All current non-rigid structure from motion (NRSfM) algorithms are limited with respect to: (i) the number of images, and (ii) the type of shape variability they can handle. This has hampered the practical utility of NRSfM for many applications within vision. In this paper we propose a novel deep neural network to recover camera poses and 3D points solely from an ensemble of 2D image coordinates. The proposed neural network is mathematically interpretable as a multi-layer block sparse dictionary learning problem, and can handle problems of unprecedented scale and shape complexity. Extensive experiments demonstrate the impressive performance of our approach where we exhibit superior precision and robustness against all available state-of-the-art works. The considerable model capacity of our approach affords remarkable generalization to unseen data. We propose a quality measure (based on the network weights) which circumvents the need for 3D ground-truth to ascertain the confidence we have in the reconstruction. Once the network's weights are estimated (for a non-rigid object) we show how our approach can effectively recover 3D shape from a single image -- outperforming comparable methods that rely on direct 3D supervision.
We consider the dictionary learning problem, where the aim is to model the given data as a linear combination of a few columns of a matrix known as a dictionary, where the sparse weights forming the linear combination are known as coefficients. Since the dictionary and coefficients, parameterizing the linear model are unknown, the corresponding optimization is inherently non-convex. This was a major challenge until recently, when provable algorithms for dictionary learning were proposed. Yet, these provide guarantees only on the recovery of the dictionary, without explicit recovery guarantees on the coefficients. Moreover, any estimation error in the dictionary adversely impacts the ability to successfully localize and estimate the coefficients. This potentially limits the utility of existing provable dictionary learning methods in applications where coefficient recovery is of interest. To this end, we develop NOODL: a simple Neurally plausible alternating Optimization-based Online Dictionary Learning algorithm, which recovers both the dictionary and coefficients exactly at a geometric rate, when initialized appropriately. Our algorithm, NOODL, is also scalable and amenable for large scale distributed implementations in neural architectures, by which we mean that it only involves simple linear and non-linear operations. Finally, we corroborate these theoretical results via experimental evaluation of the proposed algorithm with the current state-of-the-art techniques. Keywords: dictionary learning, provable dictionary learning, online dictionary learning, non-convex, sparse coding, support recovery, iterative hard thresholding, matrix factorization, neural architectures, neural networks, noodl, sparse representations, sparse signal processing.
We study the problem of globally recovering a dictionary from a set of signals via $\ell_1$-minimization. We assume that the signals are generated as i.i.d. random linear combinations of the $K$ atoms from a complete reference dictionary $D^*\in \mathbb R^{K\times K}$, where the linear combination coefficients are from either a Bernoulli type model or exact sparse model. First, we obtain a necessary and sufficient norm condition for the reference dictionary $D^*$ to be a sharp local minimum of the expected $\ell_1$ objective function. Our result substantially extends that of Wu and Yu (2015) and allows the combination coefficient to be non-negative. Secondly, we obtain an explicit bound on the region within which the objective value of the reference dictionary is minimal. Thirdly, we show that the reference dictionary is the unique sharp local minimum, thus establishing the first known global property of $\ell_1$-minimization dictionary learning. Motivated by the theoretical results, we introduce a perturbation-based test to determine whether a dictionary is a sharp local minimum of the objective function. In addition, we also propose a new dictionary learning algorithm based on Block Coordinate Descent, called DL-BCD, which is guaranteed to have monotonic convergence. Simulation studies show that DL-BCD has competitive performance in terms of recovery rate compared to many state-of-the-art dictionary learning algorithms.
Dictionary leaning (DL) and dimensionality reduction (DR) are powerful tools to analyze high-dimensional noisy signals. This paper presents a proposal of a novel Riemannian joint dimensionality reduction and dictionary learning (R-JDRDL) on symmetric positive definite (SPD) manifolds for classification tasks. The joint learning considers the interaction between dimensionality reduction and dictionary learning procedures by connecting them into a unified framework. We exploit a Riemannian optimization framework for solving DL and DR problems jointly. Finally, we demonstrate that the proposed R-JDRDL outperforms existing state-of-the-arts algorithms when used for image classification tasks.
Condition monitoring is central to the efficient operation of wind farms due to the challenging operating conditions, rapid technology development and large number of aging wind turbines. In particular, predictive maintenance planning requires the early detection of faults with few false positives. Achieving this type of detection is a challenging problem due to the complex and weak signatures of some faults, particularly the faults that occur in some of the drivetrain bearings. Here, we investigate recently proposed condition monitoring methods based on unsupervised dictionary learning using vibration data recorded over 46 months under typical industrial operations. Thus, we contribute novel test results and real world data that are made publicly available. The results of former studies addressing condition monitoring tasks using dictionary learning indicate that unsupervised feature learning is useful for diagnosis and anomaly detection purposes. However, these studies are based on small sets of labeled data from test rigs operating under controlled conditions that focus on classification tasks, which are useful for quantitative method comparisons but gives little insight into how useful these approaches are in practice. In this study, dictionaries are learned from gearbox vibrations in six different turbines, and the dictionaries are subsequently propagated over a few years of monitoring data when faults are known to occur. We perform the experiment using two different sparse coding algorithms to investigate if the algorithm selected affects the features of abnormal conditions. We calculate the dictionary distance between the initial and propagated dictionaries and find the time periods of abnormal dictionary adaptation starting six months before a drivetrain bearing replacement and one year before the resulting gearbox replacement.
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.
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.
Blind deconvolution is the problem of recovering a convolutional kernel $\boldsymbol a_0$ and an activation signal $\boldsymbol x_0$ from their convolution $\boldsymbol y = \boldsymbol a_0 \circledast \boldsymbol x_0$. This problem is ill-posed without further constraints or priors. This paper studies the situation where the nonzero entries in the activation signal are sparsely and randomly populated. We normalize the convolution kernel to have unit Frobenius norm and cast the sparse blind deconvolution problem as a nonconvex optimization problem over the sphere. With this spherical constraint, every spurious local minimum turns out to be close to some signed shift truncation of the ground truth, under certain hypotheses. This benign property motivates an effective two stage algorithm that recovers the ground truth from the partial information offered by a suboptimal local minimum. This geometry-inspired algorithm recovers the ground truth for certain microscopy problems, also exhibits promising performance in the more challenging image deblurring problem. Our insights into the global geometry and the two stage algorithm extend to the convolutional dictionary learning problem, where a superposition of multiple convolution signals is observed.
We address the vessel segmentation problem by building upon the multiscale feature learning method of Kiros et al., which achieves the current top score in the VESSEL12 MICCAI challenge. Following their idea of feature learning instead of hand-crafted filters, we have extended the method to learn 3D features. The features are learned in an unsupervised manner in a multi-scale scheme using dictionary learning via least angle regression. The 3D feature kernels are further convolved with the input volumes in order to create feature maps. Those maps are used to train a supervised classifier with the annotated voxels. In order to process the 3D data with a large number of filters a parallel implementation has been developed. The algorithm has been applied on the example scans and annotations provided by the VESSEL12 challenge. We have compared our setup with Kiros et al. by running their implementation. Our current results show an improvement in accuracy over the slice wise method from 96.66$\pm$1.10% to 97.24$\pm$0.90%.
Sparse coding techniques for image processing traditionally rely on a processing of small overlapping patches separately followed by averaging. This has the disadvantage that the reconstructed image no longer obeys the sparsity prior used in the processing. For this purpose convolutional sparse coding has been introduced, where a shift-invariant dictionary is used and the sparsity of the recovered image is maintained. Most such strategies target the $\ell_0$ "norm" or the $\ell_1$ norm of the whole image, which may create an imbalanced sparsity across various regions in the image. In order to face this challenge, the $\ell_{0,\infty}$ "norm" has been proposed as an alternative that "operates locally while thinking globally". The approaches taken for tackling the non-convexity of these optimization problems have been either using a convex relaxation or local pursuit algorithms. In this paper, we present an efficient greedy method for sparse coding and dictionary learning, which is specifically tailored to $\ell_{0,\infty}$, and is based on matching pursuit. We demonstrate the usage of our approach in salt-and-pepper noise removal and image inpainting. A code package which reproduces the experiments presented in this work is available at https://web.eng.tau.ac.il/~raja
This work addresses the problem of reconstructing biomedical signals from their lower dimensional projections. Traditionally Compressed Sensing (CS) based techniques have been employed for this task. These are transductive inversion processes, the problem with these approaches is that the inversion is time-consuming and hence not suitable for real-time applications. With the recent advent of deep learning, Stacked Sparse Denoising Autoencoder (SSDAE) has been used for learning inversion in an inductive setup. The training period for inductive learning is large but is very fast during application -- capable of real-time speed. This work proposes a new approach for inductive learning of the inversion process. It is based on Coupled Analysis Dictionary Learning. Results on Biomedical signal reconstruction show that our proposed approach is very fast and yields result far better than CS and SSDAE.
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.
Facial image retrieval is a challenging task since faces have many similar features (areas), which makes it difficult for the retrieval systems to distinguish faces of different people. With the advent of deep learning, deep networks are often applied to extract powerful features that are used in many areas of computer vision. This paper investigates the application of different deep learning models for face image retrieval, namely, Alexlayer6, Alexlayer7, VGG16layer6, VGG16layer7, VGG19layer6, and VGG19layer7, with two types of dictionary learning techniques, namely $K$-means and $K$-SVD. We also investigate some coefficient learning techniques such as the Homotopy, Lasso, Elastic Net and SSF and their effect on the face retrieval system. The comparative results of the experiments conducted on three standard face image datasets show that the best performers for face image retrieval are Alexlayer7 with $K$-means and SSF, Alexlayer6 with $K$-SVD and SSF, and Alexlayer6 with $K$-means and SSF. The APR and ARR of these methods were further compared to some of the state of the art methods based on local descriptors. The experimental results show that deep learning outperforms most of those methods and therefore can be recommended for use in practice of face image retrieval
Machine hearing or listening represents an emerging area. Conventional approaches rely on the design of handcrafted features specialized to a specific audio task and that can hardly generalized to other audio fields. For example, Mel-Frequency Cepstral Coefficients (MFCCs) and its variants were successfully applied to computational auditory scene recognition while Chroma vectors are good at music chord recognition. Unfortunately, these predefined features may be of variable discrimination power while extended to other tasks or even within the same task due to different nature of clips. Motivated by this need of a principled framework across domain applications for machine listening, we propose a generic and data-driven representation learning approach. For this sake, a novel and efficient supervised dictionary learning method is presented. The method learns dissimilar dictionaries, one per each class, in order to extract heterogeneous information for classification. In other words, we are seeking to minimize the intra-class homogeneity and maximize class separability. This is made possible by promoting pairwise orthogonality between class specific dictionaries and controlling the sparsity structure of the audio clip's decomposition over these dictionaries. The resulting optimization problem is non-convex and solved using a proximal gradient descent method. Experiments are performed on both computational auditory scene (East Anglia and Rouen) and synthetic music chord recognition datasets. Obtained results show that our method is capable to reach state-of-the-art hand-crafted features for both applications.
In this paper, we propose a semi-supervised dictionary learning method that uses both the information in labelled and unlabelled data and jointly trains a linear classifier embedded on the sparse codes. The manifold structure of the data in the sparse code space is preserved using the same approach as the Locally Linear Embedding method (LLE). This enables one to enforce the predictive power of the unlabelled data sparse codes. We show that our approach provides significant improvements over other methods. The results can be further improved by training a simple nonlinear classifier as SVM on the sparse codes.
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.
In the last decade, traditional dictionary learning methods have been successfully applied to various pattern classification tasks. Although these methods produce sparse representations of signals which are robust against distortions and missing data, such representations quite often turn out to be unsuitable if the final objective is signal classification. In order to overcome or at least to attenuate such a weakness, several new methods which incorporate discriminative information into sparse-inducing models have emerged in recent years. In particular, methods for discriminative dictionary learning have shown to be more accurate (in terms of signal classification) than the traditional ones, which are only focused on minimizing the total representation error. In this work, we present both a novel multi-class discriminative measure and an innovative dictionary learning method. For a given dictionary, this new measure, which takes into account not only when a particular atom is used for representing signals coming from a certain class and the magnitude of its corresponding representation coefficient, but also the effect that such an atom has in the total representation error, is capable of efficiently quantifying the degree of discriminability of each one of the atoms. On the other hand, the new dictionary construction method yields dictionaries which are highly suitable for multi-class classification tasks. Our method was tested with a widely used database for handwritten digit recognition and compared with three state-of-the-art classification methods. The results show that our method significantly outperforms the other three achieving good recognition rates and additionally, reducing the computational cost of the classifier.
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.
Poultry farms are an important contributor to the human food chain. Worldwide, humankind keeps an enormous number of domesticated birds (e.g. chickens) for their eggs and their meat, providing rich sources of low-fat protein. However, around the world, there have been growing concerns about the quality of life for the livestock in poultry farms; and increasingly vocal demands for improved standards of animal welfare. Recent advances in sensing technologies and machine learning allow the possibility of automatically assessing the health of some individual birds, and employing the lessons learned to improve the welfare for all birds. This task superficially appears to be easy, given the dramatic progress in recent years in classifying human behaviors, and given that human behaviors are presumably more complex. However, as we shall demonstrate, classifying chicken behaviors poses several unique challenges, chief among which is creating a generalizable dictionary of behaviors from sparse and noisy data. In this work we introduce a novel time series dictionary learning algorithm that can robustly learn from weakly labeled data sources.
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.