Convolutional dictionary learning (CDL) estimates shift invariant basis adapted to multidimensional data. CDL has proven useful for image denoising or inpainting, as well as for pattern discovery on multivariate signals. As estimated patterns can be positioned anywhere in signals or images, optimization techniques face the difficulty of working in extremely high dimensions with millions of pixels or time samples, contrarily to standard patch-based dictionary learning. To address this optimization problem, this work proposes a distributed and asynchronous algorithm, employing locally greedy coordinate descent and an asynchronous locking mechanism that does not require a central server. This algorithm can be used to distribute the computation on a number of workers which scales linearly with the encoded signal's size. Experiments confirm the scaling properties which allows us to learn patterns on large scales images from the Hubble Space Telescope.
Binary data matrices can represent many types of data such as social networks, votes, or gene expression. In some cases, the analysis of binary matrices can be tackled with nonnegative matrix factorization (NMF), where the observed data matrix is approximated by the product of two smaller nonnegative matrices. In this context, probabilistic NMF assumes a generative model where the data is usually Bernoulli-distributed. Often, a link function is used to map the factorization to the $[0,1]$ range, ensuring a valid Bernoulli mean parameter. However, link functions have the potential disadvantage to lead to uninterpretable models. Mean-parameterized NMF, on the contrary, overcomes this problem. We propose a unified framework for Bayesian mean-parameterized nonnegative binary matrix factorization models (NBMF). We analyze three models which correspond to three possible constraints that respect the mean-parametrization without the need for link functions. Furthermore, we derive a novel collapsed Gibbs sampler and a collapsed variational algorithm to infer the posterior distribution of the factors. Next, we extend the proposed models to a nonparametric setting where the number of used latent dimensions is automatically driven by the observed data. We analyze the performance of our NBMF methods in multiple datasets for different tasks such as dictionary learning and prediction of missing data. Experiments show that our methods provide similar or superior results than the state of the art, while automatically detecting the number of relevant components.
In this paper, we propose several dictionary learning algorithms for sparse representations that also impose specific structures on the learned dictionaries such that they are numerically efficient to use: reduced number of addition/multiplications and even avoiding multiplications altogether. We base our work on factorizations of the dictionary in highly structured basic building blocks (binary orthonormal, scaling and shear transformations) for which we can write closed-form solutions to the optimization problems that we consider. We show the effectiveness of our methods on image data where we can compare against well-known numerically efficient transforms such as the fast Fourier and the fast discrete cosine transforms.
We describe new results and algorithms for two different, but related, problems which deal with circulant matrices: learning shift-invariant components from training data and calculating the shift (or alignment) between two given signals. In the first instance, we deal with the shift-invariant dictionary learning problem while the latter bears the name of (compressive) shift retrieval. We formulate these problems using circulant and convolutional matrices (including unions of such matrices), define optimization problems that describe our goals and propose efficient ways to solve them. Based on these findings, we also show how to learn a wavelet-like dictionary from training data. We connect our work with various previous results from the literature and we show the effectiveness of our proposed algorithms using synthetic, ECG signals and images.
In this paper, we consider the problem of selecting representatives from a data set for arbitrary supervised/unsupervised learning tasks. We identify a subset $S$ of a data set $A$ such that 1) the size of $S$ is much smaller than $A$ and 2) $S$ efficiently describes the entire data set, in a way formalized via convex optimization. In order to generate $|S| = k$ exemplars, our kernelizable algorithm, Frank-Wolfe Sparse Representation (FWSR), only needs to execute $\approx k$ iterations with a per-iteration cost that is quadratic in the size of $A$. This is in contrast to other state of the art methods which need to execute until convergence with each iteration costing an extra factor of $d$ (dimension of the data). Moreover, we also provide a proof of linear convergence for our method. We support our results with empirical experiments; we test our algorithm against current methods in three different experimental setups on four different data sets. FWSR outperforms other exemplar finding methods both in speed and accuracy in almost all scenarios.
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.
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.
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.
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.
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.
Medical imaging tasks often involve multiple contrasts, such as T1- and T2-weighted magnetic resonance imaging (MRI) data. These contrasts capture information associated with the same underlying anatomy and thus exhibit similarities. In this paper, we propose a Coupled Dictionary Learning based multi-contrast MRI reconstruction (CDLMRI) approach to leverage an available guidance contrast to restore the target contrast. Our approach consists of three stages: coupled dictionary learning, coupled sparse denoising, and $k$-space consistency enforcing. The first stage learns a group of dictionaries that capture correlations among multiple contrasts. By capitalizing on the learned adaptive dictionaries, the second stage performs joint sparse coding to denoise the corrupted target image with the aid of a guidance contrast. The third stage enforces consistency between the denoised image and the measurements in the $k$-space domain. Numerical experiments on the retrospective under-sampling of clinical MR images demonstrate that incorporating additional guidance contrast via our design improves MRI reconstruction, compared to state-of-the-art approaches.
We propose a fast, accurate matching method for estimating dense pixel correspondences across scenes. It is a challenging problem to estimate dense pixel correspondences between images depicting different scenes or instances of the same object category. While most such matching methods rely on hand-crafted features such as SIFT, we learn features from a large amount of unlabeled image patches using unsupervised learning. Pixel-layer features are obtained by encoding over the dictionary, followed by spatial pooling to obtain patch-layer features. The learned features are then seamlessly embedded into a multi-layer match- ing framework. We experimentally demonstrate that the learned features, together with our matching model, outperforms state-of-the-art methods such as the SIFT flow, coherency sensitive hashing and the recent deformable spatial pyramid matching methods both in terms of accuracy and computation efficiency. Furthermore, we evaluate the performance of a few different dictionary learning and feature encoding methods in the proposed pixel correspondences estimation framework, and analyse the impact of dictionary learning and feature encoding with respect to the final matching performance.
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.
We consider the problem of recovering a complete (i.e., square and invertible) matrix $\mathbf A_0$, from $\mathbf Y \in \mathbb R^{n \times p}$ with $\mathbf Y = \mathbf A_0 \mathbf X_0$, provided $\mathbf X_0$ is sufficiently sparse. This recovery problem is central to the theoretical understanding of dictionary learning, which seeks a sparse representation for a collection of input signals, and finds numerous applications in modern signal processing and machine learning. We give the first efficient algorithm that provably recovers $\mathbf A_0$ when $\mathbf X_0$ has $O(n)$ nonzeros per column, under suitable probability model for $\mathbf X_0$. In contrast, prior results based on efficient algorithms provide recovery guarantees when $\mathbf X_0$ has only $O(n^{1-\delta})$ nonzeros per column for any constant $\delta \in (0, 1)$. Our algorithmic pipeline centers around solving a certain nonconvex optimization problem with a spherical constraint, and hence is naturally phrased in the language of manifold optimization. To show this apparently hard problem is tractable, we first provide a geometric characterization of the high-dimensional objective landscape, which shows that with high probability there are no "spurious" local minima. This particular geometric structure allows us to design a Riemannian trust region algorithm over the sphere that provably converges to one local minimizer with an arbitrary initialization, despite the presence of saddle points. The geometric approach we develop here may also shed light on other problems arising from nonconvex recovery of structured signals.
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized methods, that reduce the complexity in one of the matrix dimension, but not in both of them. In this paper, we tackle very large matrices in both dimensions. We propose a new factoriza-tion method that scales gracefully to terabyte-scale datasets, that could not be processed by previous algorithms in a reasonable amount of time. We demonstrate the efficiency of our approach on massive functional Magnetic Resonance Imaging (fMRI) data, and on matrix completion problems for recommender systems, where we obtain significant speed-ups compared to state-of-the art coordinate descent methods.
Is it possible to find the sparsest vector (direction) in a generic subspace $\mathcal{S} \subseteq \mathbb{R}^p$ with $\mathrm{dim}(\mathcal{S})= n < p$? This problem can be considered a homogeneous variant of the sparse recovery problem, and finds connections to sparse dictionary learning, sparse PCA, and many other problems in signal processing and machine learning. In this paper, we focus on a **planted sparse model** for the subspace: the target sparse vector is embedded in an otherwise random subspace. Simple convex heuristics for this planted recovery problem provably break down when the fraction of nonzero entries in the target sparse vector substantially exceeds $O(1/\sqrt{n})$. In contrast, we exhibit a relatively simple nonconvex approach based on alternating directions, which provably succeeds even when the fraction of nonzero entries is $\Omega(1)$. To the best of our knowledge, this is the first practical algorithm to achieve linear scaling under the planted sparse model. Empirically, our proposed algorithm also succeeds in more challenging data models, e.g., sparse dictionary learning.
A multiple instance dictionary learning method using functions of multiple instances (DL-FUMI) is proposed to address target detection and two-class classification problems with inaccurate training labels. Given inaccurate training labels, DL-FUMI learns a set of target dictionary atoms that describe the most distinctive and representative features of the true positive class as well as a set of nontarget dictionary atoms that account for the shared information found in both the positive and negative instances. Experimental results show that the estimated target dictionary atoms found by DL-FUMI are more representative prototypes and identify better discriminative features of the true positive class than existing methods in the literature. DL-FUMI is shown to have significantly better performance on several target detection and classification problems as compared to other multiple instance learning (MIL) dictionary learning algorithms on a variety of MIL problems.
The ability of deep convolutional neural networks (CNN) to learn discriminative spectro-temporal patterns makes them well suited to environmental sound classification. However, the relative scarcity of labeled data has impeded the exploitation of this family of high-capacity models. This study has two primary contributions: first, we propose a deep convolutional neural network architecture for environmental sound classification. Second, we propose the use of audio data augmentation for overcoming the problem of data scarcity and explore the influence of different augmentations on the performance of the proposed CNN architecture. Combined with data augmentation, the proposed model produces state-of-the-art results for environmental sound classification. We show that the improved performance stems from the combination of a deep, high-capacity model and an augmented training set: this combination outperforms both the proposed CNN without augmentation and a "shallow" dictionary learning model with augmentation. Finally, we examine the influence of each augmentation on the model's classification accuracy for each class, and observe that the accuracy for each class is influenced differently by each augmentation, suggesting that the performance of the model could be improved further by applying class-conditional data augmentation.
We propose a Deep Texture Encoding Network (Deep-TEN) with a novel Encoding Layer integrated on top of convolutional layers, which ports the entire dictionary learning and encoding pipeline into a single model. Current methods build from distinct components, using standard encoders with separate off-the-shelf features such as SIFT descriptors or pre-trained CNN features for material recognition. Our new approach provides an end-to-end learning framework, where the inherent visual vocabularies are learned directly from the loss function. The features, dictionaries and the encoding representation for the classifier are all learned simultaneously. The representation is orderless and therefore is particularly useful for material and texture recognition. The Encoding Layer generalizes robust residual encoders such as VLAD and Fisher Vectors, and has the property of discarding domain specific information which makes the learned convolutional features easier to transfer. Additionally, joint training using multiple datasets of varied sizes and class labels is supported resulting in increased recognition performance. The experimental results show superior performance as compared to state-of-the-art methods using gold-standard databases such as MINC-2500, Flickr Material Database, KTH-TIPS-2b, and two recent databases 4D-Light-Field-Material and GTOS. The source code for the complete system are publicly available.