A Review on Non Linear Dimensionality Reduction Techniques for Face Recognition

Principal component Analysis (PCA) has gained much attention among researchers to address the pboblem of high dimensional data sets.during last decade a non-linear variantof PCA has been used to reduce the dimensions on a non linear hyperplane.This paper reviews the various Non linear techniques ,applied on real and artificial data .It is observed that Non-Linear PCA outperform in the counterpart in most cases .However exceptions are noted

Enhancing Deep Learning Models through Tensorization: A Comprehensive Survey and Framework

The burgeoning growth of public domain data and the increasing complexity of deep learning model architectures have underscored the need for more efficient data representation and analysis techniques. This paper is motivated by the work of (Helal, 2023) and aims to present a comprehensive overview of tensorization. This transformative approach bridges the gap between the inherently multidimensional nature of data and the simplified 2-dimensional matrices commonly used in linear algebra-based machine learning algorithms. This paper explores the steps involved in tensorization, multidimensional data sources, various multiway analysis methods employed, and the benefits of these approaches. A small example of Blind Source Separation (BSS) is presented comparing 2-dimensional algorithms and a multiway algorithm in Python. Results indicate that multiway analysis is more expressive. Contrary to the intuition of the dimensionality curse, utilising multidimensional datasets in their native form and applying multiway analysis methods grounded in multilinear algebra reveal a profound capacity to capture intricate interrelationships among various dimensions while, surprisingly, reducing the number of model parameters and accelerating processing. A survey of the multi-away analysis methods and integration with various Deep Neural Networks models is presented using case studies in different application domains.Comment: 34 pages, 8 figures, 4 table

Registration of 3D Point Clouds and Meshes: A Survey From Rigid to Non-Rigid

Three-dimensional surface registration transforms multiple three-dimensional data sets into the same coordinate system so as to align overlapping components of these sets. Recent surveys have covered different aspects of either rigid or nonrigid registration, but seldom discuss them as a whole. Our study serves two purposes: 1) To give a comprehensive survey of both types of registration, focusing on three-dimensional point clouds and meshes and 2) to provide a better understanding of registration from the perspective of data fitting. Registration is closely related to data fitting in which it comprises three core interwoven components: model selection, correspondences and constraints, and optimization. Study of these components 1) provides a basis for comparison of the novelties of different techniques, 2) reveals the similarity of rigid and nonrigid registration in terms of problem representations, and 3) shows how overfitting arises in nonrigid registration and the reasons for increasing interest in intrinsic techniques. We further summarize some practical issues of registration which include initializations and evaluations, and discuss some of our own observations, insights and foreseeable research trends

Advanced Multilinear Data Analysis and Sparse Representation Approaches and Their Applications

Multifactor analysis plays an important role in data analysis since most real-world datasets usually exist with a combination of numerous factors. These factors are usually not independent but interdependent together. Thus, it is a mistake if a method only considers one aspect of the input data while ignoring the others. Although widely used, Multilinear PCA (MPCA), one of the leading multilinear analysis methods, still suffers from three major drawbacks. Firstly, it is very sensitive to outliers and noise and unable to cope with missing values. Secondly, since MPCA deals with huge multidimensional datasets, it is usually computationally expensive. Finally, it loses original local geometry structures due to the averaging process. This thesis sheds new light on the tensor decomposition problem via the ideas of fast low-rank approximation in random projection and tensor completion in compressed sensing. We propose a novel approach called Compressed Submanifold Multifactor Analysis (CSMA) to solve the three problems mentioned above. Our approach is able to deal with the problem of missing values and outliers via our proposed novel sparse Higher-order Singular Value Decomposition approach, named HOSVD-L1 decomposition. The Random Projection method is used to obtain the fast low-rank approximation of a given multifactor dataset. In addition, our method can preserve geometry of the original data. In the second part of this thesis, we present a novel pattern classification approach named Sparse Class-dependent Feature Analysis (SCFA), to connect the advantages of sparse representation in an overcomplete dictionary, with a powerful nonlinear classifier. The classifier is based on the estimation of class-specific optimal filters, by solving an L1-norm optimization problem using the Alternating Direction Method of Multipliers. Our method as well as its Reproducing Kernel Hilbert Space (RKHS) version is tolerant to the presence of noise and other variations in an image. Our proposed methods achieve very high classification accuracies in face recognition on two challenging face databases, i.e. the CMU Pose, Illumination and Expression (PIE) database and the Extended YALE-B that exhibit pose and illumination variations; and the AR database that has occluded images. In addition, they also exhibit robustness on other evaluation modalities, such as object classification on the Caltech101 database. Our method outperforms state-of-the-art methods on all these databases and hence they show their applicability to general computer vision and pattern recognition problems

Human Shape from Silhouettes Using Generative HKS Descriptors and Cross-Modal Neural Networks

In this work, we present a novel method for capturing human body shape from a single scaled silhouette. We combine deep correlated features capturing different 2D views, and embedding spaces based on 3D cues in a novel convolutional neural network (CNN) based architecture. We first train a CNN to find a richer body shape representation space from pose invariant 3D human shape descriptors. Then, we learn a mapping from silhouettes to this representation space, with the help of a novel architecture that exploits the correlation of multi-view data during training time, to improve prediction at test time. We extensively validate our results on synthetic and real data, demonstrating significant improvements in accuracy as compared to the state-of-the-art, and providing a practical system for detailed human body measurements from a single image