A methodology to compare dimensionality reduction algorithms in terms of loss of quality

Dimensionality Reduction (DR) is attracting more attention these days as a result of the increasing need to handle huge amounts of data effectively. DR methods allow the number of initial features to be reduced considerably until a set of them is found that allows the original properties of the data to be kept. However, their use entails an inherent loss of quality that is likely to affect the understanding of the data, in terms of data analysis. This loss of quality could be determinant when selecting a DR method, because of the nature of each method. In this paper, we propose a methodology that allows different DR methods to be analyzed and compared as regards the loss of quality produced by them. This methodology makes use of the concept of preservation of geometry (quality assessment criteria) to assess the loss of quality. Experiments have been carried out by using the most well-known DR algorithms and quality assessment criteria, based on the literature. These experiments have been applied on 12 real-world datasets. Results obtained so far show that it is possible to establish a method to select the most appropriate DR method, in terms of minimum loss of quality. Experiments have also highlighted some interesting relationships between the quality assessment criteria. Finally, the methodology allows the appropriate choice of dimensionality for reducing data to be established, whilst giving rise to a minimum loss of quality

Geodesic Distance Function Learning via Heat Flow on Vector Fields

Learning a distance function or metric on a given data manifold is of great importance in machine learning and pattern recognition. Many of the previous works first embed the manifold to Euclidean space and then learn the distance function. However, such a scheme might not faithfully preserve the distance function if the original manifold is not Euclidean. Note that the distance function on a manifold can always be well-defined. In this paper, we propose to learn the distance function directly on the manifold without embedding. We first provide a theoretical characterization of the distance function by its gradient field. Based on our theoretical analysis, we propose to first learn the gradient field of the distance function and then learn the distance function itself. Specifically, we set the gradient field of a local distance function as an initial vector field. Then we transport it to the whole manifold via heat flow on vector fields. Finally, the geodesic distance function can be obtained by requiring its gradient field to be close to the normalized vector field. Experimental results on both synthetic and real data demonstrate the effectiveness of our proposed algorithm

Machine Learning in Aerodynamic Shape Optimization

Machine learning (ML) has been increasingly used to aid aerodynamic shape optimization (ASO), thanks to the availability of aerodynamic data and continued developments in deep learning. We review the applications of ML in ASO to date and provide a perspective on the state-of-the-art and future directions. We first introduce conventional ASO and current challenges. Next, we introduce ML fundamentals and detail ML algorithms that have been successful in ASO. Then, we review ML applications to ASO addressing three aspects: compact geometric design space, fast aerodynamic analysis, and efficient optimization architecture. In addition to providing a comprehensive summary of the research, we comment on the practicality and effectiveness of the developed methods. We show how cutting-edge ML approaches can benefit ASO and address challenging demands, such as interactive design optimization. Practical large-scale design optimizations remain a challenge because of the high cost of ML training. Further research on coupling ML model construction with prior experience and knowledge, such as physics-informed ML, is recommended to solve large-scale ASO problems

Face Recognition Methodologies Using Component Analysis: The Contemporary Affirmation of The Recent Literature

This paper explored the contemporary affirmation of the recent literature in the context of face recognition systems, a review motivated by contradictory claims in the literature. This paper shows how the relative performance of recent claims based on methodologies such as PCA and ICA, which are depend on the task statement. It then explores the space of each model acclaimed in recent literature. In the process, this paper verifies the results of many of the face recognition models in the literature, and relates them to each other and to this work

A New Paradigm for Knowledge Discovery and Design in Nanophotonics Based on Artificial Intelligence

The design of photonic devices in the nanoscale regime outperforming the bulky optical components has been a long-lasting challenge in state-of-the-art applications. Accordingly, devising a comprehensive model to understand and explain the physics and dynamics of light-matter interaction in these nanostructures is a substantial step toward realizing novel photonic devices. This thesis presents a new paradigm based on leveraging the intelligent aspect of artificial intelligence (AI) to design nanostructure and understand the underlying physics of light-matter interactions. Considering a large number of design parameters and the complex and non-unique nature of the input-output relations in nanophotonic structures, conventional approaches cannot be used for their design and analysis. The dimensionality reduction (DR) techniques in this research considerably reduce the computing requirements. This thesis also focuses on developing a reliable inverse design approach by overcoming the non-uniqueness challenge. This thesis presents a double-step DR technique to reduce the complexity of the inverse design problem while preserving the necessary information for finding the optimum nanostructure for the desired functionality. I established an approach based on defining physics-driven metrics to explore the low-dimensional manifold of design-response space and provide a sweet region in the reduced design space for the desired functionality. In the later part of the thesis, we have shown that we achieved the optimum nanostructure for a particular desired response by employing manifold learning while minimizing the geometrical complexity. Also, in this thesis, we have developed a manifold learning-based technique for accelerating the design of nanostructures focusing on selecting the optimum material and geometric parameters.Ph.D