Generalized Multidimensional Scaling Research Articles

Deep convolutional neural network optimized with hybrid marine predator’s and nomadic people optimization for cardiac arrhythmia classification using ECG signals

Electrocardiogram (ECG) accounts are generally utilized for analyzing and figure cardiovascular arrhythmias for examining the heart ailment. In this situation, medical professionals may need to review the ECG records over a longer period of time to diagnose cardiac arrhythmias. Heart arrhythmia is a regular indication of cardiovascular arrhythmia. Several deep learning models have been suggested to classify the Cardiac Arrhythmia. But, the existing methods do not reach adequate efficiency and increase the computational time. To overcome these issues, deep convolutional neural network optimized with hybrid marine predators and nomadic people optimization for cardiac arrhythmia classification using electrocardiogram signals is proposed in this manuscript. The input data is pre-processed using anisotropic diffusion Kuwahara filtering (ADKF) for removing noise, error, blur and histogram noises. Then Term frequency-inverse document frequency (TF-IDF) based feature extraction is utilized for feature extraction. Afterward, the extracting features are given to the Weibull Distributive Generalized Multidimensional Scaling (WDGMS) feature selection for features selection. Thus, hybrid Marine Predator’s Algorithm (MPA) and Nomadic people optimizer (NPO) is employed for optimizing the DCNN weight parameters. The proposed Deep CNN-Hyb (MPA-NPO)-AC method is implemented in python. Thus the proposed Deep CNN-Hyb(MPA-NPO)-AC method attains 14.03 %, 22.30 % and 16.35 % lower error rate; 3.32 %, 4.27 %, 5.39 % and 2.05 % greater AUC compared with existing methods, like time-series augmented signals with deep learning (SVM-CA-ECG), Linearly Adaptive Sine–Cosine Algorithm along application in Deep Neural Network for Feature Optimization in Arrhythmia Categorization utilizing ECG Signals (DNN-CA-ECG) and Categorization of normal sinus rhythm, abnormal arrhythmia and congestive heart fault ECG signals under LSTM with hybrid CNN-SVM deep neural network (CNN-CA-ECG) respectively.

Ellipse fitting via low-rank generalized multidimensional scaling matrix recovery

This paper develops a novel ellipse fitting algorithm by recovering a low-rank generalized multidimensional scaling (GMDS) matrix. The main contributions of this paper are: i) Based on the derived Givens transform-like ellipse equation, we construct a GMDS matrix characterized by three unknown auxiliary parameters (UAPs), which are functions of several ellipse parameters; ii) Since the GMDS matrix will have low rank when the UAPs are correctly determined, its recovery and the estimation of UAPs are formulated as a rank minimization problem. We then apply the alternating direction method of multipliers as the solver; iii) By utilizing the fact that the noise subspace of the GMDS matrix is orthogonal to the corresponding manifold, we determine the remaining ellipse parameters by solving a specially designed least squares problem. Simulation and experimental results are presented to demonstrate the effectiveness of the proposed algorithm.

Towards Topological-Transformation Robust Shape Comparison: A Sparse Representation Based Manifold Embedding Approach

Non-rigid shape comparison based on manifold embeddingusing Generalized Multidimensional Scaling(GMDS) has attracted much attention for its highaccuracy. However, this method requires that shape surfaceis not elastic. In other words, it is sensitive totopological transformations such as stretching and compressing.To tackle this problem, we propose a new approachthat constructs a high-dimensional space to embedthe manifolds of shapes based on sparse representation,which is able to completely withstand rigid transformationsand considerably tolerate topological transformations.Experiments on TOSCA shapes validate theproposed approach.

Analysis of Two-Dimensional Non-Rigid Shapes

Analysis of deformable two-dimensional shapes is an important problem, encountered in numerous pattern recognition, computer vision and computer graphics applications. In this paper, we address three major problems in the analysis of non-rigid shapes: similarity, partial similarity, and correspondence. We present an axiomatic construction of similarity criteria for deformation-invariant shape comparison, based on intrinsic geometric properties of the shapes, and show that such criteria are related to the Gromov-Hausdorff distance. Next, we extend the problem of similarity computation to shapes which have similar parts but are dissimilar when considered as a whole, and present a construction of set-valued distances, based on the notion of Pareto optimality. Finally, we show that the correspondence between non-rigid shapes can be obtained as a byproduct of the non-rigid similarity problem. As a numerical framework, we use the generalized multidimensional scaling (GMDS) method, which is the numerical core of the three problems addressed in this paper.

The integration of multidimensional scaling and multivariate analysis with optimal transformations

The recent history of multidimensional data analysis suggests two distinct traditions that have developed along quite different lines. In multidimensional scaling (MDS), the available data typically describe the relationships among a set of objects in terms of similarity/dissimilarity (or (pseudo-)distances). In multivariate analysis (MVA), data usually result from observation on a collection of variables over a common set of objects. This paper starts from a very general multidimensional scaling task, defined on distances between objects derived from one or more sets of multivariate data. Particular special cases of the general problem, following familiar notions from MVA, will be discussed that encompass a variety of analysis techniques, including the possible use of optimal variable transformation. Throughout, it will be noted how certain data analysis approaches are equivalent to familiar MVA solutions when particular problem specifications are combined with particular distance approximations.

Multidimensional scaling models with inequality and equality constraints

Recently, a lot of attention has been brought to constrained estimation theory in multidimensional scaling models. So far, only equality constraints have been thoroughly studied. In this paper, the optimization theory is extended to general multidi-mensional scaling models with both inequality and equality constraints. A Newton-Raphson based algorithm is developed to produce the constrained least squares estimate. To illustrate the theory, some classical color data are reanalyzed in the context of the linear Euclidean distance model.

Functional relations in multidimensional scaling

Theory testing with multidimensional scaling models requires the ability to specify models with functional relations among parameters, to estimate the parameters of such models, and to compare the resulting models to models without functional constraints. The non‐linear optimization theory relevant to general multidimensional scaling models with functional relations is developed via first‐order necessary conditions. A Gauss‐Newton based algorithm is developed to implement the theory. The specific case of constraints to yield a circular configuration in the linear Euclidian distance model is studied in detail, and it is applied to some classical colour data.