This work learns sparse tensor representations using mixtures of separable dictionaries.
problem Learning sparse representations of tensor data with structured models.
method Proposes and explores learning a mixture of separable dictionaries with sufficient conditions for local identifiability.
result Developed computational algorithms for batch and online learning.
Structured sparse coding and the related structured dictionary learning problems are novel research areas in machine learning. In this paper we present a new application of structured dictionary learning for collaborative filtering based recommender systems. Our extensive numerical experiments demonstrate that the pres…
STARK learns structured dictionaries for tensor data.
problem Representing multidimensional data with structured dictionaries.
method Solves a convex relaxation of a nonconvex rank-1 tensor recovery problem.
result Empirical results show promising performance for tensors of any order.
Detects financial fraud schemes in networks using graph structure learning.
problem Identifying financial fraud schemes in complex networks.
method Adapting dictionary learning to network topologies, imposing Laplacian structure on dictionaries.
result Proposed methods effectively represent graph structure information for anomaly detection.
Many techniques in computer vision, machine learning, and statistics rely on the fact that a signal of interest admits a sparse representation over some dictionary. Dictionaries are either available analytically, or can be learned from a suitable training set. While analytic dictionaries permit to capture the global st…
The paper proposes a method to learn discriminative multilevel dictionaries for supervised image classification.
problem Improving sparse representation for supervised image classification.
method Learning structured multilevel dictionaries with discriminative constraints for each class, using reconstruction errors of image patches.
result Competitive results compared to state-of-the-art methods on texture image classification.
PerCDL learns personalized dictionaries for physiological signals combining global and local structures.
problem Representing datasets with both global and local structures in human physiological signals.
method Personalized Convolutional Dictionary Learning (PerCDL) that combines a global and personalized local dictionary.
result PerCDL effectively learns interpretable representations for human locomotion data.
A new tree-based method for adaptive dictionary learning.
problem Sparse encoding and multiscale structure in data.
method Hierarchical clustering and binary partition tree for adaptive dictionary learning.
result Dictionary atoms are organized in a multiscale structure, leading to better reconstruction.
Novel algorithm learns sparse signal representations over topological spaces.
problem Sparse representation of signals over combinatorial topological spaces.
method Leveraging Hodge theory, the paper embeds topology into a dictionary structure via concatenated sub-dictionaries, each as a polynomial of Hodge Laplacians, and optimizes the dictionary coefficients and sparse signal representation via iterative alternating algorithms.
result Efficiently learned sparse representations and underlying relational structure of topological signals.
In sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties -- the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent signals residing on weighted graphs, an additional design challenge is to incorporate …
Proposes DCADL for efficient image classification with reduced complexity.
problem Efficiency and discriminative capability in DL methods for image classification.
method Jointly learns a convolutional analysis dictionary and a universal classifier, reducing time complexity.
result Achieves competitive accuracy with reduced computational cost.
The paper proposes efficient dictionary learning algorithms that avoid multiplications for sparse representations.
problem Sparse representation with reduced computational complexity.
method Factorizations of the dictionary into binary orthonormal, scaling, and shear transformations with closed-form solutions.
result The proposed methods are effective and can be compared to well-known transforms like FFT and DCT.
Two algorithms converge to dictionary learning with geometric rate for non-uniform data.
problem Dictionary learning for non-uniform data models.
method Derivation of convergence conditions for MOD and ODL.
result Both algorithms converge to the generating dictionary with geometric rate under certain conditions.
New algorithm improves convergence of dictionary learning models.
problem Learning rich image features from data using structured unitary sparsifying operators.
method Alternating minimization for structured unitary sparsifying operator learning with convergence analysis.
result The algorithm converges to the underlying sparsifying model of the data under mild assumptions.
A dictionary connects symplectic to contact geometry, with applications to complex and G-structures.
problem Formalizing the relationship between symplectic and contact geometry.
method Developing a Symplectic-to-Contact Dictionary.
result The dictionary can be applied to complex and G-structures, revealing new geometries.
Paper provides conditions for local recovery of tensor data's Kronecker-structured dictionaries.
problem Local recovery of Kronecker-structured dictionaries for tensor data.
method Derives sufficient conditions for local recovery of coordinate dictionaries.
result Sufficient conditions guarantee recovery of individual coordinate dictionaries up to specified error.
DeepAM optimizes deep neural networks for image super-resolution.
problem Image super-resolution using deep neural networks.
method L-layer analysis dictionary model with IPAD and CAD.
result DeepAM outperforms deep neural networks with back-propagation.
Dictionary learning algorithms have been successfully used in both reconstructive and discriminative tasks, where the input signal is represented by a linear combination of a few dictionary atoms. While these methods are usually developed under ℓ1 sparsity constrain (prior) in the input domain, recent studies hav…
Dictionary learning is the problem of estimating the collection of atomic elements that provide a sparse representation of measured/collected signals or data. This paper finds fundamental limits on the sample complexity of estimating dictionaries for tensor data by proving a lower bound on the minimax risk. This lower …
The paper tackles energy disaggregation by improving dictionary learning with deep neural models.
problem Decomposing electricity signals of a whole home into its operating devices.
method Proposes a novel optimization program that learns both the dictionary and sparse coefficients using a deep neural model (LSTM-AE) to capture temporal energy signals.
result Significant improvement in disaggregation accuracy and F-score metrics compared to state-of-the-art methods.
Sparse coding, which is the decomposition of a vector using only a few basis elements, is widely used in machine learning and image processing. The basis set, also called dictionary, is learned to adapt to specific data. This approach has proven to be very effective in many image processing tasks. Traditionally, the di…
Graph-Dictionary model for sparse multivariate signal representation.
problem Capturing complex relational information in multivariate signals.
method Graph dictionaries and bilinear primal-dual splitting algorithm.
result Graph-dictionary model outperforms baselines in signal reconstruction and classification.
Proposes a new dictionary learning method for high-dimensional graph signals.
problem Challenges of traditional sparse representation methods in high-dimensional graph signals.
method Integrates graph topology implicitly through sparse combinations of graph-wavelet functions and explicitly through graph constraints.
result Demonstrates effectiveness in high-dimensional graph signal processing.
We develop methods to learn dictionaries invariant under group symmetries, useful in cryo-EM and tracking.
problem Learning dictionaries invariant under group symmetries.
method Representation theory, non-abelian Fourier analysis, matrix orbitopes, alternating minimization.
result Effective dictionary learning for SO(3) symmetries with guarantees.
Paper proposes semi-supervised method for dictionary learning.
problem Learning from both labeled and unlabeled data.
method Uses semi-supervised dictionary learning with LLE for manifold preservation.
result Significant improvements over other methods demonstrated.
Dictionary Learning has proven to be a powerful tool for many image processing tasks, where atoms are typically defined on small image patches. As a drawback, the dictionary only encodes basic structures. In addition, this approach treats patches of different locations in one single set, which means a loss of informati…
New algorithms compare and improve convolutional dictionary learning methods.
problem Challenges in learning convolutional dictionaries.
method Comprehensive comparison and development of new algorithms.
result Identifies most effective methods for convolutional dictionary learning.
New technique halves scan time for multi-echo MR images.
problem Slow acquisition of multi-echo magnetic resonance images.
method Structured deep dictionary learning for adaptive reconstruction.
result Scan time reduced by half compared to state-of-the-art.
New online method learns from all images, supports incomplete data.
problem High memory usage and limited training data in batch methods.
method Online convolutional dictionary learning with spatial mask support.
result Improved performance and better scalability with training set size.
DeepCAM learns convolutional dictionaries for image processing.
problem Processing high-dimensional signals like images efficiently.
method Introduces a Deep Convolutional Analysis Dictionary Model (DeepCAM) using convolutional dictionaries.
result DeepCAM achieves performance comparable to other methods on single image super-resolution.
Predicts COVID-19 spread using dictionary learning and online NMF.
problem Limited daily case data for accurate prediction.
method Joint dictionary learning and online NMF for short evolution instances.
result Learned dictionary patterns improve predictions over time.
From concentration inequalities for the suprema of Gaussian or Rademacher processes an inequality is derived. It is applied to sharpen existing and to derive novel bounds on the empirical Rademacher complexities of unit balls in various norms appearing in the context of structured sparsity and multitask dictionary lear…
This paper addresses image classification through learning a compact and discriminative dictionary efficiently. Given a structured dictionary with each atom (columns in the dictionary matrix) related to some label, we propose cross-label suppression constraint to enlarge the difference among representations for differe…
GPCDL uses Gaussian Processes to learn smooth templates from data.
problem Lack of smoothness in learned templates leads to overfitting and poor predictive performance.
method GPCDL incorporates Gaussian Process priors to enforce smoothness in the learned templates.
result GPCDL outperforms unregularized CDL in accuracy and predictive performance across various SNRs and applications.
Paper presents a method for robust surface reconstruction from noisy gradients using adaptive dictionary learning.
problem Reconstructing surfaces from noisy photometric stereo normal vector maps.
method Adaptive dictionary learning to sparsely represent spatial patches of the surface, enforcing smoothness constraints.
result The method effectively learns the underlying surface structure and is robust to noise.
DDL technique improves accuracy of deep neural networks against adversarial perturbations.
problem Improving accuracy of deep neural networks in the presence of adversarial perturbations.
method Denoising Dictionary Learning (DDL) technique applied to MNIST and CIFAR10 datasets.
result DDL significantly improves reconstruction quality and accuracy of deep neural networks on perturbed data.
Paper improves dictionary learning by addressing local and global coherence issues.
problem Improving dictionary learning by addressing local and global coherence issues.
method The paper uses the ITKrM algorithm to prove contraction under relaxed conditions and proposes replacing bad dictionaries with carefully designed candidates.
result The adaptive version of ITKrM can recover a generating dictionary from randomly initialized dictionaries of various sizes and learn meaningful dictionaries on image data.
A new algorithm improves kernel-based sparse coding for better data representation.
problem Lack of consistency between training and test optimization frameworks in K-SRC.
method Confident K-SRC (CKSC) with novel discriminative terms and supervised dictionary learning.
result Improves discriminative performance and recall phase in classification.
RKCA combines sparse dictionary learning and robust component analysis for robust low-rank modeling.
problem Learning robust low-rank representations from noisy data.
method Kronecker-decomposable component analysis (RKCA) with efficient learning algorithm.
result RKCA achieves robustness to gross corruption and low-rank modeling.
We present a sparse estimation and dictionary learning framework for compressed fiber sensing based on a probabilistic hierarchical sparse model. To handle severe dictionary coherence, selective shrinkage is achieved using a Weibull prior, which can be related to non-convex optimization with p-norm constraints for $0…
NOODL solves dictionary and coefficient recovery for online learning.
problem Non-convex optimization challenges in dictionary learning.
method NOODL: Neurally plausible alternating Optimization-based Online Dictionary Learning.
result Exact recovery of dictionary and coefficients at geometric rate.
Bayesian method improves dictionary learning for complex problems.
problem Efficiently identifying relevant dictionary entries for complex inverse problems.
method Bayesian group sparsity coding and deflation steps to compress and identify relevant subdictionaries.
result Significant computational complexity reduction and improved glitch detection in LIGO experiment.
Classifiers based on sparse representations have recently been shown to provide excellent results in many visual recognition and classification tasks. However, the high cost of computing sparse representations at test time is a major obstacle that limits the applicability of these methods in large-scale problems, or in…
New method improves signal classification accuracy.
problem Traditional dictionary learning struggles with signal classification accuracy.
method Incorporates discriminative information into sparse-inducing models.
result Significantly outperforms state-of-the-art methods in multi-class classification.
Paper proposes robust dictionary learning using concave losses.
problem Sensitivity to outliers in traditional dictionary learning methods.
method Generic framework based on concave losses, with results on composition of concave functions.
result Method better detects outliers and generates better dictionaries.
Robust method learns nonlinear structures robustly to noise.
problem Learning nonlinear structures in noisy data.
method Robust Non-Linear Matrix Factorization (RNLMF).
result RNLMF achieves noticeable improvements in denoising and clustering.
Sparse representations using learned dictionaries are being increasingly used with success in several data processing and machine learning applications. The availability of abundant training data necessitates the development of efficient, robust and provably good dictionary learning algorithms. Algorithmic stability an…
This paper studies the problem of data-adaptive representations for big, distributed data. It is assumed that a number of geographically-distributed, interconnected sites have massive local data and they are interested in collaboratively learning a low-dimensional geometric structure underlying these data. In contrast …