Data factorization methods have met with considerable success in discovering latent features of the signals encountered in wide-ranging applications. In this way, the representation bases, which make up the columns of the basis matrix or dictionary, are learned from the available samples of the target environment. An example is the sparse representation (SR) in which the dictionary is intended to best represent the data with a small number of atoms, much smaller than the dimension of the signal space. It has been shown that, in addition to a more informative representation of signals, imposing sparsity constraints on the representation coefficients can improve the generalization performance and the computational efficiency [1, 2, 3]. Furthermore, the sparse representation is more robust to noise, redundancy, and missing data. These features are mainly attributed to the fact that the intrinsic dimension of natural signals is usually much smaller than their apparent dimension and hence SR in an appropriate dictionary can extract these intrinsic features more efficiently. SR has been a successful strategy and has received considerable attention and achieved state-of-the-art results in many applications, e.g.

On the one hand, the dictionary is too large and the computational complexity In recent years, deep dictionary learning (DDL)has attracted a is too high for large-scale classification problems. On the great amount of attention due to its effectiveness for representation other hand, the original input training samples may contain learning and visual recognition. However, most existing noise, which leads to the inappropriate dictionary and suffers methods focus on unsupervised deep dictionary learning, failing from the problem of poor robustness. To address the abovementioned to further explore the category information. To make full issues, several supervised dictionary learning algorithms use of the category information of different samples, we propose such as D-KSVD [6] and LC-KSVD [7] have been a novel deep dictionary learning model with an intraclass proposed by introducing category information for dictionary constraint (DDLIC) for visual classification.

A method for online tensor dictionary learning is proposed. With the assumption of separable dictionaries, tensor contraction is used to diminish a $N$-way model of $\mathcal{O}\left(L^N\right)$ into a simple matrix equation of $\mathcal{O}\left(NL^2\right)$ with a real-time capability. To avoid numerical instability due to inversion of sparse matrix, a class of stochastic gradient with memory is formulated via a least-square solution to guarantee convergence and robustness. Both gradient descent with exact line search and Newton's method are discussed and realized. Extensions onto how to deal with bad initialization and outliers are also explained in detail. Experiments on two synthetic signals confirms an impressive performance of our proposed method.

ABSTRACT We present a method for fast resting-state fMRI spatial decompositions of very large datasets, based on the reduction of the temporal dimension before applying dictionary learning on concatenated individual records from groups of subjects. Introducing a measure of correspondence between spatial decompositions of rest fMRI, we demonstrates that time-reduced dictionary learning produces result as reliable as non-reduced decompositions. We also show that this reduction significantly improves computational scalability. Index Terms-- resting-state fMRI, sparse decomposition, dictionary learning, online learning, rangefinder 1. INTRODUCTION Resting-state fMRI data analysis traditionally implies, as an initial step, to decompose a set of raw 4D records (time-series sampled in a volumic voxel grid) into a sum of spatially located functional networks that isolate a part of the brain signals. Functional networks, that can be seen as a set of brain activation maps, form a relevant basis for the experiment signals that captures its essence in a low-dimensional space.

Dictionary learning algorithms have been successfully used for both reconstructive and discriminative tasks, where an input signal is represented with a sparse linear combination of dictionary atoms. While these methods are mostly developed for single-modality scenarios, recent studies have demonstrated the advantages of feature-level fusion based on the joint sparse representation of the multimodal inputs. In this paper, we propose a multimodal task-driven dictionary learning algorithm under the joint sparsity constraint (prior) to enforce collaborations among multiple homogeneous/heterogeneous sources of information. In this task-driven formulation, the multimodal dictionaries are learned simultaneously with their corresponding classifiers. The resulting multimodal dictionaries can generate discriminative latent features (sparse codes) from the data that are optimized for a given task such as binary or multiclass classification. Moreover, we present an extension of the proposed formulation using a mixed joint and independent sparsity prior which facilitates more flexible fusion of the modalities at feature level. The efficacy of the proposed algorithms for multimodal classification is illustrated on four different applications -- multimodal face recognition, multi-view face recognition, multi-view action recognition, and multimodal biometric recognition. It is also shown that, compared to the counterpart reconstructive-based dictionary learning algorithms, the task-driven formulations are more computationally efficient in the sense that they can be equipped with more compact dictionaries and still achieve superior performance.

This letter proposes a dictionary learning algorithm for blind one bit compressed sensing. In the blind one bit compressed sensing framework, the original signal to be reconstructed from one bit linear random measurements is sparse in an unknown domain. In this context, the multiplication of measurement matrix $\Ab$ and sparse domain matrix $\Phi$, \ie $\Db=\Ab\Phi$, should be learned. Hence, we use dictionary learning to train this matrix. Towards that end, an appropriate continuous convex cost function is suggested for one bit compressed sensing and a simple steepest-descent method is exploited to learn the rows of the matrix $\Db$. Experimental results show the effectiveness of the proposed algorithm against the case of no dictionary learning, specially with increasing the number of training signals and the number of sign measurements.

Performing signal processing tasks on compressive measurements of data has received great attention in recent years. In this paper, we extend previous work on compressive dictionary learning by showing that more general random projections may be used, including sparse ones. More precisely, we examine compressive K-means clustering as a special case of compressive dictionary learning and give theoretical guarantees for its performance for a very general class of random projections. We then propose a memory and computation efficient dictionary learning algorithm, specifically designed for analyzing large volumes of high-dimensional data, which learns the dictionary from very sparse random projections. Experimental results demonstrate that our approach allows for reduction of computational complexity and memory/data access, with controllable loss in accuracy.

Dictionary learning algorithms have been successfully used in both reconstructive and discriminative tasks, where the input signal is represented by a linear combination of a few dictionary atoms. While these methods are usually developed under $\ell_1$ sparsity constrain (prior) in the input domain, recent studies have demonstrated the advantages of sparse representation using structured sparsity priors in the kernel domain. In this paper, we propose a supervised dictionary learning algorithm in the kernel domain for hyperspectral image classification. In the proposed formulation, the dictionary and classifier are obtained jointly for optimal classification performance. The supervised formulation is task-driven and provides learned features from the hyperspectral data that are well suited for the classification task. Moreover, the proposed algorithm uses a joint ($\ell_{12}$) sparsity prior to enforce collaboration among the neighboring pixels. The simulation results illustrate the efficiency of the proposed dictionary learning algorithm.

In sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties -- the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent signals residing on weighted graphs, an additional design challenge is to incorporate the intrinsic geometric structure of the irregular data domain into the atoms of the dictionary. In this work, we propose a parametric dictionary learning algorithm to design data-adapted, structured dictionaries that sparsely represent graph signals. In particular, we model graph signals as combinations of overlapping local patterns. We impose the constraint that each dictionary is a concatenation of subdictionaries, with each subdictionary being a polynomial of the graph Laplacian matrix, representing a single pattern translated to different areas of the graph. The learning algorithm adapts the patterns to a training set of graph signals. Experimental results on both synthetic and real datasets demonstrate that the dictionaries learned by the proposed algorithm are competitive with and often better than unstructured dictionaries learned by state-of-the-art numerical learning algorithms in terms of sparse approximation of graph signals. In contrast to the unstructured dictionaries, however, the dictionaries learned by the proposed algorithm feature localized atoms and can be implemented in a computationally efficient manner in signal processing tasks such as compression, denoising, and classification.

This article addresses the issue of representing electroencephalographic (EEG) signals in an efficient way. While classical approaches use a fixed Gabor dictionary to analyze EEG signals, this article proposes a data-driven method to obtain an adapted dictionary. To reach an efficient dictionary learning, appropriate spatial and temporal modeling is required. Inter-channels links are taken into account in the spatial multivariate model, and shift-invariance is used for the temporal model. Multivariate learned kernels are informative (a few atoms code plentiful energy) and interpretable (the atoms can have a physiological meaning). Using real EEG data, the proposed method is shown to outperform the classical multichannel matching pursuit used with a Gabor dictionary, as measured by the representative power of the learned dictionary and its spatial flexibility. Moreover, dictionary learning can capture interpretable patterns: this ability is illustrated on real data, learning a P300 evoked potential. Keywords: Dictionary learning, orthogonal matching pursuit, multivariate, shift-invariance, EEG, evoked potentials, P300. 1. Introduction Scalp electroencephalography (EEG) measures electrical activity produced by post-synaptic potentials of large neuronal assemblies. Although this old medical imaging technique suffers from poor spatial resolution, EEG is still widely used in medical contexts (e.g. EEG devices are relatively cheap compared to other imaging techniques (e.g. MEG, fMRI, PET), and they offer both high temporal resolution (a short period of time between two acquisitions) and very low latency (a delay between the mental task and the recording on the electrodes).