Related papers: Online Multilinear Dictionary Learning
Tensor regression has shown to be advantageous in learning tasks with multi-directional relatedness. Given massive multiway data, traditional methods are often too slow to operate on or suffer from memory bottleneck. In this paper, we…
We propose an efficient online dictionary learning algorithm for kernel-based sparse representations. In this framework, input signals are nonlinearly mapped to a high-dimensional feature space and represented sparsely using a virtual…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
This paper concerns dictionary learning, i.e., sparse coding, a fundamental representation learning problem. We show that a subgradient descent algorithm, with random initialization, can provably recover orthogonal dictionaries on a natural…
Sparsity and low-rank models have been popular for reconstructing images and videos from limited or corrupted measurements. Dictionary or transform learning methods are useful in applications such as denoising, inpainting, and medical image…
Many machine learning applications use latent variable models to explain structure in data, whereby visible variables (= coordinates of the given datapoint) are explained as a probabilistic function of some hidden variables. Finding…
We give a new approach to the dictionary learning (also known as "sparse coding") problem of recovering an unknown $n\times m$ matrix $A$ (for $m \geq n$) from examples of the form \[ y = Ax + e, \] where $x$ is a random vector in $\mathbb…
In this paper we consider the dictionary learning problem for sparse representation. We first show that this problem is NP-hard by polynomial time reduction of the densest cut problem. Then, using successive convex approximation strategies,…
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,…
This paper provides fundamental limits on the sample complexity of estimating dictionaries for tensor data. The specific focus of this work is on $K$th-order tensor data and the case where the underlying dictionary can be expressed in terms…
Over the past decade, learning a dictionary from input images for sparse modeling has been one of the topics which receive most research attention in image processing and compressed sensing. Most existing dictionary learning methods…
Matrix congruence extends naturally to the setting of tensors. We apply methods from tensor decomposition, algebraic geometry and numerical optimization to this group action. Given a tensor in the orbit of another tensor, we compute a…
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…
We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…
Dictionary learning is the task of determining a data-dependent transform that yields a sparse representation of some observed data. The dictionary learning problem is non-convex, and usually solved via computationally complex iterative…
This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…
It is often difficult to learn new mathematics semantically and syntactically, even when there are similarities in the words and meaning when discussed aloud. The goal of this document is to facilitate learning through explanations and…
A dictionary is a database of standard vectors, so that other vectors / signals are expressed as linear combinations of dictionary vectors, and the task of learning a dictionary for a given data is to find a good dictionary so that the…
Training dense passage representations via contrastive learning has been shown effective for Open-Domain Passage Retrieval (ODPR). Existing studies focus on further optimizing by improving negative sampling strategy or extra pretraining.…
In this paper we propose an algorithm to classify tensor data. Our methodology is built on recent studies about matrix classification with the trace norm constrained weight matrix and the tensor trace norm. Similar to matrix classification,…