Nonlinear Optimization And Dimensional Reduction Via Spearman Correlation Analysis

During the era of Industry 4.0,the industrial computer vision and its related applications are getting success and popularity day by day.It also plays a vital role in the enhancement of computer vision algorithms due to the increment of multimedia data dimensions and algorithm complexity.This study introduces multiple models in which,introduced state-of-the-art Spearman correlation analysis algorithm(Canonical correlation analysis with Rank),and its algebraic extensions along with deep learning models is proposed.Further,most of these models are inspired by the transfer learning approach.These models introduces for the Non-linear multi-dimensional datasets.The multi-dimensional data and its correspondence applications face multiple challenges due to the nonlinearity of data.The proposed models present the solution of nonlinear optimization,complexity's issues,and dimensional reduction with implementations on problems related datasets.Further,the presented study sub-divided into three parts.First,I have introduced the Kernel extensions of Spearman correlation algorithms relates to the nonlinear issues of multidimensional datasets from one-dimensional Spearman correlation to extended two-dimensional Spearman correlation algorithm then it lead into further extension as three-dimensional Spearman correlation analysis and so on.Additionally,the implementations of these three extensions of Spearman correlation algorithms into models with transfer learning approaches are presented as well.Then,second part presents Spearman correlation algorithms lead to further extension and used into proposed model that is associated with informative projection and multi-view nonlinearity issues of multi-dimensional dataset.In the last,the presented Spearman correlation algorithms is extended and used in proposed model that models solve the image resolution nonlinearity between data and its challenges.The details of each parts' description are presented below.The first part is based on extensions of Spearman Correlation Analysis from classical onedimensional Spearman correlation to two-dimensional Spearman correlation and lead to threedimensional Spearman correlation respectively to address data driven processing through multiple proposed models to solve nonlinear optimizations and dimensionality reduction in multidimensional data with transfer learning approach.Further,dealing with multi-dimensional multimedia datasets using traditional algorithms,to date,researchers have been facing limitations and challenges because mostly sub-space learning algorithms and their developments cannot perform satisfactorily most of the time due to linear and non-linear data dependency.The proposed extensions based models directly finds the relations between two sets of multi-dimensional dataset without converting the data into required matrices such as 2D-matrices or corresponding visual feature vectors.Besides,it dramatically reduces the multi-dimensional reduction and computational algorithm complexity.The proposed models also present the extracted information and translate it into computational decisions as well with multiple data driven approach.To do so,the introduced extensions of Spearman correlation are presented into three models.First,introduces classical one-dimensional Spearman correlation analysis with transfer learning approach on multi-dimensional data.The model is employed with transfer learning strategy as,first all data inputs videos is segmented into frames for extraction of the deep visual features from deep learning model “Inception-V3” then the presented model is used one-dimensional Spearman correlation analysis for pairwise-correlation analysis among the overlapped videos' deep visual features.In the end,cosine distance matric is applied for linear similar background and modelling.This model detects and gives correlated analytics between casual and temporal regional activities on the basis of similarities and primary dissimilarities in the same scene captured by multipleoverlapping cameras.Additionally,six popular multi-dimensional datasets those features are different to each other's are also evaluated and process for data driven through classical Spearman correlation based model.I have introduced an algorithm as two-dimensional Spearman correlation analysis;the present algorithm is the second extension of previous presented classical Spearman correlation analysis through algebraic solution for multivariate two-dimensional monotonic(linear or non-linear)multi-media datasets.In a way,two different images with nonlinearity challenges like different dimensions are processed with correspondence techniques such as reshaping images into 1D or vectors.The implementation of proposed algorithm performs on four remarkable dataset along with fifth cross-dataset of all four datasets.Further,one-dimensional,and two-dimensional Spearman correlation analysis lead to threedimensional Spearman correlation analysis algorithm and used in to state of the art proposed model “Deep Three Dimensional Spearman Correlation Analysis(D3D-SCA)”.Three components are employed in the proposed D3D-SCA model:(1)customized deep learning model(Inception_V3)for deep feature mapping,(2)proposed three-dimensional Spearman correlation analysis for comparing pairwise deep features directly without singular matrix,spatial dilemma and conversion problem,and(3)the customized Xception classifier with automatic online updating ability and adjustable neural architecture for low latency mobile-computing models.The motivation of the proposed model is to advance the scalability of existing computer vision applications based on image-to-videos' recognition,detection,and re-identification approaches.Extensive findings on datasets named “3D Objects on turntable and Caltech 101” demonstrate the effectiveness of the proposed model.The second part of the study presents a model and introduces an algorithm for multidimensional informative projection or multi-view of variables via Spearman correlation analysis(SCA)with deep learning model as “Multi-Dimension projection for non-linear data via Spearman correlation analysis(MD-SCA)”.The proposed algorithm is an extension of Spearman correlation analysis to extract linear or nonlinear information of projections through pairwise correlation analysis.These multi-dimensional informative projections are used as informative patterns in pattern recognition applications.The proposed algorithm extends SCA through linear algebraic solution for the optimization problem,the problem of dual representation of high multidimensional data,and structural dilemma issues along with deep learning model.Additionally,the proposed model decreases the quadratic algorithm complexity among linear and non-linear data through Spearman rank ability.The demonstration of the proposed approach performs on twobench mark data sets: Face96 and Yale Face Database.The third part of the study presents a model as Deep Spearman correlation analysis(DSCA)for image super resolutions' related application.As for projection methods,linear subspace learning algorithms and multi-subspace learning algorithms are significantly popular.However,they have some limitations and crucial issues during the processing of multi-dimensional or nonlinear data that usually decreases the recognition rate of non-linear correlation among the lowresolution images to high-resolution images because of dimensions variation and illusion in the data.Besides,it creates challenges for recognitions related applications.The objective of the proposed model is to sort out non-linear resolution issues in computer vision applications.This model introduces an algorithmic-based approach named deep Spearman correlation analysis that implements on two datasets as “ReId vehicle license number plate dataset” and “MNIST handwriting dataset” to solve non-linearity between 2D-matrices of high-resolution and lowresolution images and shows the correlation among them.It contains three components:(1)proposed well-trained Deep Convolutional Neural Network(DCNN)used to extract deep feature maps for matching the informative projection,(2)introduced extension of regularized Spearman correlation analysis algorithm for matching the information projection between LR to HR images,and(3)the Radial basis function network(RBFN)used for mapping of correlational features from low resolution input features to relatively high resolution prototype features.In the end,it leads pattern recognition tasks such as recognition detection and classification by customized Xception classifiers.