Subspace Classifier Research Articles

A stable mixed finite element method for nearly incompressible linear elastostatics

AbstractWe present a new, stable, mixed finite element (FE) method for linear elastostatics of nearly incompressible solids. The method is the automatic variationally stable FE method of Calo et al., in which we consider a Petrov–Galerkin weak formulation where the stress and displacement variables are in the space H(div) and H1, respectively. This allows us to employ a fully conforming FE discretization for any elastic solid using classical FE subspaces of H(div) and H1. Hence, the resulting FE approximation yields both continuous stresses and displacements. To ensure stability of the method, we employ the philosophy of the discontinuous Petrov–Galerkin method of Demkowicz and Gopalakrishnan and use optimal test spaces. Thus, the resulting FE discretization is stable even as the Poisson's ratio , and the system of linear algebraic equations is symmetric and positive definite. Our method also comes with a built‐in a posteriori error estimator as well as indicators which are used to drive mesh adaptive refinements. We present several numerical verifications of our method including comparisons to existing FE technologies.

Submodules in Polydomains and Noncommutative Varieties

Tensor product of Fock spaces is analogous to the Hardy space over the unit polydisc. This plays an important role in the development of noncommutative operator theory and function theory in the sense of noncommutative polydomains and noncommutative varieties. In this paper we study joint invariant subspaces of tensor product of full Fock spaces and noncommutative varieties. We also obtain, in particular, by using techniques of noncommutative varieties, a classification of joint invariant subspaces of n-fold tensor products of Drury–Arveson spaces.

Collaborative coding and dictionary learning for nearest subspace classification

Collaborative coding and dictionary learning for nearest subspace classification

Does Physical Activity Predict Obesity-A Machine Learning and Statistical Method-Based Analysis.

Background: Obesity prevalence has become one of the most prominent issues in global public health. Physical activity has been recognized as a key player in the obesity epidemic. Objectives: The objectives of this study are to (1) examine the relationship between physical activity and weight status and (2) assess the performance and predictive power of a set of popular machine learning and traditional statistical methods. Methods: National Health and Nutrition Examination Survey (NHANES, 2003 to 2006) data were used. A total of 7162 participants met our inclusion criteria (3682 males and 3480 females), with average age ranging from 48.6 (normal weight) to 52.1 years old (overweight). Eleven classifying algorithms—including logistic regression, naïve Bayes, Radial Basis Function (RBF), local k-nearest neighbors (k-NN), classification via regression (CVR), random subspace, decision table, multiobjective evolutionary fuzzy classifier, random tree, J48, and multilayer perceptron—were implemented and evaluated, and they were compared with traditional logistic regression model estimates. Results: With physical activity and basic demographic status, of all methods analyzed, the random subspace classifier algorithm achieved the highest overall accuracy and area under the receiver operating characteristic (ROC) curve (AUC). The duration of vigorous-intensity activity in one week and the duration of moderate-intensity activity in one week were important attributes. In general, most algorithms showed similar performance. Logistic regression was middle-ranking in terms of overall accuracy, sensitivity, specificity, and AUC among all methods. Conclusions: Physical activity was an important factor in predicting weight status, with gender, age, and race/ethnicity being less but still essential factors associated with weight outcomes. Tailored intervention policies and programs should target the differences rooted in these demographic factors to curb the increase in the prevalence of obesity and reduce disparities among sub-demographic populations.

Text classification based on the word subspace representation

In this paper, we propose a novel framework for text classification based on subspace-based methods. Recent studies showed the advantages of modeling texts as linear subspaces in a high-dimensional word vector space, to which we refer as word subspace. Therefore, we propose solving topic classification and sentiment analysis by using the word subspace along with different subspace-based methods. We explore the word embeddings geometry to decide which subspace-based method is more suitable for each task. We empirically demonstrate that a word subspace generated from sets of texts is a unique representation of a semantic topic that can be spanned by basis vectors derived from different texts. Therefore, texts can be classified by comparing their word subspace with the topic class subspaces. We achieve this framework by using the mutual subspace method that effectively handles multiple subspaces for classification. For sentiment analysis, as word embeddings do not necessarily consider sentiment information (i.e., opposite sentiment words have similar word vectors), we introduce the orthogonal mutual subspace method, to push opposite sentiment words apart. Furthermore, as there may be overlap between the sentiment class subspaces due to overlapping topics, we propose modeling a sentiment class by a set of multiple word subspaces, generated from each text belonging to the class. We further model the sentiment classes on a Grassmann manifold by using the Grassmann subspace method and its discriminative extension, the Grassmann orthogonal subspace method. We show the validity of each framework through experiments on four widely used datasets.

Krylov Subspace Methods for Regularized Models in Acoustic Temperature Reconstruction From Simulated and Real Measurements

In a microwave heating system, there is usually an anomaly like thermal runaway or local overheating due to the propagation characteristics of electromagnetic waves during the heating process. The anomalous situation can be coped with by analyzing the temperature information obtained from acoustic travel time tomography. The aim of the research is to investigate the possibility of applying the acoustic approach to microwave heating. When applying acoustic tomography, an ill-conditioned least-squares problem is formulated, and the problem is hard to solve for super bad condition numbers of the coefficient matrices. In computational mathematics, researchers make a lot of effort in developing Krylov subspace methods to solve ill-conditioned problems. Some existing methods show slow convergence for practical applications, which motivates us to improve one Krylov subspace method based on real cases. Our method can be treated as an application of heavy ball minimal residual (HBMR) method to regularized least-squares problems. Based on the data collected from a measurement platform that simulates the internal circumstance of the heating system, our method is compared with certain classical Krylov subspace methods from aspects of convergence rate, reconstruction accuracy, and anti-interference capacity. Numerical experiments demonstrate a significant improvement in convergence rate on our method for regularized ill-conditioned problems. In addition, we display how to select an optimal kernel function. Details of choosing the optimal parameter are shown as well.

Kaczmarz method for saddle point systems

The Kaczmarz method is presented for solving saddle point systems. The convergence is analyzed. Numerical examples, compared with classical Krylov subspace methods, SOR-like method (2001) and recent modified SOR-like method (2014), show that the Kaczmarz algorithm is efficient in convergence rate and CPU time.

Word Recognition using Embedded Prototype Subspace Classifiers on a New Imbalanced Dataset

This paper presents an approach towards word recognition based on embedded prototype subspace classification.The purpose of this paper is three-fold. Firstly, a new dataset for word recognition is presented, which is extractedfrom the Esposalles database consisting of the Barcelona cathedral marriage records. Secondly, different clusteringtechniques are evaluated for Embedded Prototype Subspace Classifiers. The dataset, containing 30 different classesof words is heavily imbalanced, and some word classes are very similar, which renders the classification task ratherchallenging. For ease of use, no stratified sampling is done in advance, and the impact of different data splits isevaluated for different clustering techniques. It will be demonstrated that the original clustering technique based onscaling the bandwidth has to be adjusted for this new dataset. Thirdly, an algorithm is therefore proposed that findskclusters, striving to obtain a certain amount of feature points in each cluster, rather than finding some clustersbased on scaling the Silverman’s rule of thumb. Furthermore, Self Organising Maps are also evaluated as both aclustering and embedding technique.

The N-Tuple Subspace Classifier: Extensions and Survey

This article is written in recognition of W. Bledsoe, who with Browning, introduced the N-tuple subspace classifier in 1959. This 1959 article was the first article to introduce subspace classifiers and the sum rule to combine the outputs of the classifiers. A mathematical notation is given to easily express in a precise and unambiguous way everything going on in the N-tuple subspace classifier. Extensions of the N-tuple method are discussed using a generalized product expression and we relate the generalization to graphical models. We discuss the sum rule, the product rule, and the plurality voting rule for combining the scores of the subspace classifiers. We selected a representative sample of papers that the 1959 N-tuple subspace classifier inspired. Some of the papers introduced specialized improvements. Many of the papers showed the value of the N-tuple subspace classifier in all kinds of applications and compared the results of one or more varieties of the N-tuple subspace classifier with other state-of-the-art classifiers. Their experiments showed that the N-tuple subspace classifier was competitive with the state-of-the-art classifiers and often had a higher accuracy. Finally, we highlight some papers that describe experiments of the N-tuple subspace classifier executing in a quantum computer.

PSubCLUS: A Parallel Subspace Clustering Algorithm Based On Spark

Clustering is one of the most important unsupervised machine learning tasks. It is widely used to solve problems of intrusion detection, text analysis, image segmentation etc. Subspace clustering is the most important method for high-dimensional data clustering. In order to solve the problem of parallel subspace clustering for high-dimensional big data, this paper proposes a parallel subspace clustering algorithm based on spark named PSubCLUS which is inspired by SubCLU, a classical subspace clustering algorithm. While Spark is the most popular big data parallel processing platform currently, PSubCLUS uses the Resilient Distributed Datasets (RDD) provided by Spark to store data points in a distributed way. The two main performing stages of this algorithm, one-dimensional subspace clustering and iterative clustering, can be executed in parallel on each worker node of cluster. PSubCLUS also uses a repartition method based on the number of data points to achieve load balancing. Experimental results show that PSubCLUS has good parallel speedup and ideal load balancing effect, which is suitable for solving the parallel subspace clustering of high-dimensional big data.

A novel acoustic scene classification model using the late fusion of convolutional neural networks and different ensemble classifiers

Recent evidence suggests that convolutional neural networks (CNNs) can model acoustic scene classification (ASC) with high accuracy. Ensemble classifiers have also shown high accuracy in different machine learning areas. However, little is known about fusion models between CNNs and different ensemble classifiers for ASC. This study presents an enhanced CNN classification model using the late fusion between CNNs and ensemble classifiers to predict different classes of acoustic scenes. A CNN model was first built to classify fifteen acoustic scene environments. Different ensemble classifier models were then used for this classification problem. Late fusion of CNN and ensemble classifier models was then applied. The results showed that late fusion models have higher classification accuracy, as compared to individual CNN or ensemble classifier models. The best model was obtained by fusion of the CNN and discriminant random subspace classifier with an increase in the average accuracy of 10% as compared to the average accuracy of the CNN model. When compared with previous research on ASC, the late fusion model between CNN and ensemble classifiers showed higher accuracy. Therefore, this method has robust applicability for future ASC problems.

Eigenstructure assignment in linear geometric control

The focus of this paper is the connection between two foundational areas of linear time-invariant (LTI) systems theory: geometric control and eigenstructure assignment. In particular, we study the properties of the null-spaces of the reachability matrix pencil and of the Rosenbrock system matrix, which have been extensively used as two computational building blocks for the calculation of pole placing state feedback matrices and pole placing friends of output-nulling subspaces. Our objective is to show that the subspaces in the chains of kernels obtained in the construction of these feedback matrices interact with each other in ways that are entirely independent from the choice of eigenvalues. So far, these chains of subspaces have only been studied in the case of stationarity. In this case, it is known that these chains converge to the classic Kalman reachable subspace ℛ for the reachability matrix pencil and to the largest reachability subspace ℛ⋆ in the case of the Rosenbrock matrix, respectively. Here we are interested in showing that even before stationarity has been reached, the partial chains are linked to structural properties of the system, and are therefore independent of the closed-loop eigenvalues that we wish to assign. We further characterize these subspaces by investigating the notion of largest subspace on which it is possible to assign the closed-loop spectrum (possibly maintaining the output at zero) without resorting to non-trivial Jordan forms.

Meromorphic Extensions of $$(\cdot , W)$$-Meromorphic Functions

In this paper we establish some classes of subspaces W of the dual $$F'$$ of a locally convex space F such that every F-valued (F, W)-meromorphic function (with/without local boundedness) on a domain D in $$\mathbb {C}^n,$$ in the sense $$u \circ f$$ is meromorphic for all $$u \in W,$$ is meromorphic. Further, combining those results with studing on (BB)-Zorn property we give conditions for Frechet spaces E, F and subspaces W of $$F'$$ under which (F, W)-meromorphic functions can be meromorphically extended to a domain D of E from a subset $$D \cap E_B$$ where $$E_B$$ is the linear hull of some balanced convex compact subset B of E. Using these results we get the answers of the following questions: (1) When does the domain of meromorphy of a $$(\cdot , W)$$ -meromorphic function on a Riemann domain D over a Frechet space coincide with the envelope of holomorphy of D? (2) When will $$(\cdot , W)$$ -meromorphic functions be able to extend meromorphically through an analytic subset of codimension $$\ge 2$$ of a domain in a Frechet space?

A Comparison Study of Subspace Identification of Blast Furnace Ironmaking Process

Blast Furnace (BF) iron making process is an extremely complex industrial process. The molten iron silicon content is considered as an important indicator of the thermal status of the blast furnace. The stabilization control of blast furnace depends on the molten iron silicon content. Three classic subspace identification methods including MOESP (Multivariable Output-Error State sPace), CVA (Canonical Variate Analysis) and SSARX (Subspace identification method ARX) are considered to establish the state space model of blast furnace ironmaking process. The inputs to the model are the most responsible and easily measured variables for the fluctuation of thermal state in blast furnace while the output to the model is the molten iron silicon content. The identified state space models are then tested on datasets obtained from No.1 BF in LiuGang Iron and Steel Group Co. of China. Experiment results show that the blast furnace ironmaking process can be reliably modeled by these subspace identification methods. Further, the SSARX method outperforms over the other two subspace identification methods with closed loop data.

A new subspace minimization conjugate gradient method based on modified secant equation for unconstrained optimization

In this paper, a new subspace minimization conjugate gradient method based on modified secant equation is proposed and analyzed. For a classical subspace minimization conjugate gradient method, the search direction is derived by minimizing an approximate quadratic model of objective function in a two-dimensional subspace. Generally, the approximate Hessian matrix in the above quadratic model is required to satisfy the standard secant equation, while we consider an approximate Hessian matrix which satisfies the modified secant equation. We give some rules such that if these rules are satisfied, we choose the standard secant equation, otherwise we choose the modified one. We can prove that the proposed directions satisfy the sufficient descent property under some extra conditions. We also present a modified nonmonotone Wolfe line search and establish the global convergence of the proposed method for general nonlinear functions under mild assumptions. Numerical comparisons are given with famous CG_DESCENT (5.3) (Hager and Zhang in SIAM J Optim 16(1):170–192, 2005) and SMCG_BB (Liu and Liu in J Optim Theory Appl 180(3):879–906, 2019), and show that the proposed algorithm is very promising.

Spatiotemporal analysis of deforestation in the Chapare region of Bolivia using LANDSAT images

AbstractThe purpose of this study is to quantify (a) spatiotemporal deforestation patterns, and (b) the relationships between changes in the main land‐cover types in the Chapare region of Bolivia. We applied subspace classification methods to LANDSAT data from 1986, 1999, and 2018 and used grid cells at scales of 150, 300, 600, and 900 m to measure deforestation trajectories. The 150 m grids provided better detail to determine deforestation trajectories than coarser‐scale grid cells. Differences in grid‐cell scale did not influence the statistical trends in land‐cover changes significantly. Changes in forest area were negatively correlated with changes in cropland (r = −.44), grassland (r = −.34), swamp grassland (r = −.38), and regrowth (r = −.32) areas. Correlations between forest losses in cropland, grassland, and regrowth change analyses were weaker between 1999 and 2018 compared to 1986 to 1999. Forest cover declined from 6,635 km2 (1986) to 3,800 km2 (2018), and the deforestation rate increased from an annual average of 1.36% between 1986 and 1999 to 2.0% between 1999 and 2018. The key proximate drivers of forest clearance rates and patterns were increasing population, agricultural expansion, and road building. While coca is an economically important crop in Chapare, its direct and indirect effects on deforestation could not be determined unambiguously. It is probable that the expansion of agriculture will lead to further deforestation and forest fragmentation and, along with decreases in forest cover, further changes will take place between non‐forest categories.

Numerical index of vector-valued function spaces

ABSTRACT In this paper, we study the relationship between numerical index of a Banach space E and the numerical index of a class of subspaces of , the space of all continuous E-valued functions defined on a compact Hausdorff topological space Ω. The subspaces considered, satisfy an invariance condition and a norm attaining condition proposed by J. Jamison. As a consequence, we prove that the numerical indices of several classes of vector-valued function spaces are less than or equal to the numerical index of the respective range spaces.

On the stability of projection-based model order reduction for convection-dominated laminar and turbulent flows

In the literature on nonlinear projection-based model order reduction for computational fluid dynamics problems, it is often claimed that due to modal truncation, a projection-based reduced-order model (PROM) does not resolve the dissipative regime of the turbulent energy cascade and therefore is numerically unstable. Efforts at addressing this claim have ranged from attempting to model the effects of the truncated modes to enriching the classical subspace of approximation in order to account for the truncated phenomena. The objective of this paper is to challenge this claim. Exploring the relationship between projection-based model order reduction and semi-discretization and using numerical evidence from three relevant flow problems, this paper argues in an orderly manner that the real culprit behind most if not all reported numerical instabilities of PROMs for turbulence and convection-dominated turbulent flow problems is the Galerkin framework that has been used for constructing the PROMs. The paper also shows that alternatively, a Petrov-Galerkin framework can be used to construct numerically stable and accurate PROMs for convection-dominated laminar as well as turbulent flow problems, without resorting to additional closure models or tailoring of the subspace of approximation. It also shows that such alternative PROMs deliver significant speed-up factors.

Invariant Subspace Classification and Exact Explicit Solutions to a Class of Nonlinear Wave Equation

In this paper, the invariant subspace classification of a class of nonlinear shallow water wave equation is given, then some exact explicit solutions to the nonlinear equation are provided by using the invariant subspace method. This method is a dynamical system method by nature, for its key step is to transform a nonlinear partial differential equation (PDE) into ordinary differential equation (ODE) systems, then by solving the ODE systems, the exact solutions to the nonlinear PDE are obtained.

Robust Subspace Clustering With Low-Rank Structure Constraint

In this paper, a novel low-rank structural model is proposed for segmenting data drawn from a high-dimensional space. Our method is based on the fact that all groups clustered from a high-dimensional dataset are distributed in multiple low-rank subspaces. In general, it’s a very difficult task to find the low-rank structures hidden in data. Different from the classical sparse subspace clustering (SSC) and low-rank representation (LRR) which all take two steps including building the affinity matrix and spectral clustering, we introduce a new rank constraint into our model. This constraint allows our model to learn a subspace indicator which can capture different clusters directly from the data without any postprocessing. To further approximate the rank constraint, a piecewise function is utilized as the relaxing item for the proposed model. Besides, under the subspace indicator constraints, the integer programming problem is avoided, which makes our algorithm more efficient and scalable. In addition, we prove the convergence of the proposed algorithm in theory and further discuss the general case in which subspaces don’t pass through the origin. Experiment results on both synthetic and real-world datasets demonstrate that our algorithm significantly outperforms the state-of-the-art methods.