Principal Component Analysis - Engineering Applications

Dimensionality reduction is one of the preprocessing steps in many machine learning applications and it is used to transform the features into a lower dimension space. Principal Component Analysis (PCA) technique is one of the most famous unsupervised dimensionality reduction techniques. The goal of the PCA is to find the space, which represents the direction of the maximum variance of the given data. This paper highlights the basic background needed to understand and implement the PCA technique. This paper starts with basic definitions of the PCA technique and the algorithms of two methods of calculating PCA, namely, the covariance matrix and Singular Value Decomposition (SVD) methods. Moreover, a number of numerical examples are illustrated to show how the PCA space is calculated in easy steps. Three experiments are conducted to show how to apply PCA in the real applications including biometrics, image compression, and visualization of high-dimensional datasets.

Journal of Signal and Information Processing, 2013

PRINCIPAL …, 2012

— Principal Component Analysis (PCA) is a powerful statistical technique for variable reduction, It used when variables are highly correlated. PCA becomes an essential tool for multivariate data analysis and unsupervised dimension reduction. PCA incorporated with AI techniques to improve performance of many applications like image processing, pattern recognition, classification and anomaly detection. The goal of this survey is to provide a comprehensive review of the literature related to Principal Component Analysis (PCA).

Academia Letters, 2021

The „religious man“ (homo religiosus) is characterized by religious emotion, religious knowledge, religious practice, and involvement with a religious community. The historical survey offered in this extended paper sketches six stages of the evolution of homo religious in global history. The respective sections are entitled: (1) the era of the shamans and the discovery of the gods; (2) the era of the experienced elders and the invention of festivals; (3) the era of the divine kings and the invention of the cultic veneration of gods; (4) the activity of prophets and the Axial-Age invention of religious criticism and theology; (5) the era of the bishops and the invention of the congregation; (6) the era of the individual and the invention of piety. While each era is dominated by a leading type of homo religious, that type is accompanied by others. Thus, the era of the divine kings saw the emergence of priests associated with temples and the emergence of the pious individual who cultivates an emotional relationship with a personal god or divine patron. And the era of the bishops includes the development of a class of religious virtuosi that practices asceticism. Reference is made to the theory of the Axial Age (Karl Jaspers) and Robert N. Bellah’s classic essay on religious evolution (1964).

2017

Organise en deux parties, ce cours synthetique et intuitif presente les bases theoriques et pratiques des systemes d’information geographique. Il ne requiert pas de connaissances prealables en informatique et donne la possibilite d’acquerir rapidement les notions de base qui vous permettent de creer des bases de donnees spatiales et de fabriquer des cartes geographiques Il s’agit d’un cours pratique qui repose sur l’utilisation de logiciels libres, notamment QGIS. Cet ouvrage fait partie de la collection BOOC (Book and Open Online Courses) qui accompagne les MOOCs (Massive Open Online Courses) proposes par l’Ecole polytechnique federale de Lausanne. Ces livres rassemblent l’essentiel a retenir pour l’obtention du certificat et ont une grande valeur pedagogique.

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