Related papers: A Fast Implementation for the Canonical Polyadic D…
We propose a novel algorithm for the computation of canonical polyadic decomposition (CPD) of large-scale tensors. The proposed algorithm generalizes the random projection (RAP) technique, which is often used to compute large-scale…
Canonical Polyadic (CP) tensor decomposition is a fundamental technique for analyzing high-dimensional tensor data. While the Alternating Least Squares (ALS) algorithm is widely used for computing CP decomposition due to its simplicity and…
In general, algorithms for order-3 CANDECOMP/-PARAFAC (CP), also coined canonical polyadic decomposition (CPD), are easily to implement and can be extended to higher order CPD. Unfortunately, the algorithms become computationally demanding,…
This paper introduces a novel collaborative neurodynamic model for computing nonnegative Canonical Polyadic Decomposition (CPD). The model relies on a system of recurrent neural networks to solve the underlying nonconvex optimization…
The tensor rank decomposition, also known as canonical polyadic(CP) or simply tensor decomposition, has a long history in multilinear algebra. However, computing a rank decomposition becomes particularly challenging when the rank lies…
Most state of the art deep neural networks are overparameterized and exhibit a high computational cost. A straightforward approach to this problem is to replace convolutional kernels with its low-rank tensor approximations, whereas the…
Because of the attractiveness of the canonical polyadic (CP) tensor decomposition in various applications, several algorithms have been designed to compute it, but efficient ones are still lacking. Iterative deflation algorithms based on…
The canonical polyadic (CP) decomposition is one of the most widely used tensor decomposition techniques. The conventional CP decomposition algorithm combines alternating least squares (ALS) with the normal equation. However, the normal…
Tensor decomposition is a fundamental unsupervised machine learning method in data science, with applications including network analysis and sensor data processing. This work develops a generalized canonical polyadic (GCP) low-rank tensor…
Tensor Networks (TNs) have recently been used to speed up kernel machines by constraining the model weights, yielding exponential computational and storage savings. In this paper we prove that the outputs of Canonical Polyadic Decomposition…
Neural Network designs are quite diverse, from VGG-style to ResNet-style, and from Convolutional Neural Networks to Transformers. Towards the design of efficient accelerators, many works have adopted a dataflow-based, inter-layer pipelined…
In the present work, a method is proposed in order to compute a Canonical Polyadic (CP) approximation of a given tensor. It is based on a greedy method and an adaptation of the TT-SVD method. The proposed approach can be straightforwardly…
Tensor decompositions are powerful tools for large data analytics as they jointly model multiple aspects of data into one framework and enable the discovery of the latent structures and higher-order correlations within the data. One of the…
A rising problem in the compression of Deep Neural Networks is how to reduce the number of parameters in convolutional kernels and the complexity of these layers by low-rank tensor approximation. Canonical polyadic tensor decomposition…
This paper proposes fast randomized algorithms for computing the Kronecker Tensor Decomposition (KTD). The proposed algorithms can decompose a given tensor into the KTD format much faster than the existing state-of-the-art algorithms. Our…
Tensor decomposition has been widely used in machine learning and high-volume data analysis. However, large-scale tensor factorization often consumes huge memory and computing cost. Meanwhile, modernized computing hardware such as tensor…
Physiological signals are often organized in the form of multiple dimensions (e.g., channel, time, task, and 3D voxel), so it is better to preserve original organization structure when processing. Unlike vector-based methods that destroy…
Efficient modelling of feature interactions underpins supervised learning for non-sequential tasks, characterized by a lack of inherent ordering of features (variables). The brute force approach of learning a parameter for each interaction…
Tensor decomposition methods are widely used for model compression and fast inference in convolutional neural networks (CNNs). Although many decompositions are conceivable, only CP decomposition and a few others have been applied in…
To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new…