the graph where nodes represent molecules and edges represent pairwise relations. Then, manifold ranking algorithm is developed for query-oriented extractive summarization, where the influence of query is propagated to other molecules through the structure of the constructed graph. When evaluated on four SAR datasets, MRKNN algorithm can provide a feasible way to exploit the intrinsic structure of similarity relationships. Results have validated the efficacy of the proposed algorithm.

This paper introduces a new algorithm called locality discriminating projection (LDP) for subspace learning, which provides a new scheme for discriminant analysis by considering both the manifold structure and the prior class information.... more

This paper introduces a new algorithm called locality discriminating projection (LDP) for subspace learning, which provides a new scheme for discriminant analysis by considering both the manifold structure and the prior class information. In the LDP algorithm, the overlap among the class-specific manifolds is approximated by an invader graph, and a locality discriminant criterion is proposed to find the projections that best preserve the within-class local structures while decrease the between-class overlap. The feasibility of the LDP algorithm has been successfully tested in text data and visual recognition experiments. Experiment results show it is an effective technique for data modeling and classification comparing to linear discriminant analysis, locality preserving projection, and marginal Fisher analysis.