arXiv subjects

Andrzej Cichocki

Publications and source records attributed to Andrzej Cichocki.

At least 37 records · Page 2Linked to original sources

arXiv2023

Image Reconstruction using Superpixel Clustering and Tensor Completion

This paper presents a pixel selection method for compact image representation based on superpixel segmentation and tensor completion. Our method divides the image into several regions that capture important textures or semantics and selects a representative pixel from each region to store. We experiment with different criteria for choosing the representative pixel and find that the centroid pixel performs the best. We also propose two smooth tensor completion algorithms that can effectively reconstruct different types of images from the selected pixels. Our experiments show that our superpixel-based method achieves better results than uniform sampling for various missing ratios.

cs.CV↗

arXiv2023

Adaptive Cross Tubal Tensor Approximation

In this paper, we propose a new adaptive cross algorithm for computing a low tubal rank approximation of third-order tensors, with less memory and lower computational complexity than the truncated tensor SVD (t-SVD). This makes it applicable for decomposing large-scale tensors. We conduct numerical experiments on synthetic and real-world datasets to confirm the efficiency and feasibility of the proposed algorithm. The simulation results show more than one order of magnitude acceleration in the computation of low tubal rank (t-SVD) for large-scale tensors. An application to pedestrian attribute recognition is also presented.

math.NA↗

arXiv2023

Robust Low-Tubal-rank tensor recovery Using Discrete Empirical Interpolation Method with Optimized Slice/Feature Selection

In this paper, we extend the Discrete Empirical Interpolation Method (DEIM) to the third-order tensor case based on the t-product and use it to select important/ significant lateral and horizontal slices/features. The proposed Tubal DEIM (TDEIM) is investigated both theoretically and numerically. The experimental results show that the TDEIM can provide more accurate approximations than the existing methods. An application of the proposed method to the supervised classification task is also presented.

math.NA↗

arXiv2023

Cross Tensor Approximation for Image and Video Completion

This paper proposes a general framework to use the cross tensor approximation or tensor ColUmn-Row (CUR) approximation for reconstructing incomplete images and videos. The key importance of the new algorithms is their simplicity and ease of implementation with low computational complexity. For the case of data tensors with 1) structural missing components or 2) a high missing rate, we propose an efficient smooth tensor CUR algorithms which first make the sampled fibers smooth and then apply the proposed CUR algorithms. The numerical experiments show the significant benefit of this smoothing procedure. The main contribution of this paper is to develop/investigate improved multistage CUR algorithms with filtering (smoothing ) preprocessing for tensor completion. The second contribution is a detailed comparison of the performance of image recovery for four different CUR strategies via extensive computer simulations. Our simulations clearly indicated that the proposed algorithms are much faster than most of the existing state-of-the-art algorithms developed for tensor completion, while performance is comparable and often even better. Furthermore, we will provide in GitHub the MATLAB codes which can be used for various applications. Moreover, to our best knowledge, the CUR (cross approximation) algorithms have not been investigated nor compared till now for image and video completion.

math.NA↗

arXiv2022

TTOpt: A Maximum Volume Quantized Tensor Train-based Optimization and its Application to Reinforcement Learning

We present a novel procedure for optimization based on the combination of efficient quantized tensor train representation and a generalized maximum matrix volume principle. We demonstrate the applicability of the new Tensor Train Optimizer (TTOpt) method for various tasks, ranging from minimization of multidimensional functions to reinforcement learning. Our algorithm compares favorably to popular evolutionary-based methods and outperforms them by the number of function evaluations or execution time, often by a significant margin.

cs.LG↗

arXiv2022

How to Train Unstable Looped Tensor Network

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 (CPD) and Tucker tensor decomposition (TKD) are two solutions to this problem and provide promising results. However, CPD often fails due to degeneracy, making the networks unstable and hard to fine-tune. TKD does not provide much compression if the core tensor is big. This motivates using a hybrid model of CPD and TKD, a decomposition with multiple Tucker models with small core tensor, known as block term decomposition (BTD). This paper proposes a more compact model that further compresses the BTD by enforcing core tensors in BTD identical. We establish a link between the BTD with shared parameters and a looped chain tensor network (TC). Unfortunately, such strongly constrained tensor networks (with loop) encounter severe numerical instability, as proved by y (Landsberg, 2012) and (Handschuh, 2015a). We study perturbation of chain tensor networks, provide interpretation of instability in TC, demonstrate the problem. We propose novel methods to gain the stability of the decomposition results, keep the network robust and attain better approximation. Experimental results will confirm the superiority of the proposed methods in compression of well-known CNNs, and TC decomposition under challenging scenarios

cs.LG↗

arXiv2021

Randomized Algorithms for Computation of Tucker decomposition and Higher Order SVD (HOSVD)

Big data analysis has become a crucial part of new emerging technologies such as the internet of things, cyber-physical analysis, deep learning, anomaly detection, etc. Among many other techniques, dimensionality reduction plays a key role in such analyses and facilitates feature selection and feature extraction. Randomized algorithms are efficient tools for handling big data tensors. They accelerate decomposing large-scale data tensors by reducing the computational complexity of deterministic algorithms and the communication among different levels of the memory hierarchy, which is the main bottleneck in modern computing environments and architectures. In this paper, we review recent advances in randomization for the computation of Tucker decomposition and Higher Order SVD (HOSVD). We discuss random projection and sampling approaches, single-pass, and multi-pass randomized algorithms, and how to utilize them in the computation of the Tucker decomposition and the HOSVD. Simulations on synthetic and real datasets are provided to compare the performance of some of the best and most promising algorithms.

math.NA↗

arXiv2021

L3C-Stereo: Lossless Compression for Stereo Images

A large number of autonomous driving tasks need high-definition stereo images, which requires a large amount of storage space. Efficiently executing lossless compression has become a practical problem. Commonly, it is hard to make accurate probability estimates for each pixel. To tackle this, we propose L3C-Stereo, a multi-scale lossless compression model consisting of two main modules: the warping module and the probability estimation module. The warping module takes advantage of two view feature maps from the same domain to generate a disparity map, which is used to reconstruct the right view so as to improve the confidence of the probability estimate of the right view. The probability estimation module provides pixel-wise logistic mixture distributions for adaptive arithmetic coding. In the experiments, our method outperforms the hand-crafted compression methods and the learning-based method on all three datasets used. Then, we show that a better maximum disparity can lead to a better compression effect. Furthermore, thanks to a compression property of our model, it naturally generates a disparity map of an acceptable quality for the subsequent stereo tasks.

eess.IV↗

arXiv2021

Deep Learning in EEG: Advance of the Last Ten-Year Critical Period

Deep learning has achieved excellent performance in a wide range of domains, especially in speech recognition and computer vision. Relatively less work has been done for EEG, but there is still significant progress attained in the last decade. Due to the lack of a comprehensive and topic widely covered survey for deep learning in EEG, we attempt to summarize recent progress to provide an overview, as well as perspectives for future developments. We first briefly mention the artifacts removal for EEG signal and then introduce deep learning models that have been utilized in EEG processing and classification. Subsequently, the applications of deep learning in EEG are reviewed by categorizing them into groups such as brain-computer interface, disease detection, and emotion recognition. They are followed by the discussion, in which the pros and cons of deep learning are presented and future directions and challenges for deep learning in EEG are proposed. We hope that this paper could serve as a summary of past work for deep learning in EEG and the beginning of further developments and achievements of EEG studies based on deep learning.

eess.SP↗

arXiv2021

Meta-Solver for Neural Ordinary Differential Equations

A conventional approach to train neural ordinary differential equations (ODEs) is to fix an ODE solver and then learn the neural network's weights to optimize a target loss function. However, such an approach is tailored for a specific discretization method and its properties, which may not be optimal for the selected application and yield the overfitting to the given solver. In our paper, we investigate how the variability in solvers' space can improve neural ODEs performance. We consider a family of Runge-Kutta methods that are parameterized by no more than two scalar variables. Based on the solvers' properties, we propose an approach to decrease neural ODEs overfitting to the pre-defined solver, along with a criterion to evaluate such behaviour. Moreover, we show that the right choice of solver parameterization can significantly affect neural ODEs models in terms of robustness to adversarial attacks. Recently it was shown that neural ODEs demonstrate superiority over conventional CNNs in terms of robustness. Our work demonstrates that the model robustness can be further improved by optimizing solver choice for a given task. The source code to reproduce our experiments is available at https://github.com/juliagusak/neural-ode-metasolver.

cs.LG↗

arXiv2020

Improving EEG Decoding via Clustering-based Multi-task Feature Learning

Accurate electroencephalogram (EEG) pattern decoding for specific mental tasks is one of the key steps for the development of brain-computer interface (BCI), which is quite challenging due to the considerably low signal-to-noise ratio of EEG collected at the brain scalp. Machine learning provides a promising technique to optimize EEG patterns toward better decoding accuracy. However, existing algorithms do not effectively explore the underlying data structure capturing the true EEG sample distribution, and hence can only yield a suboptimal decoding accuracy. To uncover the intrinsic distribution structure of EEG data, we propose a clustering-based multi-task feature learning algorithm for improved EEG pattern decoding. Specifically, we perform affinity propagation-based clustering to explore the subclasses (i.e., clusters) in each of the original classes, and then assign each subclass a unique label based on a one-versus-all encoding strategy. With the encoded label matrix, we devise a novel multi-task learning algorithm by exploiting the subclass relationship to jointly optimize the EEG pattern features from the uncovered subclasses. We then train a linear support vector machine with the optimized features for EEG pattern decoding. Extensive experimental studies are conducted on three EEG datasets to validate the effectiveness of our algorithm in comparison with other state-of-the-art approaches. The improved experimental results demonstrate the outstanding superiority of our algorithm, suggesting its prominent performance for EEG pattern decoding in BCI applications.

eess.SP↗

arXiv2020

Future Trends for Human-AI Collaboration: A Comprehensive Taxonomy of AI/AGI Using Multiple Intelligences and Learning Styles

This article discusses some trends and concepts in developing new generation of future Artificial General Intelligence (AGI) systems which relate to complex facets and different types of human intelligence, especially social, emotional, attentional and ethical intelligence. We describe various aspects of multiple human intelligences and learning styles, which may impact on a variety of AI problem domains. Using the concept of 'multiple intelligences' rather than a single type of intelligence, we categorize and provide working definitions of various AGI depending on their cognitive skills or capacities. Future AI systems will be able not only to communicate with human users and each other, but also to efficiently exchange knowledge and wisdom with abilities of cooperation, collaboration and even co-creating something new and valuable and have meta-learning capacities. Multi-agent systems such as these can be used to solve problems that would be difficult to solve by any individual intelligent agent. Key words: Artificial General Intelligence (AGI), multiple intelligences, learning styles, physical intelligence, emotional intelligence, social intelligence, attentional intelligence, moral-ethical intelligence, responsible decision making, creative-innovative intelligence, cognitive functions, meta-learning of AI systems.

cs.AI↗

arXiv2020

Reduced-Order Modeling of Deep Neural Networks

We introduce a new method for speeding up the inference of deep neural networks. It is somewhat inspired by the reduced-order modeling techniques for dynamical systems.The cornerstone of the proposed method is the maximum volume algorithm. We demonstrate efficiency on neural networks pre-trained on different datasets. We show that in many practical cases it is possible to replace convolutional layers with much smaller fully-connected layers with a relatively small drop in accuracy.

cs.LG↗

arXiv2020

Interpolation Technique to Speed Up Gradients Propagation in Neural ODEs

We propose a simple interpolation-based method for the efficient approximation of gradients in neural ODE models. We compare it with the reverse dynamic method (known in the literature as "adjoint method") to train neural ODEs on classification, density estimation, and inference approximation tasks. We also propose a theoretical justification of our approach using logarithmic norm formalism. As a result, our method allows faster model training than the reverse dynamic method that was confirmed and validated by extensive numerical experiments for several standard benchmarks.

cs.NE↗

arXiv2020

Stable Low-rank Tensor Decomposition for Compression of Convolutional Neural Network

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 Canonical Polyadic tensor Decomposition is one of the most suited models. However, fitting the convolutional tensors by numerical optimization algorithms often encounters diverging components, i.e., extremely large rank-one tensors but canceling each other. Such degeneracy often causes the non-interpretable result and numerical instability for the neural network fine-tuning. This paper is the first study on degeneracy in the tensor decomposition of convolutional kernels. We present a novel method, which can stabilize the low-rank approximation of convolutional kernels and ensure efficient compression while preserving the high-quality performance of the neural networks. We evaluate our approach on popular CNN architectures for image classification and show that our method results in much lower accuracy degradation and provides consistent performance.

cs.CV↗

arXiv2020

Towards Understanding Normalization in Neural ODEs

Normalization is an important and vastly investigated technique in deep learning. However, its role for Ordinary Differential Equation based networks (neural ODEs) is still poorly understood. This paper investigates how different normalization techniques affect the performance of neural ODEs. Particularly, we show that it is possible to achieve 93% accuracy in the CIFAR-10 classification task, and to the best of our knowledge, this is the highest reported accuracy among neural ODEs tested on this problem.

cs.LG↗

arXiv2020

Using Reinforcement Learning in the Algorithmic Trading Problem

The development of reinforced learning methods has extended application to many areas including algorithmic trading. In this paper trading on the stock exchange is interpreted into a game with a Markov property consisting of states, actions, and rewards. A system for trading the fixed volume of a financial instrument is proposed and experimentally tested; this is based on the asynchronous advantage actor-critic method with the use of several neural network architectures. The application of recurrent layers in this approach is investigated. The experiments were performed on real anonymized data. The best architecture demonstrated a trading strategy for the RTS Index futures (MOEX:RTSI) with a profitability of 66% per annum accounting for commission. The project source code is available via the following link: http://github.com/evgps/a3c_trading.

q-fin.TR↗

arXiv2020

Block Hankel Tensor ARIMA for Multiple Short Time Series Forecasting

This work proposes a novel approach for multiple time series forecasting. At first, multi-way delay embedding transform (MDT) is employed to represent time series as low-rank block Hankel tensors (BHT). Then, the higher-order tensors are projected to compressed core tensors by applying Tucker decomposition. At the same time, the generalized tensor Autoregressive Integrated Moving Average (ARIMA) is explicitly used on consecutive core tensors to predict future samples. In this manner, the proposed approach tactically incorporates the unique advantages of MDT tensorization (to exploit mutual correlations) and tensor ARIMA coupled with low-rank Tucker decomposition into a unified framework. This framework exploits the low-rank structure of block Hankel tensors in the embedded space and captures the intrinsic correlations among multiple TS, which thus can improve the forecasting results, especially for multiple short time series. Experiments conducted on three public datasets and two industrial datasets verify that the proposed BHT-ARIMA effectively improves forecasting accuracy and reduces computational cost compared with the state-of-the-art methods.

cs.LG↗