In this paper, we propose the multi-domain dictionary learn- ing (MDDL) to make dictionary learning-based classification more robust to data representing in different domains. We use adversarial neural networks to generate data in different styles, and collect all the generated data into a miscellaneous dictionary. To tackle the dictionary learning with many sam- ples, we compute the weighting matrix that compress the mis- cellaneous dictionary from multi-sample per class to single sample per class. We show that the time complexity solv- ing the proposed MDDL with weighting matrix is the same as solving the dictionary with single sample per class. More- over, since the weighting matrix could help the solver rely more on the training data, which possibly lie in the same do- main with the testing data, the classification could be more accurate.
Hyperspectral imagery collected from airborne or satellite sources inevitably suffers from spectral variability, making it difficult for spectral unmixing to accurately estimate abundance maps. The classical unmixing model, the linear mixing model (LMM), generally fails to handle this sticky issue effectively. To this end, we propose a novel spectral mixture model, called the augmented linear mixing model (ALMM), to address spectral variability by applying a data-driven learning strategy in inverse problems of hyperspectral unmixing. The proposed approach models the main spectral variability (i.e., scaling factors) generated by variations in illumination or typography separately by means of the endmember dictionary. It then models other spectral variabilities caused by environmental conditions (e.g., local temperature and humidity, atmospheric effects) and instrumental configurations (e.g., sensor noise), as well as material nonlinear mixing effects, by introducing a spectral variability dictionary. To effectively run the data-driven learning strategy, we also propose a reasonable prior knowledge for the spectral variability dictionary, whose atoms are assumed to be low-coherent with spectral signatures of endmembers, which leads to a well-known low coherence dictionary learning problem. Thus, a dictionary learning technique is embedded in the framework of spectral unmixing so that the algorithm can learn the spectral variability dictionary and estimate the abundance maps simultaneously. Extensive experiments on synthetic and real datasets are performed to demonstrate the superiority and effectiveness of the proposed method in comparison with previous state-of-the-art methods.
This paper concerns dictionary learning, i.e., sparse coding, a fundamental representation learning problem. We show that a subgradient descent algorithm, with random initialization, can provably recover orthogonal dictionaries on a natural nonsmooth, nonconvex $\ell_1$ minimization formulation of the problem, under mild statistical assumptions on the data. This is in contrast to previous provable methods that require either expensive computation or delicate initialization schemes. Our analysis develops several tools for characterizing landscapes of nonsmooth functions, which might be of independent interest for provable training of deep networks with nonsmooth activations (e.g., ReLU), among numerous other applications. Preliminary experiments corroborate our analysis and show that our algorithm works well empirically in recovering orthogonal dictionaries.
Classification methods based on sparse estimation have drawn much attention recently, due to their effectiveness in processing high-dimensional data such as images. In this paper, a method to improve the performance of a sparse representation classification (SRC) approach is proposed; it is then applied to the problem of online process monitoring of human workers, specifically manual material handling (MMH) operations monitored using wearable sensors (involving 111 sensor channels). Our proposed method optimizes the design matrix (aka dictionary) in the linear model used for SRC, minimizing its ill-posedness to achieve a sparse solution. This procedure is based on the idea of dictionary learning (DL): we optimize the design matrix formed by training datasets to minimize both redundancy and coherency as well as reducing the size of these datasets. Use of such optimized training data can subsequently improve classification accuracy and help decrease the computational time needed for the SRC; it is thus more applicable for online process monitoring. Performance of the proposed methodology is demonstrated using wearable sensor data obtained from manual material handling experiments, and is found to be superior to those of benchmark methods in terms of accuracy, while also requiring computational time appropriate for MMH online monitoring.
Biometric recognition on partial captured targets is challenging, where only several partial observations of objects are available for matching. In this area, deep learning based methods are widely applied to match these partial captured objects caused by occlusions, variations of postures or just partial out of view in person re-identification and partial face recognition. However, most current methods are not able to identify an individual in case that some parts of the object are not obtainable, while the rest are specialized to certain constrained scenarios. To this end, we propose a robust general framework for arbitrary biometric matching scenarios without the limitations of alignment as well as the size of inputs. We introduce a feature post-processing step to handle the feature maps from FCN and a dictionary learning based Spatial Feature Reconstruction (SFR) to match different sized feature maps in this work. Moreover, the batch hard triplet loss function is applied to optimize the model. The applicability and effectiveness of the proposed method are demonstrated by the results from experiments on three person re-identification datasets (Market1501, CUHK03, DukeMTMC-reID), two partial person datasets (Partial REID and Partial iLIDS) and two partial face datasets (CASIA-NIR-Distance and Partial LFW), on which state-of-the-art performance is ensured in comparison with several state-of-the-art approaches. The code is released online and can be found on the website: https://github.com/lingxiao-he/Partial-Person-ReID.
Traditional dictionary learning based CT reconstruction methods are patch-based and the features learned with these methods often contain shifted versions of the same features. To deal with these problems, the convolutional sparse coding (CSC) has been proposed and introduced into various applications. In this paper, inspired by the successful applications of CSC in the field of signal processing, we propose a novel sparse-view CT reconstruction method based on CSC with gradient regularization on feature maps. By directly working on whole image, which need not to divide the image into overlapped patches like dictionary learning based methods, the proposed method can maintain more details and avoid the artifacts caused by patch aggregation. Experimental results demonstrate that the proposed method has better performance than several existing algorithms in both qualitative and quantitative aspects.
Using low-frequency (UHF to L-band) ultra-wideband (UWB) synthetic aperture radar (SAR) technology for detecting buried and obscured targets, e.g. bomb or mine, has been successfully demonstrated recently. Despite promising recent progress, a significant open challenge is to distinguish obscured targets from other (natural and manmade) clutter sources in the scene. The problem becomes exacerbated in the presence of noisy responses from rough ground surfaces. In this paper, we present three novel sparsity-driven techniques, which not only exploit the subtle features of raw captured data but also take advantage of the polarization diversity and the aspect angle dependence information from multi-channel SAR data. First, the traditional sparse representation-based classification (SRC) is generalized to exploit shared information of classes and various sparsity structures of tensor coefficients for multi-channel data. Corresponding tensor dictionary learning models are consequently proposed to enhance classification accuracy. Lastly, a new tensor sparsity model is proposed to model responses from multiple consecutive looks of objects, which is a unique characteristic of the dataset we consider. Extensive experimental results on a high-fidelity electromagnetic simulated dataset and radar data collected from the U.S. Army Research Laboratory side-looking SAR demonstrate the advantages of proposed tensor sparsity models.
We consider the problem of demixing a sequence of source signals from the sum of noisy bilinear measurements. It is a generalized mathematical model for blind demixing with blind deconvolution, which is prevalent across the areas of dictionary learning, image processing, and communications. However, state-of- the-art convex methods for blind demixing via semidefinite programming are computationally infeasible for large-scale problems. Although the existing nonconvex algorithms are able to address the scaling issue, they normally require proper regularization to establish optimality guarantees. The additional regularization yields tedious algorithmic parameters and pessimistic convergence rates with conservative step sizes. To address the limitations of existing methods, we thus develop a provable nonconvex demixing procedure viaWirtinger flow, much like vanilla gradient descent, to harness the benefits of regularization-free fast convergence rate with aggressive step size and computational optimality guarantees. This is achieved by exploiting the benign geometry of the blind demixing problem, thereby revealing that Wirtinger flow enforces the regularization-free iterates in the region of strong convexity and qualified level of smoothness, where the step size can be chosen aggressively.
In this paper, we propose a novel Deep Micro-Dictionary Learning and Coding Network (DDLCN). DDLCN has most of the standard deep learning layers (pooling, fully, connected, input/output, etc.) but the main difference is that the fundamental convolutional layers are replaced by novel compound dictionary learning and coding layers. The dictionary learning layer learns an over-complete dictionary for the input training data. At the deep coding layer, a locality constraint is added to guarantee that the activated dictionary bases are close to each other. Next, the activated dictionary atoms are assembled together and passed to the next compound dictionary learning and coding layers. In this way, the activated atoms in the first layer can be represented by the deeper atoms in the second dictionary. Intuitively, the second dictionary is designed to learn the fine-grained components which are shared among the input dictionary atoms. In this way, a more informative and discriminative low-level representation of the dictionary atoms can be obtained. We empirically compare the proposed DDLCN with several dictionary learning methods and deep learning architectures. The experimental results on four popular benchmark datasets demonstrate that the proposed DDLCN achieves competitive results compared with state-of-the-art approaches.
This paper addresses the energy disaggregation problem, i.e. decomposing the electricity signal of a whole home to its operating devices. First, we cast the problem as a dictionary learning (DL) problem where the key electricity patterns representing consumption behaviors are extracted for each device and stored in a dictionary matrix. The electricity signal of each device is then modeled by a linear combination of such patterns with sparse coefficients that determine the contribution of each device in the total electricity. Although popular, the classic DL approach is prone to high error in real-world applications including energy disaggregation, as it merely finds linear dictionaries. Moreover, this method lacks a recurrent structure; thus, it is unable to leverage the temporal structure of energy signals. Motivated by such shortcomings, we propose a novel optimization program where the dictionary and its sparse coefficients are optimized simultaneously with a deep neural model extracting powerful nonlinear features from the energy signals. A long short-term memory auto-encoder (LSTM-AE) is proposed with tunable time dependent states to capture the temporal behavior of energy signals for each device. We learn the dictionary in the space of temporal features captured by the LSTM-AE rather than the original space of the energy signals; hence, in contrast to the traditional DL, here, a nonlinear dictionary is learned using powerful temporal features extracted from our deep model. Real experiments on the publicly available Reference Energy Disaggregation Dataset (REDD) show significant improvement compared to the state-of-the-art methodologies in terms of the disaggregation accuracy and F-score metrics.
In dictionary selection, several atoms are selected from finite candidates that successfully approximate given data points in the sparse representation. We propose a novel efficient greedy algorithm for dictionary selection. Not only does our algorithm work much faster than the known methods, but it can also handle more complex sparsity constraints, such as average sparsity. Using numerical experiments, we show that our algorithm outperforms the known methods for dictionary selection, achieving competitive performances with dictionary learning algorithms in a smaller running time.
Sparse component analysis (SCA), also known as complete dictionary learning, is the following problem: Given an input matrix $M$ and an integer $r$, find a dictionary $D$ with $r$ columns and a matrix $B$ with $k$-sparse columns (that is, each column of $B$ has at most $k$ non-zero entries) such that $M \approx DB$. A key issue in SCA is identifiability, that is, characterizing the conditions under which $D$ and $B$ are essentially unique (that is, they are unique up to permutation and scaling of the columns of $D$ and rows of $B$). Although SCA has been vastly investigated in the last two decades, only a few works have tackled this issue in the deterministic scenario, and no work provides reasonable bounds in the minimum number of samples (that is, columns of $M$) that leads to identifiability. In this work, we provide new results in the deterministic scenario when the data has a low-rank structure, that is, when $D$ is (under)complete. While previous bounds feature a combinatorial term $r \choose k$, we exhibit a sufficient condition involving $\mathcal{O}(r^3/(r-k)^2)$ samples that yields an essentially unique decomposition, as long as these data points are well spread among the subspaces spanned by $r-1$ columns of $D$. We also exhibit a necessary lower bound on the number of samples that contradicts previous results in the literature when $k$ equals $r-1$. Our bounds provide a drastic improvement compared to the state of the art, and imply for example that for a fixed proportion of zeros (constant and independent of $r$, e.g., 10\% of zero entries in $B$), one only requires $\mathcal{O}(r)$ data points to guarantee identifiability.
This paper studies Dictionary Learning problems wherein the learning task is distributed over a multi-agent network, modeled as a time-varying directed graph. This formulation is relevant, for instance, in Big Data scenarios where massive amounts of data are collected/stored in different locations (e.g., sensors, clouds) and aggregating and/or processing all data in a fusion center might be inefficient or unfeasible, due to resource limitations, communication overheads or privacy issues. We develop a unified decentralized algorithmic framework for this class of nonconvex problems, which is proved to converge to stationary solutions at a sublinear rate. The new method hinges on Successive Convex Approximation techniques, coupled with a decentralized tracking mechanism aiming at locally estimating the gradient of the smooth part of the sum-utility. To the best of our knowledge, this is the first provably convergent decentralized algorithm for Dictionary Learning and, more generally, bi-convex problems over (time-varying) (di)graphs.
Recent works on adaptive sparse and on low-rank signal modeling have demonstrated their usefulness in various image / video processing applications. Patch-based methods exploit local patch sparsity, whereas other works apply low-rankness of grouped patches to exploit image non-local structures. However, using either approach alone usually limits performance in image reconstruction or recovery applications. In this work, we propose a simultaneous sparsity and low-rank model, dubbed STROLLR, to better represent natural images. In order to fully utilize both the local and non-local image properties, we develop an image restoration framework using a transform learning scheme with joint low-rank regularization. The approach owes some of its computational efficiency and good performance to the use of transform learning for adaptive sparse representation rather than the popular synthesis dictionary learning algorithms, which involve approximation of NP-hard sparse coding and expensive learning steps. We demonstrate the proposed framework in various applications to image denoising, inpainting, and compressed sensing based magnetic resonance imaging. Results show promising performance compared to state-of-the-art competing methods.
Zero-shot learning (ZSL) aims to recognize objects of novel classes without any training samples of specific classes, which is achieved by exploiting the semantic information and auxiliary datasets. Recently most ZSL approaches focus on learning visual-semantic embeddings to transfer knowledge from the auxiliary datasets to the novel classes. However, few works study whether the semantic information is discriminative or not for the recognition task. To tackle such problem, we propose a coupled dictionary learning approach to align the visual-semantic structures using the class prototypes, where the discriminative information lying in the visual space is utilized to improve the less discriminative semantic space. Then, zero-shot recognition can be performed in different spaces by the simple nearest neighbor approach using the learned class prototypes. Extensive experiments on four benchmark datasets show the effectiveness of the proposed approach.
Archetypal scenarios for change detection generally consider two images acquired through sensors of the same modality. However, in some specific cases such as emergency situations, the only images available may be those acquired through sensors of different modalities. This paper addresses the problem of unsupervisedly detecting changes between two observed images acquired by sensors of different modalities with possibly different resolutions. These sensor dissimilarities introduce additional issues in the context of operational change detection that are not addressed by most of the classical methods. This paper introduces a novel framework to effectively exploit the available information by modelling the two observed images as a sparse linear combination of atoms belonging to a pair of coupled overcomplete dictionaries learnt from each observed image. As they cover the same geographical location, codes are expected to be globally similar, except for possible changes in sparse spatial locations. Thus, the change detection task is envisioned through a dual code estimation which enforces spatial sparsity in the difference between the estimated codes associated with each image. This problem is formulated as an inverse problem which is iteratively solved using an efficient proximal alternating minimization algorithm accounting for nonsmooth and nonconvex functions. The proposed method is applied to real images with simulated yet realistic and real changes. A comparison with state-of-the-art change detection methods evidences the accuracy of the proposed strategy.
Sparse dictionary learning is a popular method for representing signals as linear combinations of a few elements from a dictionary that is learned from the data. In the classical setting, signals are represented as vectors and the dictionary learning problem is posed as a matrix factorization problem where the data matrix is approximately factorized into a dictionary matrix and a sparse matrix of coefficients. However, in many applications in computer vision and medical imaging, signals are better represented as matrices or tensors (e.g. images or videos), where it may be beneficial to exploit the multi-dimensional structure of the data to learn a more compact representation. One such approach is separable dictionary learning, where one learns separate dictionaries for different dimensions of the data. However, typical formulations involve solving a non-convex optimization problem; thus guaranteeing global optimality remains a challenge. In this work, we propose a framework that builds upon recent developments in matrix factorization to provide theoretical and numerical guarantees of global optimality for separable dictionary learning. We propose an algorithm to find such a globally optimal solution, which alternates between following local descent steps and checking a certificate for global optimality. We illustrate our approach on diffusion magnetic resonance imaging (dMRI) data, a medical imaging modality that measures water diffusion along multiple angular directions in every voxel of an MRI volume. State-of-the-art methods in dMRI either learn dictionaries only for the angular domain of the signals or in some cases learn spatial and angular dictionaries independently. In this work, we apply the proposed separable dictionary learning framework to learn spatial and angular dMRI dictionaries jointly and provide preliminary validation on denoising phantom and real dMRI brain data.
A discriminative structured analysis dictionary is proposed for the classification task. A structure of the union of subspaces (UoS) is integrated into the conventional analysis dictionary learning to enhance the capability of discrimination. A simple classifier is also simultaneously included into the formulated functional to ensure a more complete consistent classification. The solution of the algorithm is efficiently obtained by the linearized alternating direction method of multipliers. Moreover, a distributed structured analysis dictionary learning is also presented to address large scale datasets. It can group-(class-) independently train the structured analysis dictionaries by different machines/cores/threads, and therefore avoid a high computational cost. A consensus structured analysis dictionary and a global classifier are jointly learned in the distributed approach to safeguard the discriminative power and the efficiency of classification. Experiments demonstrate that our method achieves a comparable or better performance than the state-of-the-art algorithms in a variety of visual classification tasks. In addition, the training and testing computational complexity are also greatly reduced.
Given a convolutional dictionary underlying a set of observed signals, can a carefully designed auto-encoder recover the dictionary in the presence of noise? We introduce an auto-encoder architecture, termed constrained recurrent sparse auto-encoder (CRsAE), that answers this question in the affirmative. Given an input signal and an approximate dictionary, the encoder finds a sparse approximation using FISTA. The decoder reconstructs the signal by applying the dictionary to the output of the encoder. The encoder and decoder in CRsAE parallel the sparse-coding and dictionary update steps in optimization-based alternating-minimization schemes for dictionary learning. As such, the parameters of the encoder and decoder are not independent, a constraint which we enforce for the first time. We derive the back-propagation algorithm for CRsAE. CRsAE is a framework for blind source separation that, only knowing the number of sources (dictionary elements), and assuming sparsely-many can overlap, is able to separate them. We demonstrate its utility in the context of spike sorting, a source separation problem in computational neuroscience. We demonstrate the ability of CRsAE to recover the underlying dictionary and characterize its sensitivity as a function of SNR.
Recently, the problem of blind image separation has been widely investigated, especially the medical image denoise which is the main step in medical diag-nosis. Removing the noise without affecting relevant features of the image is the main goal. Sparse decomposition over redundant dictionaries become of the most used approaches to solve this problem. NMF codes naturally favor sparse, parts-based representations. In sparse representation, signals represented as a linear combination of a redundant dictionary atoms. In this paper, we propose an algorithm based on sparse representation over the redundant dictionary and Non-Negative Matrix Factorization (N-NMF). The algorithm initializes a dic-tionary based on training samples constructed from noised image, then it searches for the best representation for the source by using the approximate matching pursuit (AMP). The proposed N-NMF gives a better reconstruction of an image from denoised one. We have compared our numerical results with different image denoising techniques and we have found the performance of the proposed technique is promising. Keywords: Image denoising, sparse representation, dictionary learning, matching pursuit, non-negative matrix factorization.