Visual neuroprostheses are the only FDA-approved technology for the treatment of retinal degenerative blindness. Although recent work has demonstrated a systematic relationship between electrode location and the shape of the elicited visual percept, this knowledge has yet to be incorporated into retinal prosthesis design, where electrodes are typically arranged on either a rectangular or hexagonal grid. Here we optimize the intraocular placement of epiretinal electrodes using dictionary learning. Importantly, the optimization process is informed by a previously established and psychophysically validated model of simulated prosthetic vision. We systematically evaluate three different electrode placement strategies across a wide range of possible phosphene shapes and recommend electrode arrangements that maximize visual subfield coverage. In the near future, our work may guide the prototyping of next-generation neuroprostheses.
Dictionary learning and sparse coding have been widely studied as mechanisms for unsupervised feature learning. Unsupervised learning could bring enormous benefit to the processing of hyperspectral images and to other remote sensing data analysis because labelled data are often scarce in this field. We propose a method for clustering the pixels of hyperspectral images using sparse coefficients computed from a representative dictionary as features. We show empirically that the proposed method works more effectively than clustering on the original pixels. We also demonstrate that our approach, in certain circumstances, outperforms the clustering results of features extracted using principal component analysis and non-negative matrix factorisation. Furthermore, our method is suitable for applications in repetitively clustering an ever-growing amount of high-dimensional data, which is the case when working with hyperspectral satellite imagery.
The unsupervised domain adaptive person re-identification (re-ID) task has been a challenge because, unlike the general domain adaptive tasks, there is no overlap between the classes of source and target domain data in the person re-ID, which leads to a significant domain gap. State-of-the-art unsupervised re-ID methods train the neural networks using a memory-based contrastive loss. However, performing contrastive learning by treating each unlabeled instance as a class will lead to the problem of class collision, and the updating intensity is inconsistent due to the difference in the number of instances of different categories when updating in the memory bank. To address such problems, we propose Prototype Dictionary Learning for person re-ID which is able to utilize both source domain data and target domain data by one training stage while avoiding the problem of class collision and the problem of updating intensity inconsistency by cluster-level prototype dictionary learning. In order to reduce the interference of domain gap on the model, we propose a local-enhance module to improve the domain adaptation of the model without increasing the number of model parameters. Our experiments on two large datasets demonstrate the effectiveness of the prototype dictionary learning. 71.5\% mAP is achieved in the Market-to-Duke task, which is a 2.3\% improvement compared to the state-of-the-art unsupervised domain adaptive re-ID methods. It achieves 83.9\% mAP in the Duke-to-Market task, which improves by 4.4\% compared to the state-of-the-art unsupervised adaptive re-ID methods.
Many applications like audio and image processing show that sparse representations are a powerful and efficient signal modeling technique. Finding an optimal dictionary that generates at the same time the sparsest representations of data and the smallest approximation error is a hard problem approached by dictionary learning (DL). We study how DL performs in detecting abnormal samples in a dataset of signals. In this paper we use a particular DL formulation that seeks uniform sparse representations model to detect the underlying subspace of the majority of samples in a dataset, using a K-SVD-type algorithm. Numerical simulations show that one can efficiently use this resulted subspace to discriminate the anomalies over the regular data points.
Stochastic majorization-minimization (SMM) is a class of stochastic optimization algorithms that proceed by sampling new data points and minimizing a recursive average of surrogate functions of an objective function. The surrogates are required to be strongly convex and convergence rate analysis for the general non-convex setting was not available. In this paper, we propose an extension of SMM where surrogates are allowed to be only weakly convex or block multi-convex, and the averaged surrogates are approximately minimized with proximal regularization or block-minimized within diminishing radii, respectively. For the general nonconvex constrained setting with non-i.i.d. data samples, we show that the first-order optimality gap of the proposed algorithm decays at the rate $O((\log n)^{1+\epsilon}/n^{1/2})$ for the empirical loss and $O((\log n)^{1+\epsilon}/n^{1/4})$ for the expected loss, where $n$ denotes the number of data samples processed. Under some additional assumption, the latter convergence rate can be improved to $O((\log n)^{1+\epsilon}/n^{1/2})$. As a corollary, we obtain the first convergence rate bounds for various optimization methods under general nonconvex dependent data setting: Double-averaging projected gradient descent and its generalizations, proximal point empirical risk minimization, and online matrix/tensor decomposition algorithms. We also provide experimental validation of our results.
Scanning Transmission Electron Microscopy (STEM) offers high-resolution images that are used to quantify the nanoscale atomic structure and composition of materials and biological specimens. In many cases, however, the resolution is limited by the electron beam damage, since in traditional STEM, a focused electron beam scans every location of the sample in a raster fashion. In this paper, we propose a scanning method based on the theory of Compressive Sensing (CS) and subsampling the electron probe locations using a line hop sampling scheme that significantly reduces the electron beam damage. We experimentally validate the feasibility of the proposed method by acquiring real CS-STEM data, and recovering images using a Bayesian dictionary learning approach. We support the proposed method by applying a series of masks to fully-sampled STEM data to simulate the expectation of real CS-STEM. Finally, we perform the real data experimental series using a constrained-dose budget to limit the impact of electron dose upon the results, by ensuring that the total electron count remains constant for each image.
The quantitative analysis of non-invasive electrophysiology signals from electroencephalography (EEG) and magnetoencephalography (MEG) boils down to the identification of temporal patterns such as evoked responses, transient bursts of neural oscillations but also blinks or heartbeats for data cleaning. Several works have shown that these patterns can be extracted efficiently in an unsupervised way, e.g., using Convolutional Dictionary Learning. This leads to an event-based description of the data. Given these events, a natural question is to estimate how their occurrences are modulated by certain cognitive tasks and experimental manipulations. To address it, we propose a point process approach. While point processes have been used in neuroscience in the past, in particular for single cell recordings (spike trains), techniques such as Convolutional Dictionary Learning make them amenable to human studies based on EEG/MEG signals. We develop a novel statistical point process model-called driven temporal point processes (DriPP)-where the intensity function of the point process model is linked to a set of point processes corresponding to stimulation events. We derive a fast and principled expectation-maximization (EM) algorithm to estimate the parameters of this model. Simulations reveal that model parameters can be identified from long enough signals. Results on standard MEG datasets demonstrate that our methodology reveals event-related neural responses-both evoked and induced-and isolates non-task specific temporal patterns.
Motivated by the learned iterative soft thresholding algorithm (LISTA), we introduce a general class of neural networks suitable for sparse reconstruction from few linear measurements. By allowing a wide range of degrees of weight-sharing between the layers, we enable a unified analysis for very different neural network types, ranging from recurrent ones to networks more similar to standard feedforward neural networks. Based on training samples, via empirical risk minimization we aim at learning the optimal network parameters and thereby the optimal network that reconstructs signals from their low-dimensional linear measurements. We derive generalization bounds by analyzing the Rademacher complexity of hypothesis classes consisting of such deep networks, that also take into account the thresholding parameters. We obtain estimates of the sample complexity that essentially depend only linearly on the number of parameters and on the depth. We apply our main result to obtain specific generalization bounds for several practical examples, including different algorithms for (implicit) dictionary learning, and convolutional neural networks.
Implicit neural representations (INRs) have recently emerged as a promising alternative to classical discretized representations of signals. Nevertheless, despite their practical success, we still do not understand how INRs represent signals. We propose a novel unified perspective to theoretically analyse INRs. Leveraging results from harmonic analysis and deep learning theory, we show that most INR families are analogous to structured signal dictionaries whose atoms are integer harmonics of the set of initial mapping frequencies. This structure allows INRs to express signals with an exponentially increasing frequency support using a number of parameters that only grows linearly with depth. We also explore the inductive bias of INRs exploiting recent results about the empirical neural tangent kernel (NTK). Specifically, we show that the eigenfunctions of the NTK can be seen as dictionary atoms whose inner product with the target signal determines the final performance of their reconstruction. In this regard, we reveal that meta-learning has a reshaping effect on the NTK analogous to dictionary learning, building dictionary atoms as a combination of the examples seen during meta-training. Our results permit to design and tune novel INR architectures, but can also be of interest for the wider deep learning theory community.
The label-embedded dictionary learning (DL) algorithms generate influential dictionaries by introducing discriminative information. However, there exists a limitation: All the label-embedded DL methods rely on the labels due that this way merely achieves ideal performances in supervised learning. While in semi-supervised and unsupervised learning, it is no longer sufficient to be effective. Inspired by the concept of self-supervised learning (e.g., setting the pretext task to generate a universal model for the downstream task), we propose a Self-Supervised Dictionary Learning (SSDL) framework to address this challenge. Specifically, we first design a $p$-Laplacian Attention Hypergraph Learning (pAHL) block as the pretext task to generate pseudo soft labels for DL. Then, we adopt the pseudo labels to train a dictionary from a primary label-embedded DL method. We evaluate our SSDL on two human activity recognition datasets. The comparison results with other state-of-the-art methods have demonstrated the efficiency of SSDL.
Deep learning based methods hold state-of-the-art results in low-level image processing tasks, but remain difficult to interpret due to their black-box construction. Unrolled optimization networks present an interpretable alternative to constructing deep neural networks by deriving their architecture from classical iterative optimization methods without use of tricks from the standard deep learning tool-box. So far, such methods have demonstrated performance close to that of state-of-the-art models while using their interpretable construction to achieve a comparably low learned parameter count. In this work, we propose an unrolled convolutional dictionary learning network (CDLNet) and demonstrate its competitive denoising and joint denoising and demosaicing (JDD) performance both in low and high parameter count regimes. Specifically, we show that the proposed model outperforms state-of-the-art fully convolutional denoising and JDD models when scaled to a similar parameter count. In addition, we leverage the model's interpretable construction to propose a noise-adaptive parameterization of thresholds in the network that enables state-of-the-art blind denoising performance, and near perfect generalization on noise-levels unseen during training. Furthermore, we show that such performance extends to the JDD task and unsupervised learning.
Matrix Factorization plays an important role in machine learning such as Non-negative Matrix Factorization, Principal Component Analysis, Dictionary Learning, etc. However, most of the studies aim to minimize the loss by measuring the Euclidean distance, though in some fields, angle distance is known to be more important and critical for analysis. In this paper, we propose a method by adding constraints on factors to unify the Euclidean and angle distance. However, due to non-convexity of the objective and constraints, the optimized solution is not easy to obtain. In this paper we propose a general framework to systematically solve it with provable convergence guarantee with various constraints.
Subspace clustering techniques have shown promise in hyperspectral image segmentation. The fundamental assumption in subspace clustering is that the samples belonging to different clusters/segments lie in separable subspaces. What if this condition does not hold? We surmise that even if the condition does not hold in the original space, the data may be nonlinearly transformed to a space where it will be separable into subspaces. In this work, we propose a transformation based on the tenets of deep dictionary learning (DDL). In particular, we incorporate the sparse subspace clustering (SSC) loss in the DDL formulation. Here DDL nonlinearly transforms the data such that the transformed representation (of the data) is separable into subspaces. We show that the proposed formulation improves over the state-of-the-art deep learning techniques in hyperspectral image clustering.
Spatial-temporal local binary pattern (STLBP) has been widely used in dynamic texture recognition. STLBP often encounters the high-dimension problem as its dimension increases exponentially, so that STLBP could only utilize a small neighborhood. To tackle this problem, we propose a method for dynamic texture recognition using PDV hashing and dictionary learning on multi-scale volume local binary pattern (PHD-MVLBP). Instead of forming very high-dimensional LBP histogram features, it first uses hash functions to map the pixel difference vectors (PDVs) to binary vectors, then forms a dictionary using the derived binary vector, and encodes them using the derived dictionary. In such a way, the PDVs are mapped to feature vectors of the size of dictionary, instead of LBP histograms of very high dimension. Such an encoding scheme could extract the discriminant information from videos in a much larger neighborhood effectively. The experimental results on two widely-used dynamic textures datasets, DynTex++ and UCLA, show the superiority performance of the proposed approach over the state-of-the-art methods.
Sparse Representation (SR) of signals or data has a well founded theory with rigorous mathematical error bounds and proofs. SR of a signal is given by superposition of very few columns of a matrix called Dictionary, implicitly reducing dimensionality. Training dictionaries such that they represent each class of signals with minimal loss is called Dictionary Learning (DL). Dictionary learning methods like Method of Optimal Directions (MOD) and K-SVD have been successfully used in reconstruction based applications in image processing like image "denoising", "inpainting" and others. Other dictionary learning algorithms such as Discriminative K-SVD and Label Consistent K-SVD are supervised learning methods based on K-SVD. In our experience, one of the drawbacks of current methods is that the classification performance is not impressive on datasets like Telugu OCR datasets, with large number of classes and high dimensionality. There is scope for improvement in this direction and many researchers have used statistical methods to design dictionaries for classification. This chapter presents a review of statistical techniques and their application to learning discriminative dictionaries. The objective of the methods described here is to improve classification using sparse representation. In this chapter a hybrid approach is described, where sparse coefficients of input data are generated. We use a simple three layer Multi Layer Perceptron with back-propagation training as a classifier with those sparse codes as input. The results are quite comparable with other computation intensive methods. Keywords: Statistical modeling, Dictionary Learning, Discriminative Dictionary, Sparse representation, Gaussian prior, Cauchy prior, Entropy, Hidden Markov model, Hybrid Dictionary Learning
In high-throughput functional genomic screens, each gene product is commonly assumed to exhibit a singular biological function within a defined protein complex or pathway. In practice, a single gene perturbation may induce multiple cascading functional outcomes, a genetic principle known as pleiotropy. Here, we model pleiotropy in fitness screen collections by representing each gene perturbation as the sum of multiple perturbations of biological functions, each harboring independent fitness effects inferred empirically from the data. Our approach ('Webster') recovered pleiotropic functions for DNA damage proteins from genotoxic fitness screens, untangled distinct signaling pathways upstream of shared effector proteins from cancer cell fitness screens, and learned aspects of the cellular hierarchy in an unsupervised manner. Modeling compound sensitivity profiles in terms of genetically defined functions recovered compound mechanisms of action. Our approach establishes a sparse approximation mechanism for unraveling complex genetic architectures underlying high-dimensional gene perturbation readouts.
Dictionary learning aims at seeking a dictionary under which the training data can be sparsely represented. Methods in the literature typically formulate the dictionary learning problem as an optimization w.r.t. two variables, i.e., dictionary and sparse coefficients, and solve it by alternating between two stages: sparse coding and dictionary update. The key contribution of this work is a Rank-One Atomic Decomposition (ROAD) formulation where dictionary learning is cast as an optimization w.r.t. a single variable which is a set of rank one matrices. The resulting algorithm is hence single-stage. Compared with two-stage algorithms, ROAD minimizes the sparsity of the coefficients whilst keeping the data consistency constraint throughout the whole learning process. An alternating direction method of multipliers (ADMM) is derived to solve the optimization problem and the lower bound of the penalty parameter is computed to guarantees a global convergence despite non-convexity of the optimization formulation. From practical point of view, ROAD reduces the number of tuning parameters required in other benchmark algorithms. Numerical tests demonstrate that ROAD outperforms other benchmark algorithms for both synthetic data and real data, especially when the number of training samples is small.
Time series streams are ubiquitous in many application domains, e.g., transportation, network monitoring, autonomous vehicles, or the Internet of Things (IoT). Transmitting and storing large amounts of such fine-grained data is however expensive, which makes compression schemes necessary in practice. Time series streams that are transmitted together often share properties or evolve together, making them significantly correlated. Despite the rich literature on compression methods, the state-of-the-art approaches do not typically avail correlation information when compressing times series. In this work, we demonstrate how one can leverage the correlation across several related time series streams to both drastically improve the compression efficiency and reduce the accuracy loss.We present a novel compression algorithm for time series streams called CORAD (CORelation-Aware compression of time series streams based on sparse Dictionary coding). Based on sparse dictionary learning, CORAD has the unique ability to exploit the correlation across multiple related time series to eliminate redundancy and perform a more efficient compression. To ensure the accuracy of the compressed time series, we further introduce a method to threshold the information loss of the compression. Extensive validation on real-world datasets shows that CORAD drastically outperforms state-of-the-art approaches achieving up to 40:1 compression ratios while minimizing the information loss.
An increasing number of systems are being designed by gathering significant amounts of data and then optimizing the system parameters directly using the obtained data. Often this is done without analyzing the dataset structure. As task complexity, data size, and parameters all increase to millions or even billions, data summarization is becoming a major challenge. In this work, we investigate data summarization via dictionary learning~(DL), leveraging the properties of recently introduced non-negative kernel regression (NNK) graphs. Our proposed NNK-Means, unlike previous DL techniques, such as kSVD, learns geometric dictionaries with atoms that are representative of the input data space. Experiments show that summarization using NNK-Means can provide better class separation compared to linear and kernel versions of kMeans and kSVD. Moreover, NNK-Means is scalable, with runtime complexity similar to that of kMeans.
Dictionary learning aims to find a dictionary under which the training data can be sparsely represented, and it is usually achieved by iteratively applying two stages: sparse coding and dictionary update. Typical methods for dictionary update focuses on refining both dictionary atoms and their corresponding sparse coefficients by using the sparsity patterns obtained from sparse coding stage, and hence it is a non-convex bilinear inverse problem. In this paper, we propose a Rank-One Matrix Decomposition (ROMD) algorithm to recast this challenge into a convex problem by resolving these two variables into a set of rank-one matrices. Different from methods in the literature, ROMD updates the whole dictionary at a time using convex programming. The advantages hence include both convergence guarantees for dictionary update and faster convergence of the whole dictionary learning. The performance of ROMD is compared with other benchmark dictionary learning algorithms. The results show the improvement of ROMD in recovery accuracy, especially in the cases of high sparsity level and fewer observation data.