Speed-up and multi-view extensions to subclass discriminant analysis

Highlights • We present a speed-up extension to Subclass Discriminant Analysis. • We propose an extension to SDA for multi-view problems and a fast solution to it. • The proposed approaches result in lower training time and competitive performance.In this paper, we propose a speed-up approach for subclass discriminant analysis and formulate a novel efficient multi-view solution to it. The speed-up approach is developed based on graph embedding and spectral regression approaches that involve eigendecomposition of the corresponding Laplacian matrix and regression to its eigenvectors. We show that by exploiting the structure of the between-class Laplacian matrix, the eigendecomposition step can be substituted with a much faster process. Furthermore, we formulate a novel criterion for multi-view subclass discriminant analysis and show that an efficient solution to it can be obtained in a similar manner to the single-view case. We evaluate the proposed methods on nine single-view and nine multi-view datasets and compare them with related existing approaches. Experimental results show that the proposed solutions achieve competitive performance, often outperforming the existing methods. At the same time, they significantly decrease the training time

Method for determining the thermal fluctuation constants of the generalized Zhurkov equation

Reliable forecasting of the service life of building materials and products allows you to lay down the costs of repair work in a timely manner, which in modern economic realities is undoubtedly an urgent task. This paper presents the results of a study on the development and comparison with existing methods for determining the thermal fluctuation constants of the generalized Zhurkov equation. A new method is proposed for determining the thermal fluctuation constants of the generalized Zhurkov equation. Practical application of the methodology will make it possible to reliably predict the service life of building materials. The main goal is to develop a method for determining the thermal fluctuation constants of the generalized Zhurkov equation, characterized by higher reliability by reducing the number of operations entailing errors, while increasing the number of experiments conducted under identical conditions (increasing the sample when determining durability under constant operating conditions). To achieve this goal, it is necessary to solve a number of tasks: 1) analyze the main provisions of the thermal fluctuation concept; 2) develop a method for determining the thermal fluctuation constants; 3) to conduct a comparative analysis of the obtained results of determining the thermal fluctuation constants. The object of the study is the constants of thermal fluctuation. The subject of the study is a new method for determining thermal fluctuation constants. The main methods of scientific knowledge used in the development of the methodology are hypothetical (the hypothesis of a linear dependence of the change slope of direct temperatures in the coordinates of the logarithm of durability - stress) and experiment (determination of durability of samples under transverse bending under specified operating conditions). A new method was developed for determining the thermal fluctuation constants of the generalized Zhurkov equation. It allows you to determine constants by plotting only one straight line temperature and one control point at a different temperature. Application of the proposed technique allows increasing the number of samples tested in identical conditions while reducing labor costs for experimental research. An increase in the sample leads to an increase in the accuracy and reliability of predicting the service life of building materials

Self-attention fusion for audiovisual emotion recognition with incomplete data

In this paper, we consider the problem of multi-modal data analysis with a use case of audiovisual emotion recognition. We propose an architecture capable of learning from raw data and describe three variants of it with distinct modality fusion mechanisms. While most of the previous works consider the ideal scenario of presence of both modalities at all times during inference, we evaluate the robustness of the model in the unconstrained settings where one modality is absent or noisy, and propose a method to mitigate these limitations in a form of modality dropout. Most importantly, we find that following this approach not only improves performance drastically under the absence/noisy representations of one modality, but also improves the performance in a standard ideal setting, outperforming the competing methods.acceptedVersionPeer reviewe

Revisiting Classical Multiclass Linear Discriminant Analysis with a Novel Prototype-based Interpretable Solution

Linear discriminant analysis (LDA) is a fundamental method for feature extraction and dimensionality reduction. Despite having many variants, classical LDA has its own importance, as it is a keystone in human knowledge about statistical pattern recognition. For a dataset containing C clusters, the classical solution to LDA extracts at most C-1 features. Here, we introduce a novel solution to classical LDA, called LDA++, that yields C features, each interpretable as measuring similarity to one cluster. This novel solution bridges dimensionality reduction and multiclass classification. Specifically, we prove that, for homoscedastic Gaussian data and under some mild conditions, the optimal weights of a linear multiclass classifier also make an optimal solution to LDA. In addition, we show that LDA++ reveals some important new facts about LDA that remarkably changes our understanding of classical multiclass LDA after 75 years of its introduction. We provide a complete numerical solution for LDA++ for the cases 1) when the scatter matrices can be constructed explicitly, 2) when constructing the scatter matrices is infeasible, and 3) the kernel extension

Multi-view Subspace Learning for Large-Scale Multi-Modal Data Analysis

Dimensionality reduction methods play a big role within the modern machine learning techniques, and subspace learning is one of the common approaches to it. Although various methods have been proposed over the past years, many of them suffer from limitations related to the unimodality assumptions on the data and low speed in the cases of high-dimensional data (in linear formulations) or large datasets (in kernel-based formulations). In this work, several methods for overcoming these limitations are proposed. In this thesis, the problem of the large-scale multi-modal data analysis for single- and multi-view data is discussed, and several extensions for Subclass Discriminant Analysis (SDA) are proposed. First, a Spectral Regression Subclass Discriminant Analysis method relying on the Graph Embedding-based formulation of SDA is proposed as a way to reduce the training time, and it is shown how the solution can be obtained efficiently, therefore reducing the computational requirements. Secondly, a novel multi-view formulation for Subclass Discriminant Analysis is proposed, allowing to extend it to data coming from multiple views. Besides, a speed-up approach for the multi-view formulation that allows reducing the computational requirements of the method is proposed. Linear and nonlinear kernel-based formulations are proposed for all the extensions. Experiments are performed on nine single-view and nine multi-view datasets and the accuracy and speed of the proposed extensions are evaluated. Experimentally it is shown that the proposed approaches result in a significant reduction of the training time while providing competitive performance, as compared to other subspace-learning based methods