Two techniques are proposed to alleviate the computational burden of MUltiple SIgnal Classification (MUSIC) algorithm applied to Electroencephalogram (EEG) source localization. A significant reduction was achieved by parsing the cortex surface into smaller regions and nominating only a few regions for the exhaustive search inherent in the MUSIC algorithm. The nomination procedure involves a dictionary learning phase in which each region is assigned an atom matrix. Moreover, a dimensionality reduction step provided by excluding some of the electrodes is designed such that the Cramer-Rao bound of localization is maintained. It is shown by simulation that computational complexity of the MUSIC-based localization can be reduced by up to $80\%$.
Sparse coding or sparse dictionary learning has been widely used to recover underlying structure in many kinds of natural data. Here, we provide conditions guaranteeing when this recovery is universal; that is, when sparse codes and dictionaries are unique (up to natural symmetries). Our main tool is a useful lemma in combinatorial matrix theory that allows us to derive bounds on the sample sizes guaranteeing such uniqueness under various assumptions for how training data are generated. Whenever the conditions to one of our theorems are met, any sparsity-constrained learning algorithm that succeeds in reconstructing the data recovers the original sparse codes and dictionary. We also discuss potential applications to neuroscience and data analysis.
The analysis of the Nystagmus waveforms from eye-tracking records is crucial for the clinicial interpretation of this pathological movement. A major issue to automatize this analysis is the presence of natural eye movements and eye blink artefacts that are mixed with the signal of interest. We propose a method based on Convolutional Dictionary Learning that is able to automaticcaly highlight the Nystagmus waveforms, separating the natural motion from the pathological movements. We show on simulated signals that our method can indeed improve the pattern recovery rate and provide clinical examples to illustrate how this algorithm performs.
Convolutional neural networks (CNNs) have been tremendously successful in solving imaging inverse problems. To understand their success, an effective strategy is to construct simpler and mathematically more tractable convolutional sparse coding (CSC) models that share essential ingredients with CNNs. Existing CSC methods, however, underperform leading CNNs in challenging inverse problems. We hypothesize that the performance gap may be attributed in part to how they process images at different spatial scales: While many CNNs use multiscale feature representations, existing CSC models mostly rely on single-scale dictionaries. To close the performance gap, we thus propose a multiscale convolutional dictionary structure. The proposed dictionary structure is derived from the U-Net, arguably the most versatile and widely used CNN for image-to-image learning problems. We show that incorporating the proposed multiscale dictionary in an otherwise standard CSC framework yields performance competitive with state-of-the-art CNNs across a range of challenging inverse problems including CT and MRI reconstruction. Our work thus demonstrates the effectiveness and scalability of the multiscale CSC approach in solving challenging inverse problems.
Deep Neural Networks (DNNs) are vulnerable to adversarial attacks: carefully constructed perturbations to an image can seriously impair classification accuracy, while being imperceptible to humans. While there has been a significant amount of research on defending against such attacks, most defenses based on systematic design principles have been defeated by appropriately modified attacks. For a fixed set of data, the most effective current defense is to train the network using adversarially perturbed examples. In this paper, we investigate a radically different, neuro-inspired defense mechanism, starting from the observation that human vision is virtually unaffected by adversarial examples designed for machines. We aim to reject L^inf bounded adversarial perturbations before they reach a classifier DNN, using an encoder with characteristics commonly observed in biological vision: sparse overcomplete representations, randomness due to synaptic noise, and drastic nonlinearities. Encoder training is unsupervised, using standard dictionary learning. A CNN-based decoder restores the size of the encoder output to that of the original image, enabling the use of a standard CNN for classification. Our nominal design is to train the decoder and classifier together in standard supervised fashion, but we also consider unsupervised decoder training based on a regression objective (as in a conventional autoencoder) with separate supervised training of the classifier. Unlike adversarial training, all training is based on clean images. Our experiments on the CIFAR-10 show performance competitive with state-of-the-art defenses based on adversarial training, and point to the promise of neuro-inspired techniques for the design of robust neural networks. In addition, we provide results for a subset of the Imagenet dataset to verify that our approach scales to larger images.
Breast cancer is the most common cancer among women both in developed and developing countries. Early detection and diagnosis of breast cancer may reduce its mortality and improve the quality of life. Computer-aided detection (CADx) and computer-aided diagnosis (CAD) techniques have shown promise for reducing the burden of human expert reading and improve the accuracy and reproducibility of results. Sparse analysis techniques have produced relevant results for representing and recognizing imaging patterns. In this work we propose a method for Label Consistent Spatially Localized Ensemble Sparse Analysis (LC-SLESA). In this work we apply dictionary learning to our block based sparse analysis method to classify breast lesions as benign or malignant. The performance of our method in conjunction with LC-KSVD dictionary learning is evaluated using 10-, 20-, and 30-fold cross validation on the MIAS dataset. Our results indicate that the proposed sparse analyses may be a useful component for breast cancer screening applications.
Convolutional sparse representation (CSR), shift-invariant model for inverse problems, has gained much attention in the fields of signal/image processing, machine learning and computer vision. The most challenging problems in CSR implies the minimization of a composite function of the form $min_x \sum_i f_i(x) + g(x)$, where a direct and low-cost solution can be difficult to achieve. However, it has been reported that semi-distributed formulations such as ADMM consensus can provide important computational benefits. In the present work, we derive and detail a thorough theoretical analysis of an efficient consensus algorithm based on proximal gradient (PG) approach. The effectiveness of the proposed algorithm with respect to its ADMM counterpart is primarily assessed in the classic convolutional dictionary learning problem. Furthermore, our consensus method, which is generically structured, can be used to solve other optimization problems, where a sum of convex functions with a regularization term share a single global variable. As an example, the proposed algorithm is also applied to another particular convolutional problem for the anomaly detection task.
Neuro-symbolic representations have proved effective in learning structure information in vision and language. In this paper, we propose a new model architecture for learning multi-modal neuro-symbolic representations for video captioning. Our approach uses a dictionary learning-based method of learning relations between videos and their paired text descriptions. We refer to these relations as relative roles and leverage them to make each token role-aware using attention. This results in a more structured and interpretable architecture that incorporates modality-specific inductive biases for the captioning task. Intuitively, the model is able to learn spatial, temporal, and cross-modal relations in a given pair of video and text. The disentanglement achieved by our proposal gives the model more capacity to capture multi-modal structures which result in captions with higher quality for videos. Our experiments on two established video captioning datasets verifies the effectiveness of the proposed approach based on automatic metrics. We further conduct a human evaluation to measure the grounding and relevance of the generated captions and observe consistent improvement for the proposed model. The codes and trained models can be found at https://github.com/hassanhub/R3Transformer
Online nonnegative matrix factorization (ONMF) is a matrix factorization technique in the online setting where data are acquired in a streaming fashion and the matrix factors are updated each time. This enables factor analysis to be performed concurrently with the arrival of new data samples. In this article, we demonstrate how one can use online nonnegative matrix factorization algorithms to learn joint dictionary atoms from an ensemble of correlated data sets. We propose a temporal dictionary learning scheme for time-series data sets, based on ONMF algorithms. We demonstrate our dictionary learning technique in the application contexts of historical temperature data, video frames, and color images.
Various iterative reconstruction algorithms for inverse problems can be unfolded as neural networks. Empirically, this approach has often led to improved results, but theoretical guarantees are still scarce. While some progress on generalization properties of neural networks have been made, great challenges remain. In this chapter, we discuss and combine these topics to present a generalization error analysis for a class of neural networks suitable for sparse reconstruction from few linear measurements. The hypothesis class considered is inspired by the classical iterative soft-thresholding algorithm (ISTA). The neural networks in this class are obtained by unfolding iterations of ISTA and learning some of the weights. Based on training samples, we aim at learning the optimal network parameters via empirical risk minimization and thereby the optimal network that reconstructs signals from their compressive linear measurements. In particular, we may learn a sparsity basis that is shared by all of the iterations/layers and thereby obtain a new approach for dictionary learning. For this class of networks, we present a generalization bound, which is based on bounding the Rademacher complexity of hypothesis classes consisting of such deep networks via Dudley's integral. Remarkably, under realistic conditions, the generalization error scales only logarithmically in the number of layers, and at most linear in number of measurements.
For classification tasks, dictionary learning based methods have attracted lots of attention in recent years. One popular way to achieve this purpose is to introduce label information to generate a discriminative dictionary to represent samples. However, compared with traditional dictionary learning, this category of methods only achieves significant improvements in supervised learning, and has little positive influence on semi-supervised or unsupervised learning. To tackle this issue, we propose a Dynamic Label Dictionary Learning (DLDL) algorithm to generate the soft label matrix for unlabeled data. Specifically, we employ hypergraph manifold regularization to keep the relations among original data, transformed data, and soft labels consistent. We demonstrate the efficiency of the proposed DLDL approach on two remote sensing datasets.
In recent years, the attention mechanism contributes significantly to hypergraph based neural networks. However, these methods update the attention weights with the network propagating. That is to say, this type of attention mechanism is only suitable for deep learning-based methods while not applicable to the traditional machine learning approaches. In this paper, we propose a hypergraph based sparse attention mechanism to tackle this issue and embed it into dictionary learning. More specifically, we first construct a sparse attention hypergraph, asset attention weights to samples by employing the $\ell_1$-norm sparse regularization to mine the high-order relationship among sample features. Then, we introduce the hypergraph Laplacian operator to preserve the local structure for subspace transformation in dictionary learning. Besides, we incorporate the discriminative information into the hypergraph as the guidance to aggregate samples. Unlike previous works, our method updates attention weights independently, does not rely on the deep network. We demonstrate the efficacy of our approach on four benchmark datasets.
This paper presents a dictionary learning-based method with region-specific image patches to maximize the utility of the powerful sparse data processing technique for CT image reconstruction. Considering heterogeneous distributions of image features and noise in CT, region-specific customization of dictionaries is utilized in iterative reconstruction. Thoracic CT images are partitioned into several regions according to their structural and noise characteristics. Dictionaries specific to each region are then learned from the segmented thoracic CT images and applied to subsequent image reconstruction of the region. Parameters for dictionary learning and sparse representation are determined according to the structural and noise properties of each region. The proposed method results in better performance than the conventional reconstruction based on a single dictionary in recovering structures and suppressing noise in both simulation and human CT imaging. Quantitatively, the simulation study shows maximum improvement of image quality for the whole thorax can achieve 4.88% and 11.1% in terms of the Structure-SIMilarity (SSIM) and Root-Mean-Square Error (RMSE) indices, respectively. For human imaging data, it is found that the structures in the lungs and heart can be better recovered, while simultaneously decreasing noise around the vertebra effectively. The proposed strategy takes into account inherent regional differences inside of the reconstructed object and leads to improved images. The method can be readily extended to CT imaging of other anatomical regions and other applications.
In this paper, we propose a novel tensor learning and coding model for third-order data completion. Our model is to learn a data-adaptive dictionary from the given observations, and determine the coding coefficients of third-order tensor tubes. In the completion process, we minimize the low-rankness of each tensor slice containing the coding coefficients. By comparison with the traditional pre-defined transform basis, the advantages of the proposed model are that (i) the dictionary can be learned based on the given data observations so that the basis can be more adaptively and accurately constructed, and (ii) the low-rankness of the coding coefficients can allow the linear combination of dictionary features more effectively. Also we develop a multi-block proximal alternating minimization algorithm for solving such tensor learning and coding model, and show that the sequence generated by the algorithm can globally converge to a critical point. Extensive experimental results for real data sets such as videos, hyperspectral images, and traffic data are reported to demonstrate these advantages and show the performance of the proposed tensor learning and coding method is significantly better than the other tensor completion methods in terms of several evaluation metrics.
Online Tensor Factorization (OTF) is a fundamental tool in learning low-dimensional interpretable features from streaming multi-modal data. While various algorithmic and theoretical aspects of OTF have been investigated recently, a general convergence guarantee to stationary points of the objective function without any incoherence or sparsity assumptions is still lacking even for the i.i.d. case. In this work, we introduce a novel algorithm that learns a CANDECOMP/PARAFAC (CP) basis from a given stream of tensor-valued data under general constraints, including nonnegativity constraints that induce interpretability of the learned CP basis. We prove that our algorithm converges almost surely to the set of stationary points of the objective function under the hypothesis that the sequence of data tensors is generated by an underlying Markov chain. Our setting covers the classical i.i.d. case as well as a wide range of application contexts including data streams generated by independent or MCMC sampling. Our result closes a gap between OTF and Online Matrix Factorization in global convergence analysis \commHL{for CP-decompositions}. Experimentally, we show that our algorithm converges much faster than standard algorithms for nonnegative tensor factorization tasks on both synthetic and real-world data. Also, we demonstrate the utility of our algorithm on a diverse set of examples from image, video, and time-series data, illustrating how one may learn qualitatively different CP-dictionaries from the same tensor data by exploiting the tensor structure in multiple ways.
Supervised Dictionary Learning has gained much interest in the recent decade and has shown significant performance improvements in image classification. However, in general, supervised learning needs a large number of labelled samples per class to achieve an acceptable result. In order to deal with databases which have just a few labelled samples per class, semi-supervised learning, which also exploits unlabelled samples in training phase is used. Indeed, unlabelled samples can help to regularize the learning model, yielding an improvement of classification accuracy. In this paper, we propose a new semi-supervised dictionary learning method based on two pillars: on one hand, we enforce manifold structure preservation from the original data into sparse code space using Locally Linear Embedding, which can be considered a regularization of sparse code; on the other hand, we train a semi-supervised classifier in sparse code space. We show that our approach provides an improvement over state-of-the-art semi-supervised dictionary learning methods.
Feature extraction plays an important role in Electrocardiogram (ECG) Beats classification system. Compared to other popular methods, VQ method performs well in feature extraction from ECG with advantages of dimensionality reduction. In VQ method, a set of dictionaries corresponding to segments of ECG beats is trained, and VQ codes are used to represent each heartbeat. However, in practice, VQ codes optimized by k-means or k-means++ exist large quantization errors, which results in VQ codes for two heartbeats of the same type being very different. So the essential differences between different types of heartbeats cannot be representative well. On the other hand, VQ uses too much data during codebook construction, which limits the speed of dictionary learning. In this paper, we propose a new method to improve the speed and accuracy of VQ method. To reduce the computation of codebook construction, a set of sparse dictionaries corresponding to wave segments of ECG beats is constructed. After initialized, sparse dictionaries are updated efficiently by Feature-sign and Lagrange dual algorithm. Based on those dictionaries, a set of codes can be computed to represent original ECG beats.Experimental results show that features extracted from ECG by our method are more efficient and separable. The accuracy of our method is higher than other methods with less time consumption of feature extraction
We propose CLEANN, the first end-to-end framework that enables online mitigation of Trojans for embedded Deep Neural Network (DNN) applications. A Trojan attack works by injecting a backdoor in the DNN while training; during inference, the Trojan can be activated by the specific backdoor trigger. What differentiates CLEANN from the prior work is its lightweight methodology which recovers the ground-truth class of Trojan samples without the need for labeled data, model retraining, or prior assumptions on the trigger or the attack. We leverage dictionary learning and sparse approximation to characterize the statistical behavior of benign data and identify Trojan triggers. CLEANN is devised based on algorithm/hardware co-design and is equipped with specialized hardware to enable efficient real-time execution on resource-constrained embedded platforms. Proof of concept evaluations on CLEANN for the state-of-the-art Neural Trojan attacks on visual benchmarks demonstrate its competitive advantage in terms of attack resiliency and execution overhead.
Point clouds are unstructured and unordered in the embedded 3D space. In order to produce consistent responses under different permutation layouts, most existing methods aggregate local spatial points through maximum or summation operation. But such an aggregation essentially belongs to the isotropic filtering on all operated points therein, which tends to lose the information of geometric structures. In this paper, we propose a spatial transformer point convolution (STPC) method to achieve anisotropic convolution filtering on point clouds. To capture and represent implicit geometric structures, we specifically introduce spatial direction dictionary to learn those latent geometric components. To better encode unordered neighbor points, we design sparse deformer to transform them into the canonical ordered dictionary space by using direction dictionary learning. In the transformed space, the standard image-like convolution can be leveraged to generate anisotropic filtering, which is more robust to express those finer variances of local regions. Dictionary learning and encoding processes are encapsulated into a network module and jointly learnt in an end-to-end manner. Extensive experiments on several public datasets (including S3DIS, Semantic3D, SemanticKITTI) demonstrate the effectiveness of our proposed method in point clouds semantic segmentation task.
We propose a novel integrated framework that jointly models complementary information from resting-state functional MRI (rs-fMRI) connectivity and diffusion tensor imaging (DTI) tractography to extract biomarkers of brain connectivity predictive of behavior. Our framework couples a generative model of the connectomics data with a deep network that predicts behavioral scores. The generative component is a structurally-regularized Dynamic Dictionary Learning (sr-DDL) model that decomposes the dynamic rs-fMRI correlation matrices into a collection of shared basis networks and time varying subject-specific loadings. We use the DTI tractography to regularize this matrix factorization and learn anatomically informed functional connectivity profiles. The deep component of our framework is an LSTM-ANN block, which uses the temporal evolution of the subject-specific sr-DDL loadings to predict multidimensional clinical characterizations. Our joint optimization strategy collectively estimates the basis networks, the subject-specific time-varying loadings, and the neural network weights. We validate our framework on a dataset of neurotypical individuals from the Human Connectome Project (HCP) database to map to cognition and on a separate multi-score prediction task on individuals diagnosed with Autism Spectrum Disorder (ASD) in a five-fold cross validation setting. Our hybrid model outperforms several state-of-the-art approaches at clinical outcome prediction and learns interpretable multimodal neural signatures of brain organization.