Subspace Classifier Research Articles

The action of mapping class groups on de Rham quasimorphisms

We study the action of the mapping class group on the subspace of de Rham classes in the degree-two bounded cohomology of a hyperbolic surface. In particular, we show that the only fixed nontrivial finite-dimensional subspace is the one generated by the Euler class. As a consequence, we get that the action of the mapping class group on the space of de Rham quasimorphisms has no fixed points.

On affine spaces of rectangular matrices with constant rank

Let F be a field, and n≥p≥r>0 be integers. In a recent article, Rubei has determined, when F is the field of real numbers, the greatest possible dimension for an affine subspace of n–by–p matrices with entries in F in which all the elements have rank r. In this note, we generalize her result to an arbitrary field with more than r+1 elements, and we classify the spaces that reach the maximal dimension as a function of the classification of the affine subspaces of invertible matrices of Ms(F) with dimension (s2). The latter is known to be connected to the classification of nonisotropic quadratic forms over F up to congruence.

Invariant subspaces of analytic perturbations

Analytic perturbations are understood here as shifts of the form M z + F M_z + F , where M z M_z is the unilateral shift and F F is a finite rank operator on the Hardy space over the open unit disk. Here the term “a shift” refers to the multiplication operator M z M_z on some analytic reproducing kernel Hilbert space. In this paper, first, a natural class of finite rank operators is isolated for which the corresponding perturbations are analytic, and then a complete classification of invariant subspaces of those analytic perturbations is presented. Some instructive examples and several distinctive properties (like cyclicity, essential normality, hyponormality, etc.) of analytic perturbations are also described.

Sampling Error Analysis in Quantum Krylov Subspace Diagonalization

Quantum Krylov subspace diagonalization (QKSD) is an emerging method used in place of quantum phase estimation in the early fault-tolerant era, where limited quantum circuit depth is available. In contrast to the classical Krylov subspace diagonalization (KSD) or the Lanczos method, QKSD exploits the quantum computer to efficiently estimate the eigenvalues of large-size Hamiltonians through a faster Krylov projection. However, unlike classical KSD, which is solely concerned with machine precision, QKSD is inherently accompanied by errors originating from a finite number of samples. Moreover, due to difficulty establishing an artificial orthogonal basis, ill-conditioning problems are often encountered, rendering the solution vulnerable to noise. In this work, we present a nonasymptotic theoretical framework to assess the relationship between sampling noise and its effects on eigenvalues. We also propose an optimal solution to cope with large condition numbers by eliminating the ill-conditioned bases. Numerical simulations of the one-dimensional Hubbard model demonstrate that the error bound of finite samplings accurately predicts the experimental errors in well-conditioned regions.

Multi-scale superpixel-based nearest subspace classifier for mucilage detection from hyperspectral PRISMA data

Hyperspectral imaging has a critical role in observing the Earth's surface, providing images with rich spectral information. As a result, it has become an essential tool for monitoring and addressing environmental issues such as pollution, water balance, and climate change. Among these challenges, marine pollution poses a significant ecological threat, as evidenced by the recent mucilage incident in Turkey in April 2021. Mucilage, a dense mucus-like substance resulting from the overgrowth of marine plankton and microorganisms, detrimentally affects marine ecosystems when its levels surge. Traditional mucilage detection involves labour-intensive sampling and laboratory analysis, rendering it impractical for vast marine environments. Remote sensing techniques offer a promising alternative for automated mucilage detection from satellite imagery. In this study, we propose a multi-scale superpixel-based classification approach for mucilage detection, using the PRISMA satellite's hyperspectral mucilage datasets captured over the Sea of Marmara. Our method performs classification by analyzing the closeness between the subspace spanned by the samples in the superpixel and the subspace spanned by the within-class training samples. We formulate the solution to this approach via a Canonical Correlation Analysis framework and show that our proposed method outperforms its competitors, especially when the training data is limited. Our comprehensive experiments include assessing the transferability of classification methods on datasets collected from different locations and at different times. We compared the performance of our proposed method with state-of-the-art spectral-spatial classification methods, including deep learning-based random patches network (RPNet), structural-kernel collaborative representation (SKCR), and window based nearest subspace classifier (WBNSC). The results show that the proposed method outperforms existing techniques in most cases. The datasets and source code are publicly available on GitHub at https://github.com/kgtoker/MSBNSC, enabling more comprehensive access and collaboration in environmental monitoring efforts.

An adaptive kernel dictionary-based low-rank representation method for subspace clustering

Low-rank representation (LRR) is a classic subspace clustering (SC) algorithm, and many LRR-based methods have been proposed. Generally, LRR-based methods use denoized data as dictionaries for data reconstruction purpose. However, the dictionaries used in LRR-based algorithms are fixed, leading to poor clustering performance. In addition, most of these methods assume that the input data are linearly correlated. However, in practice, data are mostly nonlinearly correlated. To address these problems, we propose a novel adaptive kernel dictionary-based LRR (AKDLRR) method for SC. Specifically, to explore nonlinear information, the given data are mapped to the Hilbert space via the kernel technique. The dictionary in AKDLRR is not fixed; it adaptively learns from the data in the kernel space, making AKDLRR robust to noise and yielding good clustering performance. To solve the AKDLRR model, an efficient procedure including an alternative optimization strategy is proposed. In addition, a theoretical analysis of the convergence performance of AKDLRR is presented, which reveals that AKDLRR can converge in at most three iterations under certain conditions. The experimental results show that AKDLRR can achieve the best clustering performance and has excellent speed in comparison with other algorithms.

Semi-supervised urban haze pollution prediction based on multi-source heterogeneous data

Particulate matter (PM) is defined by the Texas Commission on Environmental Quality (TCEQ) as “a mixture of solid particles and liquid droplets found in the air”. These particles vary widely in size. Those particles that are less than 2.5 μm in aerodynamic diameter are known as Particulate Matter 2.5 or PM2.5. Urban haze pollution represented by PM2.5 is becoming serious, so air pollution monitoring is very important. However, due to high cost, the number of air monitoring stations is limited. Our work focuses on integrating multi-source heterogeneous data of Nanchang, China, which includes Taxi track, human mobility, Road networks, Points of Interest (POIs), Meteorology (e.g., temperature, dew point, humidity, wind speed, wind direction, atmospheric pressure, weather activity, weather conditions) and PM2.5 forecast data of air monitoring stations. This research presents an innovative approach to air quality prediction by integrating the above data sets from various sources and utilizing diverse architectures in Nanchang City, China. So for that, semi-supervised learning techniques will be used, namely collaborative training algorithm Co-Training (Co-T), who further adjusting algorithm Tri-Training (Tri-T). The objective is to accurately estimate haze pollution by integrating and using these multi-source heterogeneous data. We achieved this for the first time by employing a semi-supervised co-training strategy to accurately estimate pollution levels after applying the U-air system to environmental data. In particular, the algorithm of U-Air system is reproduced on these highly diverse heterogeneous data of Nanchang City, and the semi-supervised learning Co-T and Tri-T are used to conduct more detailed urban haze pollution prediction. Compared with Co-T, which train time classifier (TC) and subspace classifier (SC) respectively from the separated spatio-temporal perspective, the Tri-T is more accurate with a and faster because of its testing accuracy up to 85.62 %. The forecast results also present the potential of the city multi-source heterogeneous data and the effectiveness of the semi-supervised learning. We hope that this synthesis will motivate atmospheric environmental officials, scientists, and environmentalists in China to explore machine learning technology for controlling the discharge of pollutants and environmental management.

Synthetic unknown class learning for learning unknowns

This paper addresses the open set recognition (OSR) problem, where the goal is to correctly classify samples of known classes while detecting unknown samples to reject. In the OSR problem, “unknown” is assumed to have infinite possibilities because we have no knowledge about unknowns until they emerge. Intuitively, the more an OSR system explores the possibilities of unknowns, the more likely it is to detect unknowns. Even though several generative OSR models have been proposed to explore more by generating synthetic samples and learning them as unknowns, the generated samples are limited to a small subspace of the known classes. Thus, this paper proposes a novel synthetic unknown class learning method that constantly generates unknown-like samples while maintaining diversity between the generated samples. By learning the unknown-like samples and known samples in an alternating manner, the proposed method can not only experience diverse synthetic unknowns but also reduce overgeneralization with respect to known classes. Experiments on several benchmark datasets show that the proposed method significantly outperforms other state-of-the-art approaches by generating diverse realistic unknown samples.

Automatic Estimation of the Interference Subspace Dimension Threshold in the Subspace Projection Algorithms of Magnetoencephalography Based on Evoked State Data.

A class of algorithms based on subspace projection is widely used in the denoising of magnetoencephalography (MEG) signals. Setting the dimension of the interference (external) subspace matrix of these algorithms is the key to balancing the denoising effect and the degree of signal distortion. However, most current methods for estimating the dimension threshold rely on experience, such as observing the signal waveforms and spectrum, which may render the results too subjective and lacking in quantitative accuracy. Therefore, this study proposes a method to automatically estimate a suitable threshold. Time-frequency transformations are performed on the evoked state data to obtain the neural signal of interest and the noise signal in a specific time-frequency band, which are then used to construct the objective function describing the degree of noise suppression and signal distortion. The optimal value of the threshold in the selected range is obtained using the weighted-sum method. Our method was tested on two classical subspace projection algorithms using simulation and two sensory stimulation experiments. The thresholds estimated by the proposed method enabled the algorithms to achieve the best waveform recovery and source location error. Therefore, the threshold selected in this method enables subspace projection algorithms to achieve the best balance between noise removal and neural signal preservation in subsequent MEG analyses.

Cross-Domain Discriminative Subspace Classification Algorithm for Review Text Sentiment Recognition Oriented E-Commerce Platforms

Cross-Domain Discriminative Subspace Classification Algorithm for Review Text Sentiment Recognition Oriented E-Commerce Platforms

Direction of Arrival Estimation with Nested Arrays in Presence of Impulsive Noise: A Correlation Entropy-Based Infinite Norm Strategy

Direction of arrival (DOA) estimation with nested arrays has been widely investigated in the field of array signal processing, but most studies assume that the noise is Gaussian white noise. In practical situations, there may exist impulsive noise (a kind of heavy-tailed noise), wherein the performance of traditional subspace-based DOA estimation algorithms deteriorates significantly. In this paper, we propose a correlation entropy-based infinite norm preprocessing algorithm, which can be applicable to any type of impulsive noise. Each snapshot of the sensor array data is processed by an exponential kernel function with the infinite norm, which can effectively combat the outliers. Furthermore, we construct the equivalent second-order covariance matrix and perform DOA estimation using classical subspace methods. Simulation results demonstrate the effectiveness of the proposed method for both symmetric α-stable distribution and the Gaussian mixture model.

An accelerated deflation preconditioner for acoustic BEM systems based on subspace recycling

Following a classic Krylov subspace recycling [1] technique in the context of frequency sweep analyses performed with the acoustic BEM [2] might inflict unnecessary overhead costs. To speed up such a procedure, this work employs an accelerated recycling technique that is based on the recently proposed model order reduction framework for BEM systems [3]. Specifically, employing an affine approximation of a BEM system in combination with a Galerkin projection on the deflation basis, the operation of constructing the corresponding deflation based preconditioner is significantly accelerated. The efficiency of the deflation basis for the entire frequency range is guaranteed through an Automatic Krylov subspace Recycling (AKR) [4] algorithm, thus leading to a drastic decrease of the number of iterations required by an iterative solver. The proposed approach is tested on an academic BEM example and achieves significant acceleration of the computed frequency sweep by ensuring fast convergence of the employed iterative solver, avoiding overhead projection costs.

An Improved Two-Stage Spherical Harmonic ESPRIT-Type Algorithm

Sensor arrays are gradually becoming a current research hotspot due to their flexible beam control, high signal gain, robustness against extreme interference, and high spatial resolution. Among them, spherical microphone arrays with complex rotational symmetry can capture more sound field information than planar arrays and can convert the collected multiple speech signals into the spherical harmonic domain for processing through spherical modal decomposition. The subspace class direction of arrival (DOA) estimation algorithm is sensitive to noise and reverberation, and its performance can be improved by introducing relative sound pressure and frequency-smoothing techniques. The introduction of the relative sound pressure can increase the difference between the eigenvalues corresponding to the signal subspace and the noise subspace, which is helpful to estimate the number of active sound sources. The eigenbeam estimation of signal parameters via the rotational invariance technique (EB-ESPRIT) is a well-known subspace-based algorithm for a spherical microphone array. The EB-ESPRIT cannot estimate the DOA when the elevation angle approaches 90°. Huang et al. proposed a two-step ESPRIT (TS-ESPRIT) algorithm to solve this problem. The TS-ESPRIT algorithm estimates the elevation and azimuth angles of the signal independently, so there is a problem with DOA parameter pairing. In this paper, the DOA parameter pairing problem of the TS-ESPRIT algorithm is solved by introducing generalized eigenvalue decomposition without increasing the computation of the algorithm. At the same time, the estimation of the elevation angle is given by the arctan function, which increases the estimation accuracy of the elevation angle of the algorithm. The robustness of the algorithm in a noisy environment is also enhanced by introducing the relative sound pressure into the algorithm. Finally, the simulation and field-testing results show that the proposed method not only solves the problem of DOA parameter pairing, but also outperforms the traditional methods in DOA estimation accuracy.

Representations of fricatives in subcortical model responses: Comparisons with human consonant perception.

Fricatives are obstruent sound contrasts made by airflow constrictions in the vocal tract that produce turbulence across the constriction or at a site downstream from the constriction. Fricatives exhibit significant intra/intersubject and contextual variability. Yet, fricatives are perceived with high accuracy. The current study investigated modeled neural responses to fricatives in the auditory nerve (AN) and inferior colliculus (IC) with the hypothesis that response profiles across populations of neurons provide robust correlates to consonant perception. Stimuli were 270 intervocalic fricatives (10 speakers × 9 fricatives × 3 utterances). Computational model response profiles had characteristic frequencies that were log-spaced from 125 Hz to 8 or 20 kHz to explore the impact of high-frequency responses. Confusion matrices generated by k-nearest-neighbor subspace classifiers were based on the profiles of average rates across characteristic frequencies as feature vectors. Model confusion matrices were compared with published behavioral data. The modeled AN and IC neural responses provided better predictions of behavioral accuracy than the stimulus spectra, and IC showed better accuracy than AN. Behavioral fricative accuracy was explained by modeled neural response profiles, whereas confusions were only partially explained. Extended frequencies improved accuracy based on the model IC, corroborating the importance of extended high frequencies in speech perception.

New Constant Dimension Subspace Codes From the Mixed Dimension Construction

One of the main problems of subspace coding is to determine the maximal size of a constant dimension subspace code with given parameters. In this paper, we show that mixed dimension subspace codes can be used to construct large constant dimension subspace codes. We introduce a new class of subspace codes called mixed dimension/distance subspace codes. Using such codes, we present two constructions for large constant dimension subspace codes. The problem about the sizes of our constant dimension subspace codes is transformed into finding mixed dimension/distance subspace codes with large dimension distributions. The new constructed codes are the largest known for many sets of parameters. Our method gives at least 136 new lower bounds on the sizes of constant dimension subspace codes.

Koopman Operator Based Predictive Control With a Data Archive of Observables

Abstract The control of complex systems is often challenging due to high-dimensional nonlinear models, unmodeled phenomena, and parameter uncertainty. The increasing ubiquity of sensors measuring such systems and increased computational resources has led to an interest in purely data-driven control methods, particularly using the Koopman operator. In this paper, we elucidate the construction of a linear predictor based on a sequence of time realizations of observables drawn from a data archive of different trajectories combined with subspace identification methods for linear systems. This approach is free of any predefined set of basis functions but instead depends on the time realization of these basis functions. The prediction and control are demonstrated with examples. The basis functions can be constructed using time-delayed coordinates of the outputs, enabling the application to purely data-driven systems. The paper thus shows the link between Koopman operator-based control methods and classical subspace identification methods. The approach in this paper can be extended to adaptive online learning and control.

Iterative solution of spatial network models by subspace decomposition

We present and analyze a preconditioned conjugate gradient method (PCG) for solving spatial network problems. Primarily, we consider diffusion and structural mechanics simulations for fiber based materials, but the methodology can be applied to a wide range of models, fulfilling a set of abstract assumptions. The proposed method builds on a classical subspace decomposition into a coarse subspace, realized as the restriction of a finite element space to the nodes of the spatial network, and localized subspaces with support on mesh stars. The main contribution of this work is the convergence analysis of the proposed method. The analysis translates results from finite element theory, including interpolation bounds, to the spatial network setting. A convergence rate of the PCG algorithm, only depending on global bounds of the operator and homogeneity, connectivity and locality constants of the network, is established. The theoretical results are confirmed by several numerical experiments.

INFORMATION SPACE

The purpose. To investigate the concept of information space, to identify its types, to analyze its components, to study the mechanisms of formation of information spaces in modern conditions. Methods. The concept of both information and space, as well as their combination, is studied. The most common uses of the term "information space" in Ukrainian-language and English-language sources are identified. The mutual circulation of information both in real life and in the telecommunications space is studied. The mechanisms of formation of the individual's information space are studied. The concepts of "information space of the state" and "national information space" are considered, and their comparison is given. Results. The composition of the information space is clarified, objects – sources of information and transmission channels-are studied. For information sources, their hierarchy is given. Attention is paid to mass media and the subject of their functioning. The classification of mass media, their functions and features as social institutions are studied. The factors that influence the formation of an individual's information space are highlighted. The definition of the individual's information space is given. Examples of integrated information spaces and examples of disintegration of information spaces are given. Scientific novelty. The factors that influence the formation of an individual's information space are highlighted. The definition of mass media in a broad sense has been clarified. It is established that the basis of an individual's information space on the Internet is his personal social network, namely, the web PSN. A key factor in the formation of the individual's information space in our time is highlighted. The factors that encourage an individual to adjust their own information space are studied. Classification of subspaces of the individual's information space is given. Practical significance. The concept of information space is multi-valued and multifaceted. Identifying the components of the information space and its parameters, the relative location of existing information spaces and their place in the global information space will contribute to solving many practical tasks – from business tasks to conducting political information campaigns (influence on the electorate before elections - for example). For example, this will help improve targeting, and therefore create better targeted advertising. For the average user, the described mechanism for creating a personal information space, factors that affect the formation of the information space and its correction, is important. Knowing the above, the individual will create a more optimal and high-quality personal social network, as well as an information space based on it.

Semi-supervised classifier ensemble model for high-dimensional data

To complete the challenging task of high-dimensional data classification with limited labeled samples, we propose two semi-supervised learning models, namely the random subspace classifier ensemble model (SSRS) and its adaptive version (ASSRS). Considering the unique characteristics of high-dimensional data, SSRS selects subspaces of sample and feature dimensions and then reduces the dimensions of each subspace. To improve SSRS performance further, we designed a sample-labeling auxiliary algorithm, adaptive sample subspace algorithm, and adaptive weight voting rule for ASSRS to increase the proportion of labeled samples, obtain a suitable sample subspace for each feature subspace, and acquire a relative optimal weight for each base classifier. Experiments revealed that the performances of SSRS and ASSRS were better than those of other competitive algorithms and that the performance of ASSRS was stronger than that of SSRS. Additionally, we can accurately label samples in datasets where the proportion of labeled samples is relatively low by using SSRS and ASSRS. Because analysts are facing large numbers of high-dimensional datasets with limited labels, it is important to make accurate predictions based on a limited proportion of labeled data.

Fuzzy-Affine-Model-Based Filtering Design for Continuous-Time Roesser-Type 2-D Nonlinear Systems.

This article tackles the problem of filtering design for continuous-time Roesser-type 2-D nonlinear systems via Takagi-Sugeno (T-S) fuzzy affine models. The aim is to design an admissible piecewise affine (PWA) filter such that the filtering error system is asymptotically stable with a prescribed disturbance attenuation level. First, 2-D Roesser nonlinear systems are approximated by a kind of 2-D fuzzy affine models with norm-bounded uncertainties. Then, the premise variable space of the 2-D fuzzy affine systems is partitioned into two classes of subspaces, that is: 1) crisp regions and 2) fuzzy regions. For each region, boundary continuity matrices and characterizing matrices are constructed by utilizing the space partition information and 2-D structure. After that, novel piecewise Lyapunov functions are constructed, based on which together with S-procedure, the asymptotic stability with performance is guaranteed for the filtering error system. By the projection lemma and some elegant convexification techniques, the PWA filtering design conditions are obtained. Finally, the less conservativeness and effectiveness of the proposed approach over a common Lyapunov function-based one are illustrated by simulation studies.