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In this paper, we describe the deep learning method to reduce the dimension of the data samples under the framework Non-negative Matrix Factorization (NMF). That is to say, we try to find the good representation of the data samples for the task of NMF. To this end, a nonlinear NMF optimization model is constructed and the optimization algorithm is developed. The experimental results on some benchmark...
We investigate the use of Deep Neural Networks for the classification of image datasets where texture features are important for generating class-conditional discriminative representations. To this end, we first derive the size of the feature space for some standard textural features extracted from the input dataset and then use the theory of Vapnik-Chervonenkis dimension to show that hand-crafted...
A novel estimation algorithm is introduced for logistic regression model with nonnegative coefficients constraints. The basic idea is to decompose the model parameters as a vector of convex coefficients (the multinomial manifold) and a scaling parameter, which are then optimized alternatively based on the maximum likelihood cost function. The first and second order Riemannian geometry of the multinomial...
RGB-D action streams have aroused impressive attentions for recognition task, for its geometric characteristic and less influence of illumination. However, there exists large divergences of intra-class actions performed between sub-action, multi-subject and multi-modality, which may affect the result of action recognition. In order to solve these three problems, we propose a Sparse alignment guided...
The Gaussian process latent variable model (GPLVM) had been proved to be good at discovering low-dimension manifold from nonlinear high-dimensional data for small training sets. However, for labeled data, GPLVM cannot achieve a better result because it doesn't use the label information. It turned out to be an effective strategy to employ a discriminative prior over the latent space according to the...
Previous work has shown that perceptual texture similarity and relative attributes cannot be well described by computational features. In this paper, we propose to predict human's visual perception of texture images by learning a non-linear mapping from computational feature space to perceptual space. Hand-crafted features and deep features, which were successfully applied in texture classification...
We propose a learning vector quantization algorithm variant for prototype-based classification learning with adaptive tangent distance learning. Tangent distances were developed to achieve dissimilarity measures invariant with respect to transformations and distortions like rotation, noise, etc.. Usually, these tangent distances are predefined in applications or are estimated in preprocessing. We...
The abundance of computing and mobile devices makes the problem of user identification and verification an essential requirement for many applications. Haptics devices include the sense of touch in the form of kinesthetic and tactile feedback which provide additional features within handwritten signatures. However, they generate high dimensional data and dimensionality reduction techniques become...
Low-rank matrix recovery (MR) has been widely used in data analysis and dimensionality reduction. As a direct heuristic to MR, convex relaxation is usually degraded by the repeated calling of singular value decomposition (SVD), especially in large-scale applications. In this paper, we propose a novel Riemannian optimization method (ROAM) for MR problem by exploiting the Riemannian geometry of the...
In this paper, we employ graph embeddings for classification tasks. To do this, we explore the relationship between kernel matrices, spaces of inner products and statistical inference by viewing the embedding vectors for the nodes in the graph as a field on a Riemannian manifold. This leads to a setting where the inference process may be cast as a Maximum a Posteriori (MAP) estimation over a Gibbs...
Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are often too restrictive. One way to alleviate this limitation is to find a different representation of the data by introducing a feature space. This feature space is often learned in...
Dimensionality reduction is indispensable for high dimensional data classification. So in this paper, a novel supervised method is developed to reduce dimensions of the original data, which is named feature space distance metric learning (FSDML). Instead of distances between any two points, distances between any two feature spaces are involved in the proposed method. Besides feature space distances(FSD)...
In this paper, we develop a model-free and data efficient batch reinforcement learning algorithm for learning control of continuous state-space and discounted-reward Markov decision processes. This algorithm is an approximate value iteration which uses the manifold regularization method to learn feature representations for Q-value function approximation. The learned features can preserve the intrinsic...
Matrix manifolds such as Stiefel and Grassmann manifolds have been widely used in modern computer vision. This paper is concerned with the problem of classifying such manifold-valued data, based on the maximum likelihood estimation for the parametric probability density functions defined on the manifolds. By using a new way of computing normalisation constants for the matrix Langevin distribution...
We propose a Joint nuclear norm based nonlinear Manifold Learning through linear embedding with Classification, called JMLC. By including a feature approximation error into the existing nonlinear manifold learning framework to correlate manifold features with embedded features by a linear projection, the learnt projection can handle the outside points efficiently by embedding. Besides, to encode the...
Kernel functions based machine learning algorithms have been extensively studied over the past decades with successful applications in a variety of real-world tasks. In this paper, we formulate a kernel level composition method to embed multiple local classifiers (kernels) into one kernel function, so as to obtain a more flexible data-dependent kernel. Since such composite kernels are composed by...
Auto-encoder is a popular representation learning technique which can capture the generative model of data via a encoding and decoding procedure typically driven by reconstruction errors in an unsupervised way. In this paper, we propose a semi-supervised manifold learning based auto-encoder (named semAE). semAE is based on a regularized auto-encoder framework which leverages semi-supervised manifold...
A new non-parametric method for reducing the number of dimensions in binary and continuous data, and for measuring the complexity of binary and continuous datasets, is introduced. The method, named Structural Manifold Analysis (SMA), is based on “Generalized Invariance Structure Theory” [1–6], a theory that has been successful in characterizing and accurately predicting human concept learning and...
Gait recognition is a rising biometric technology which aims to distinguish people purely through the analysis of the way they walk, while the problem is that the dimensionality of the gait data is too high, so it is necessary to carry on dimensionality reduction task. Up to date, in the area of computer vision and pattern recognition, various dimensionality reduction algorithms have been employed...
Temporal alignment aligns two temporal sequences and is quite challenging due to drastic differences among temporal sequences and source data from different views. Canonical time warping (CTW) has shown great potential in temporal alignment tasks because it can reduce data redundancy by transforming high-dimensional data to a lower-dimensional subspace via canonical correlation analysis (CCA). However,...
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