This paper proposes a low-cost and highly accurate ECG-monitoring system intended for personalized early arrhythmia detection for wearable mobile sensors. Earlier supervised approaches for personalized ECG monitoring require both abnormal and normal heartbeats for the training of the dedicated classifier. However, in a real-world scenario where the personalized algorithm is embedded in a wearable device, such training data is not available for healthy people with no cardiac disorder history. In this study, (i) we propose a null space analysis on the healthy signal space obtained via sparse dictionary learning, and investigate how a simple null space projection or alternatively regularized least squares-based classification methods can reduce the computational complexity, without sacrificing the detection accuracy, when compared to sparse representation-based classification. (ii) Then we introduce a sparse representation-based domain adaptation technique in order to project other existing users' abnormal and normal signals onto the new user's signal space, enabling us to train the dedicated classifier without having any abnormal heartbeat of the new user. Therefore, zero-shot learning can be achieved without the need for synthetic abnormal heartbeat generation. An extensive set of experiments performed on the benchmark MIT-BIH ECG dataset shows that when this domain adaptation-based training data generator is used with a simple 1-D CNN classifier, the method outperforms the prior work by a significant margin. (iii) Then, by combining (i) and (ii), we propose an ensemble classifier that further improves the performance. This approach for zero-shot arrhythmia detection achieves an average accuracy level of 98.2% and an F1-Score of 92.8%. Finally, a personalized energy-efficient ECG monitoring scheme is proposed using the above-mentioned innovations.
The reliability of segmentation models in the medical domain depends on the model's robustness to perturbations in the input space. Robustness is a particular challenge in medical imaging exhibiting various sources of image noise, corruptions, and domain shifts. Obtaining robustness is often attempted via simulating heterogeneous environments, either heuristically in the form of data augmentation or by learning to generate specific perturbations in an adversarial manner. We propose and justify that learning a discrete representation in a low dimensional embedding space improves robustness of a segmentation model. This is achieved with a dictionary learning method called vector quantisation. We use a set of experiments designed to analyse robustness in both the latent and output space under domain shift and noise perturbations in the input space. We adapt the popular UNet architecture, inserting a quantisation block in the bottleneck. We demonstrate improved segmentation accuracy and better robustness on three segmentation tasks. Code is available at \url{https://github.com/AinkaranSanthi/Vector-Quantisation-for-Robust-Segmentation}
Supervised dictionary learning (SDL) is a classical machine learning method that simultaneously seeks feature extraction and classification tasks, which are not necessarily a priori aligned objectives. The goal of SDL is to learn a class-discriminative dictionary, which is a set of latent feature vectors that can well-explain both the features as well as labels of observed data. In this paper, we provide a systematic study of SDL, including the theory, algorithm, and applications of SDL. First, we provide a novel framework that `lifts' SDL as a convex problem in a combined factor space and propose a low-rank projected gradient descent algorithm that converges exponentially to the global minimizer of the objective. We also formulate generative models of SDL and provide global estimation guarantees of the true parameters depending on the hyperparameter regime. Second, viewed as a nonconvex constrained optimization problem, we provided an efficient block coordinate descent algorithm for SDL that is guaranteed to find an $\varepsilon$-stationary point of the objective in $O(\varepsilon^{-1}(\log \varepsilon^{-1})^{2})$ iterations. For the corresponding generative model, we establish a novel non-asymptotic local consistency result for constrained and regularized maximum likelihood estimation problems, which may be of independent interest. Third, we apply SDL for imbalanced document classification by supervised topic modeling and also for pneumonia detection from chest X-ray images. We also provide simulation studies to demonstrate that SDL becomes more effective when there is a discrepancy between the best reconstructive and the best discriminative dictionaries.
Sparsity-based methods have a long history in the field of signal processing and have been successfully applied to various image reconstruction problems. The involved sparsifying transformations or dictionaries are typically either pre-trained using a model which reflects the assumed properties of the signals or adaptively learned during the reconstruction - yielding so-called blind Compressed Sensing approaches. However, by doing so, the transforms are never explicitly trained in conjunction with the physical model which generates the signals. In addition, properly choosing the involved regularization parameters remains a challenging task. Another recently emerged training-paradigm for regularization methods is to use iterative neural networks (INNs) - also known as unrolled networks - which contain the physical model. In this work, we construct an INN which can be used as a supervised and physics-informed online convolutional dictionary learning algorithm. We evaluated the proposed approach by applying it to a realistic large-scale dynamic MR reconstruction problem and compared it to several other recently published works. We show that the proposed INN improves over two conventional model-agnostic training methods and yields competitive results also compared to a deep INN. Further, it does not require to choose the regularization parameters and - in contrast to deep INNs - each network component is entirely interpretable.
Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either low-dimensional projections of neural activity, or on learning dynamical systems that explicitly relate to the neural state over time. We discuss how these two approaches are interrelated by considering dynamical systems as representative of flows on a low-dimensional manifold. Building on this concept, we propose a new decomposed dynamical system model that represents complex non-stationary and nonlinear dynamics of time series data as a sparse combination of simpler, more interpretable components. Our model is trained through a dictionary learning procedure, where we leverage recent results in tracking sparse vectors over time. The decomposed nature of the dynamics is more expressive than previous switched approaches for a given number of parameters and enables modeling of overlapping and non-stationary dynamics. In both continuous-time and discrete-time instructional examples we demonstrate that our model can well approximate the original system, learn efficient representations, and capture smooth transitions between dynamical modes, focusing on intuitive low-dimensional non-stationary linear and nonlinear systems. Furthermore, we highlight our model's ability to efficiently capture and demix population dynamics generated from multiple independent subnetworks, a task that is computationally impractical for switched models. Finally, we apply our model to neural "full brain" recordings of C. elegans data, illustrating a diversity of dynamics that is obscured when classified into discrete states.
Image enhancement approaches often assume that the noise is signal independent, and approximate the degradation model as zero-mean additive Gaussian. However, this assumption does not hold for biomedical imaging systems where sensor-based sources of noise are proportional to signal strengths, and the noise is better represented as a Poisson process. In this work, we explore a sparsity and dictionary learning-based approach and present a novel self-supervised learning method for single-image denoising where the noise is approximated as a Poisson process, requiring no clean ground-truth data. Specifically, we approximate traditional iterative optimization algorithms for image denoising with a recurrent neural network that enforces sparsity with respect to the weights of the network. Since the sparse representations are based on the underlying image, it is able to suppress the spurious components (noise) in the image patches, thereby introducing implicit regularization for denoising tasks through the network structure. Experiments on two bio-imaging datasets demonstrate that our method outperforms the state-of-the-art approaches in terms of PSNR and SSIM. Our qualitative results demonstrate that, in addition to higher performance on standard quantitative metrics, we are able to recover much more subtle details than other compared approaches. Our code is made publicly available at https://github.com/tacalvin/Poisson2Sparse
Image processing neural networks, natural and artificial, have a long history with orientation-selectivity, often described mathematically as Gabor filters. Gabor-like filters have been observed in the early layers of CNN classifiers and even throughout low-level image processing networks. In this work, we take this observation to the extreme and explicitly constrain the filters of a natural-image denoising CNN to be learned 2D real Gabor filters. Surprisingly, we find that the proposed network (GDLNet) can achieve near state-of-the-art denoising performance amongst popular fully convolutional neural networks, with only a fraction of the learned parameters. We further verify that this parameterization maintains the noise-level generalization (training vs. inference mismatch) characteristics of the base network, and investigate the contribution of individual Gabor filter parameters to the performance of the denoiser. We present positive findings for the interpretation of dictionary learning networks as performing accelerated sparse-coding via the importance of untied learned scale parameters between network layers. Our network's success suggests that representations used by low-level image processing CNNs can be as simple and interpretable as Gabor filterbanks.
Capturing the dynamics in user preference is crucial to better predict user future behaviors because user preferences often drift over time. Many existing recommendation algorithms -- including both shallow and deep ones -- often model such dynamics independently, i.e., user static and dynamic preferences are not modeled under the same latent space, which makes it difficult to fuse them for recommendation. This paper considers the problem of embedding a user's sequential behavior into the latent space of user preferences, namely translating sequence to preference. To this end, we formulate the sequential recommendation task as a dictionary learning problem, which learns: 1) a shared dictionary matrix, each row of which represents a partial signal of user dynamic preferences shared across users; and 2) a posterior distribution estimator using a deep autoregressive model integrated with Gated Recurrent Unit (GRU), which can select related rows of the dictionary to represent a user's dynamic preferences conditioned on his/her past behaviors. Qualitative studies on the Netflix dataset demonstrate that the proposed method can capture the user preference drifts over time and quantitative studies on multiple real-world datasets demonstrate that the proposed method can achieve higher accuracy compared with state-of-the-art factorization and neural sequential recommendation methods. The code is available at https://github.com/cchao0116/S2PNM-TKDE2021.
Few-shot image generation is a challenging task even using the state-of-the-art Generative Adversarial Networks (GANs). Due to the unstable GAN training process and the limited training data, the generated images are often of low quality and low diversity. In this work, we propose a new editing-based method, i.e., Attribute Group Editing (AGE), for few-shot image generation. The basic assumption is that any image is a collection of attributes and the editing direction for a specific attribute is shared across all categories. AGE examines the internal representation learned in GANs and identifies semantically meaningful directions. Specifically, the class embedding, i.e., the mean vector of the latent codes from a specific category, is used to represent the category-relevant attributes, and the category-irrelevant attributes are learned globally by Sparse Dictionary Learning on the difference between the sample embedding and the class embedding. Given a GAN well trained on seen categories, diverse images of unseen categories can be synthesized through editing category-irrelevant attributes while keeping category-relevant attributes unchanged. Without re-training the GAN, AGE is capable of not only producing more realistic and diverse images for downstream visual applications with limited data but achieving controllable image editing with interpretable category-irrelevant directions.
Opinion summarization is the task of automatically generating summaries that encapsulate information from multiple user reviews. We present Semantic Autoencoder (SemAE) to perform extractive opinion summarization in an unsupervised manner. SemAE uses dictionary learning to implicitly capture semantic information from the review and learns a latent representation of each sentence over semantic units. A semantic unit is supposed to capture an abstract semantic concept. Our extractive summarization algorithm leverages the representations to identify representative opinions among hundreds of reviews. SemAE is also able to perform controllable summarization to generate aspect-specific summaries. We report strong performance on SPACE and AMAZON datasets, and perform experiments to investigate the functioning of our model. Our code is publicly available at https://github.com/brcsomnath/SemAE.
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.
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.
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.
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.
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.
State-of-the-art approaches for clustering high-dimensional data utilize deep auto-encoder architectures. Many of these networks require a large number of parameters and suffer from a lack of interpretability, due to the black-box nature of the auto-encoders. We introduce Mixture Model Auto-Encoders (MixMate), a novel architecture that clusters data by performing inference on a generative model. Derived from the perspective of sparse dictionary learning and mixture models, MixMate comprises several auto-encoders, each tasked with reconstructing data in a distinct cluster, while enforcing sparsity in the latent space. Through experiments on various image datasets, we show that MixMate achieves competitive performance compared to state-of-the-art deep clustering algorithms, while using orders of magnitude fewer parameters.
Comparing structured objects such as graphs is a fundamental operation involved in many learning tasks. To this end, the Gromov-Wasserstein (GW) distance, based on Optimal Transport (OT), has proven to be successful in handling the specific nature of the associated objects. More specifically, through the nodes connectivity relations, GW operates on graphs, seen as probability measures over specific spaces. At the core of OT is the idea of conservation of mass, which imposes a coupling between all the nodes from the two considered graphs. We argue in this paper that this property can be detrimental for tasks such as graph dictionary or partition learning, and we relax it by proposing a new semi-relaxed Gromov-Wasserstein divergence. Aside from immediate computational benefits, we discuss its properties, and show that it can lead to an efficient graph dictionary learning algorithm. We empirically demonstrate its relevance for complex tasks on graphs such as partitioning, clustering and completion.
While open databases are an important resource in the Deep Learning (DL) era, they are sometimes used "off-label": data published for one task are used for training algorithms for a different one. This work aims to highlight that in some cases, this common practice may lead to biased, overly-optimistic results. We demonstrate this phenomenon for inverse problem solvers and show how their biased performance stems from hidden data preprocessing pipelines. We describe two preprocessing pipelines typical of open-access databases and study their effects on three well-established algorithms developed for Magnetic Resonance Imaging (MRI) reconstruction: Compressed Sensing (CS), Dictionary Learning (DictL), and DL. In this large-scale study we performed extensive computations. Our results demonstrate that the CS, DictL and DL algorithms yield systematically biased results when naively trained on seemingly-appropriate data: the Normalized Root Mean Square Error (NRMSE) improves consistently with the preprocessing extent, showing an artificial increase of 25%-48% in some cases. Since this phenomenon is generally unknown, biased results are sometimes published as state-of-the-art; we refer to that as subtle data crimes. This work hence raises a red flag regarding naive off-label usage of Big Data and reveals the vulnerability of modern inverse problem solvers to the resulting bias.
Convolutional sparse coding improves on the standard sparse approximation by incorporating a global shift-invariant model. The most efficient convolutional sparse coding methods are based on the alternating direction method of multipliers and the convolution theorem. The only major difference between these methods is how they approach a convolutional least-squares fitting subproblem. This letter presents a solution to this subproblem, which improves the efficiency of the state-of-the-art algorithms. We also use the same approach for developing an efficient convolutional dictionary learning method. Furthermore, we propose a novel algorithm for convolutional sparse coding with a constraint on the approximation error.