A comparative study on face recognition techniques and neural network

In modern times, face recognition has become one of the key aspects of computer vision. There are at least two reasons for this trend; the first is the commercial and law enforcement applications, and the second is the availability of feasible technologies after years of research. Due to the very nature of the problem, computer scientists, neuro-scientists and psychologists all share a keen interest in this field. In plain words, it is a computer application for automatically identifying a person from a still image or video frame. One of the ways to accomplish this is by comparing selected features from the image and a facial database. There are hundreds if not thousand factors associated with this. In this paper some of the most common techniques available including applications of neural network in facial recognition are studied and compared with respect to their performance.Comment: 8 page

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Rigorous optimisation of multilinear discriminant analysis with Tucker and PARAFAC structures

Abstract Background We propose rigorously optimised supervised feature extraction methods for multilinear data based on Multilinear Discriminant Analysis (MDA) and demonstrate their usage on Electroencephalography (EEG) and simulated data. While existing MDA methods use heuristic optimisation procedures based on an ambiguous Tucker structure, we propose a rigorous approach via optimisation on the cross-product of Stiefel manifolds. We also introduce MDA methods with the PARAFAC structure. We compare the proposed approaches to existing MDA methods and unsupervised multilinear decompositions. Results We find that manifold optimisation substantially improves MDA objective functions relative to existing methods and on simulated data in general improve classification performance. However, we find similar classification performance when applied to the electroencephalography data. Furthermore, supervised approaches substantially outperform unsupervised mulitilinear methods whereas methods with the PARAFAC structure perform similarly to those with Tucker structures. Notably, despite applying the MDA procedures to raw Brain-Computer Interface data, their performances are on par with results employing ample pre-processing and they extract discriminatory patterns similar to the brain activity known to be elicited in the investigated EEG paradigms. Conclusion The proposed usage of manifold optimisation constitutes the first rigorous and monotonous optimisation approach for MDA methods and allows for MDA with the PARAFAC structure. Our results show that MDA methods applied to raw EEG data can extract discriminatory patterns when compared to traditional unsupervised multilinear feature extraction approaches, whereas the proposed PARAFAC structured MDA models provide meaningful patterns of activity

Non-Negative Tensor Factorization Applied to Music Genre Classification

Music genre classification techniques are typically applied to the data matrix whose columns are the feature vectors extracted from music recordings. In this paper, a feature vector is extracted using a texture window of one sec, which enables the representation of any 30 sec long music recording as a time sequence of feature vectors, thus yielding a feature matrix. Consequently, by stacking the feature matrices associated to any dataset recordings, a tensor is created, a fact which necessitates studying music genre classification using tensors. First, a novel algorithm for non-negative tensor factorization (NTF) is derived that extends the non-negative matrix factorization. Several variants of the NTF algorithm emerge by employing different cost functions from the class of Bregman divergences. Second, a novel supervised NTF classifier is proposed, which trains a basis for each class separately and employs basis orthogonalization. A variety of spectral, temporal, perceptual, energy, and pitch descriptors is extracted from 1000 recordings of the GTZAN dataset, which are distributed across 10 genre classes. The NTF classifier performance is compared against that of the multilayer perceptron and the support vector machines by applying a stratified 10-fold cross validation. A genre classification accuracy of 78.9% is reported for the NTF classifier demonstrating the superiority of the aforementioned multilinear classifier over several data matrix-based state-of-the-art classifiers