Supervised Dictionary Learning has gained much interest in the recent decade and has shown significant performance improvements in image classification. However, in general, supervised learning needs a large number of labelled samples per class to achieve an acceptable result. In order to deal with databases which have just a few labelled samples per class, semi-supervised learning, which also exploits unlabelled samples in training phase is used. Indeed, unlabelled samples can help to regularize the learning model, yielding an improvement of classification accuracy. In this paper, we propose a new semi-supervised dictionary learning method based on two pillars: on one hand, we enforce manifold structure preservation from the original data into sparse code space using Locally Linear Embedding, which can be considered a regularization of sparse code; on the other hand, we train a semi-supervised classifier in sparse code space. We show that our approach provides an improvement over state-of-the-art semi-supervised dictionary learning methods.
Separable, or Kronecker product, dictionaries provide natural decompositions for 2D signals, such as images. In this paper, we describe a highly parallelizable algorithm that learns such dictionaries which reaches sparse representations competitive with the previous state of the art dictionary learning algorithms from the literature but at a lower computational cost. We highlight the performance of the proposed method to sparsely represent image and hyperspectral data, and for image denoising.
We consider the problem of factorizing a structured 3-way tensor into its constituent Canonical Polyadic (CP) factors. This decomposition, which can be viewed as a generalization of singular value decomposition (SVD) for tensors, reveals how the tensor dimensions (features) interact with each other. However, since the factors are a priori unknown, the corresponding optimization problems are inherently non-convex. The existing guaranteed algorithms which handle this non-convexity incur an irreducible error (bias), and only apply to cases where all factors have the same structure. To this end, we develop a provable algorithm for online structured tensor factorization, wherein one of the factors obeys some incoherence conditions, and the others are sparse. Specifically we show that, under some relatively mild conditions on initialization, rank, and sparsity, our algorithm recovers the factors exactly (up to scaling and permutation) at a linear rate. Complementary to our theoretical results, our synthetic and real-world data evaluations showcase superior performance compared to related techniques. Moreover, its scalability and ability to learn on-the-fly makes it suitable for real-world tasks.
Discriminative features extracted from the sparse coding model have been shown to perform well for classification. Recent deep learning architectures have further improved reconstruction in inverse problems by considering new dense priors learned from data. We propose a novel dense and sparse coding model that integrates both representation capability and discriminative features. The model studies the problem of recovering a dense vector $\mathbf{x}$ and a sparse vector $\mathbf{u}$ given measurements of the form $\mathbf{y} = \mathbf{A}\mathbf{x}+\mathbf{B}\mathbf{u}$. Our first analysis proposes a geometric condition based on the minimal angle between spanning subspaces corresponding to the matrices $\mathbf{A}$ and $\mathbf{B}$ that guarantees unique solution to the model. The second analysis shows that, under mild assumptions, a convex program recovers the dense and sparse components. We validate the effectiveness of the model on simulated data and propose a dense and sparse autoencoder (DenSaE) tailored to learning the dictionaries from the dense and sparse model. We demonstrate that (i) DenSaE denoises natural images better than architectures derived from the sparse coding model ($\mathbf{B}\mathbf{u}$), (ii) in the presence of noise, training the biases in the latter amounts to implicitly learning the $\mathbf{A}\mathbf{x} + \mathbf{B}\mathbf{u}$ model, (iii) $\mathbf{A}$ and $\mathbf{B}$ capture low- and high-frequency contents, respectively, and (iv) compared to the sparse coding model, DenSaE offers a balance between discriminative power and representation.
We present a new Deep Dictionary Learning and Coding Network (DDLCN) for image recognition tasks with limited data. The proposed DDLCN has most of the standard deep learning layers (e.g., input/output, pooling, fully connected, etc.), but the fundamental convolutional layers are replaced by our proposed compound dictionary learning and coding layers. The dictionary learning learns an over-complete dictionary for 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. Then the activated dictionary atoms are assembled and passed to the 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 shared among the input dictionary atoms, thus a more informative and discriminative low-level representation of the dictionary atoms can be obtained. We empirically compare DDLCN with several leading dictionary learning methods and deep learning models. Experimental results on five popular datasets show that DDLCN achieves competitive results compared with state-of-the-art methods when the training data is limited. Code is available at https://github.com/Ha0Tang/DDLCN.
Deep learning (DL) methods have achieved state-of-the-art performance in the task of single image rain removal. Most of current DL architectures, however, are still lack of sufficient interpretability and not fully integrated with physical structures inside general rain streaks. To this issue, in this paper, we propose a model-driven deep neural network for the task, with fully interpretable network structures. Specifically, based on the convolutional dictionary learning mechanism for representing rain, we propose a novel single image deraining model and utilize the proximal gradient descent technique to design an iterative algorithm only containing simple operators for solving the model. Such a simple implementation scheme facilitates us to unfold it into a new deep network architecture, called rain convolutional dictionary network (RCDNet), with almost every network module one-to-one corresponding to each operation involved in the algorithm. By end-to-end training the proposed RCDNet, all the rain kernels and proximal operators can be automatically extracted, faithfully characterizing the features of both rain and clean background layers, and thus naturally lead to its better deraining performance, especially in real scenarios. Comprehensive experiments substantiate the superiority of the proposed network, especially its well generality to diverse testing scenarios and good interpretability for all its modules, as compared with state-of-the-arts both visually and quantitatively. The source codes are available at \url{https://github.com/hongwang01/RCDNet}.
Predicting the spread and containment of COVID-19 is a challenge of utmost importance that the broader scientific community is currently facing. One of the main sources of difficulty is that a very limited amount of daily COVID-19 case data is available, and with few exceptions, the majority of countries are currently in the "exponential spread stage," and thus there is scarce information available which would enable one to predict the phase transition between spread and containment. In this paper, we propose a novel approach to predicting the spread of COVID-19 based on dictionary learning and online nonnegative matrix factorization (online NMF). The key idea is to learn dictionary patterns of short evolution instances of the new daily cases in multiple countries at the same time, so that their latent correlation structures are captured in the dictionary patterns. We first learn such patterns by minibatch learning from the entire time-series and then further adapt them to the time-series by online NMF. As we progressively adapt and improve the learned dictionary patterns to the more recent observations, we also use them to make one-step predictions by the partial fitting. Lastly, by recursively applying the one-step predictions, we can extrapolate our predictions into the near future. Our prediction results can be directly attributed to the learned dictionary patterns due to their interpretability.
Fault detection and isolation in water distribution networks is an active topic due to its model's mathematical complexity and increased data availability through sensor placement. Here we simplify the model by offering a data driven alternative that takes the network topology into account when performing sensor placement and then proceeds to build a network model through online dictionary learning based on the incoming sensor data. Online learning is fast and allows tackling large networks as it processes small batches of signals at a time and has the benefit of continuous integration of new data into the existing network model, be it in the beginning for training or in production when new data samples are encountered. The algorithms show good performance when tested on both small and large-scale networks.
Face recognition has been widely studied due to its importance in smart cities applications. However, the case when both training and test images are corrupted is not well solved. To address such a problem, this paper proposes a locality constrained low rank representation and dictionary learning (LCLRRDL) algorithm for robust face recognition. In particular, we present three contributions in the proposed formulation. First, a low-rank representation is introduced to handle the possible contamination of the training as well as test data. Second, a locality constraint is incorporated to acknowledge the intrinsic manifold structure of training data. With the locality constraint term, our scheme induces similar samples to have similar representations. Third, a compact dictionary is learned to handle the problem of corrupted data. The experimental results on two public databases demonstrate the effectiveness of the proposed approach. Matlab code of our proposed LCLRRDL can be downloaded from https://github.com/yinhefeng/LCLRRDL.
Discriminative dictionary learning (DDL) has recently gained significant attention due to its impressive performance in various pattern classification tasks. However, the locality of atoms is not fully explored in conventional DDL approaches which hampers their classification performance. In this paper, we propose a locality constraint dictionary learning with support vector discriminative term (LCDL-SV), in which the locality information is preserved by employing the graph Laplacian matrix of the learned dictionary. To jointly learn a classifier during the training phase, a support vector discriminative term is incorporated into the proposed objective function. Moreover, in the classification stage, the identity of test data is jointly determined by the regularized residual and the learned multi-class support vector machine. Finally, the resulting optimization problem is solved by utilizing the alternative strategy. Experimental results on benchmark databases demonstrate the superiority of our proposed method over previous dictionary learning approaches on both hand-crafted and deep features. The source code of our proposed LCDL-SV is accessible at https://github.com/yinhefeng/LCDL-SV
Adverse drug-drug interactions (DDIs) remain a leading cause of morbidity and mortality. Identifying potential DDIs during the drug design process is critical for patients and society. Although several computational models have been proposed for DDI prediction, there are still limitations: (1) specialized design of drug representation for DDI predictions is lacking; (2) predictions are based on limited labelled data and do not generalize well to unseen drugs or DDIs; and (3) models are characterized by a large number of parameters, thus are hard to interpret. In this work, we develop a ChemicAl SubstrucTurE Representation (CASTER) framework that predicts DDIs given chemical structures of drugs.CASTER aims to mitigate these limitations via (1) a sequential pattern mining module rooted in the DDI mechanism to efficiently characterize functional sub-structures of drugs; (2) an auto-encoding module that leverages both labelled and unlabelled chemical structure data to improve predictive accuracy and generalizability; and (3) a dictionary learning module that explains the prediction via a small set of coefficients which measure the relevance of each input sub-structures to the DDI outcome. We evaluated CASTER on two real-world DDI datasets and showed that it performed better than state-of-the-art baselines and provided interpretable predictions.
We consider a class of nonsmooth optimization problems over the Stiefel manifold, in which the objective function is weakly convex in the ambient Euclidean space. Such problems are ubiquitous in engineering applications but still largely unexplored. We present a family of Riemannian subgradient-type methods -- namely Riemannain subgradient, incremental subgradient, and stochastic subgradient methods -- to solve these problems and show that they all have an iteration complexity of ${\cal O}(\varepsilon^{-4})$ for driving a natural stationarity measure below $\varepsilon$. In addition, we establish the local linear convergence of the Riemannian subgradient and incremental subgradient methods when the problem at hand further satisfies a sharpness property and the algorithms are properly initialized and use geometrically diminishing stepsizes. To the best of our knowledge, these are the first convergence guarantees for using Riemannian subgradient-type methods to optimize a class of nonconvex nonsmooth functions over the Stiefel manifold. The fundamental ingredient in the proof of the aforementioned convergence results is a new Riemannian subgradient inequality for restrictions of weakly convex functions on the Stiefel manifold, which could be of independent interest. We also show that our convergence results can be extended to handle a class of compact embedded submanifolds of the Euclidean space. Finally, we discuss the sharpness properties of various formulations of the robust subspace recovery and orthogonal dictionary learning problems and demonstrate the convergence performance of the algorithms on both problems via numerical simulations.
Online Matrix Factorization (OMF) is a fundamental tool for dictionary learning problems, giving an approximate representation of complex data sets in terms of a reduced number of extracted features. Convergence guarantees for most of the OMF algorithms in the literature assume independence between data matrices, and the case of dependent data streams remains largely unexplored. In this paper, we show that a non-convex generalization of the well-known OMF algorithm for i.i.d. stream of data in \citep{mairal2010online} converges almost surely to the set of critical points of the expected loss function, even when the data matrices are functions of some underlying Markov chain satisfying a mild mixing condition. This allows one to extract features more efficiently from dependent data streams, as there is no need to subsample the data sequence to approximately satisfy the independence assumption. As the main application, by combining online non-negative matrix factorization and a recent MCMC algorithm for sampling motifs from networks, we propose a novel framework of Network Dictionary Learning, which extracts ``network dictionary patches' from a given network in an online manner that encodes main features of the network. We demonstrate this technique and its application to network denoising problems on real-world network data.
Ill-posed inverse problems in imaging remain an active research topic in several decades, with new approaches constantly emerging. Recognizing that the popular dictionary learning and convolutional sparse coding are both essentially modeling the high-frequency component of an image, which convey most of the semantic information such as texture details, in this work we propose a novel multi-profile high-frequency transform-guided denoising autoencoder as prior (HF-DAEP). To achieve this goal, we first extract a set of multi-profile high-frequency components via a specific transformation and add the artificial Gaussian noise to these high-frequency components as training samples. Then, as the high-frequency prior information is learned, we incorporate it into classical iterative reconstruction process by proximal gradient descent technique. Preliminary results on highly under-sampled magnetic resonance imaging and sparse-view computed tomography reconstruction demonstrate that the proposed method can efficiently reconstruct feature details and present advantages over state-of-the-arts.
Co-occurrence statistics based word embedding techniques have proved to be very useful in extracting the semantic and syntactic representation of words as low dimensional continuous vectors. In this work, we discovered that dictionary learning can open up these word vectors as a linear combination of more elementary word factors. We demonstrate many of the learned factors have surprisingly strong semantic or syntactic meaning corresponding to the factors previously identified manually by human inspection. Thus dictionary learning provides a powerful visualization tool for understanding word embedding representations. Furthermore, we show that the word factors can help in identifying key semantic and syntactic differences in word analogy tasks and improve upon the state-of-the-art word embedding techniques in these tasks by a large margin.
We introduce a sparse scattering deep convolutional neural network, which provides a simple model to analyze properties of deep representation learning for classification. Learning a single dictionary matrix with a classifier yields a higher classification accuracy than AlexNet over the ImageNet 2012 dataset. The network first applies a scattering transform that linearizes variabilities due to geometric transformations such as translations and small deformations. A sparse $\ell^1$ dictionary coding reduces intra-class variability while preserving class separation through projections over unions of linear spaces. It is implemented in a deep convolutional network with a homotopy algorithm having an exponential convergence. A convergence proof is given in a general framework that includes ALISTA. Classification results are analyzed on ImageNet.
Diffusion magnetic resonance imaging is a noninvasive imaging technique that can indirectly infer the microstructure of tissues and provide metrics which are subject to normal variability across subjects. Potentially abnormal values or features may yield essential information to support analysis of controls and patients cohorts, but subtle confounds affecting diffusion MRI, such as those due to difference in scanning protocols or hardware, can lead to systematic errors which could be mistaken for purely biologically driven variations amongst subjects. In this work, we propose a new harmonization algorithm based on adaptive dictionary learning to mitigate the unwanted variability caused by different scanner hardware while preserving the natural biological variability present in the data. Overcomplete dictionaries, which are learned automatically from the data and do not require paired samples, are then used to reconstruct the data from a different scanner, removing variability present in the source scanner in the process. We use the publicly available database from an international challenge to evaluate the method, which was acquired on three different scanners and with two different protocols, and propose a new mapping towards a scanner-agnostic space. Results show that the effect size of the four studied diffusion metrics is preserved while removing variability attributable to the scanner. Experiments with alterations using a free water compartment, which is not simulated in the training data, shows that the effect size induced by the alterations is also preserved after harmonization. The algorithm is freely available and could help multicenter studies in pooling their data, while removing scanner specific confounds, and increase statistical power in the process.
We introduce a class of auto-encoder neural networks tailored to data from the natural exponential family (e.g., count data). The architectures are inspired by the problem of learning the filters in a convolutional generative model with sparsity constraints, often referred to as convolutional dictionary learning (CDL). Our work is the first to combine ideas from convolutional generative models and deep learning for data that are naturally modeled with a non-Gaussian distribution (e.g., binomial and Poisson). This perspective provides us with a scalable and flexible framework that can be re-purposed for a wide range of tasks and assumptions on the generative model. Specifically, the iterative optimization procedure for solving CDL, an unsupervised task, is mapped to an unfolded and constrained neural network, with iterative adjustments to the inputs to account for the generative distribution. We also show that the framework can easily be extended for discriminative training, appropriate for a supervised task. We demonstrate 1) that fitting the generative model to learn, in an unsupervised fashion, the latent stimulus that underlies neural spiking data leads to better goodness-of-fit compared to other baselines, 2) competitive performance compared to state-of-the-art algorithms for supervised Poisson image denoising, with significantly fewer parameters, and 3) gradient dynamics of shallow binomial auto-encoder.
We introduce a neural-network architecture, termed the constrained recurrent sparse autoencoder (CRsAE), that solves convolutional dictionary learning problems, thus establishing a link between dictionary learning and neural networks. Specifically, we leverage the interpretation of the alternating-minimization algorithm for dictionary learning as an approximate Expectation-Maximization algorithm to develop autoencoders that enable the simultaneous training of the dictionary and regularization parameter (ReLU bias). The forward pass of the encoder approximates the sufficient statistics of the E-step as the solution to a sparse coding problem, using an iterative proximal gradient algorithm called FISTA. The encoder can be interpreted either as a recurrent neural network or as a deep residual network, with two-sided ReLU non-linearities in both cases. The M-step is implemented via a two-stage back-propagation. The first stage relies on a linear decoder applied to the encoder and a norm-squared loss. It parallels the dictionary update step in dictionary learning. The second stage updates the regularization parameter by applying a loss function to the encoder that includes a prior on the parameter motivated by Bayesian statistics. We demonstrate in an image-denoising task that CRsAE learns Gabor-like filters, and that the EM-inspired approach for learning biases is superior to the conventional approach. In an application to recordings of electrical activity from the brain, we demonstrate that CRsAE learns realistic spike templates and speeds up the process of identifying spike times by 900x compared to algorithms based on convex optimization.
Deep generative models have been successfully applied to many applications. However, existing works experience limitations when generating large images (the literature usually generates small images, e.g. 32 * 32 or 128 * 128). In this paper, we propose a novel scheme, called deep tensor adversarial generative nets (TGAN), that generates large high-quality images by exploring tensor structures. Essentially, the adversarial process of TGAN takes place in a tensor space. First, we impose tensor structures for concise image representation, which is superior in capturing the pixel proximity information and the spatial patterns of elementary objects in images, over the vectorization preprocess in existing works. Secondly, we propose TGAN that integrates deep convolutional generative adversarial networks and tensor super-resolution in a cascading manner, to generate high-quality images from random distributions. More specifically, we design a tensor super-resolution process that consists of tensor dictionary learning and tensor coefficients learning. Finally, on three datasets, the proposed TGAN generates images with more realistic textures, compared with state-of-the-art adversarial autoencoders. The size of the generated images is increased by over 8.5 times, namely 374 * 374 in PASCAL2.