Advances in Principal Component Analysis

Abstract

The interoperability and integration of heterogeneous systems, with a high degree of autonomy and time-dependent dynamic configuration over multilevel and multidimensional feature space, raise the problem configurations complexity. Due to the emergent nature of a large collection of locally interacting components, the properties and the behavior of a collection may not be fully understood or predicted even the full knowledge of its constituents is available. The simplification is contemporary addressed through either dimensional reduction methods, like Principal Component Analysis (PCA), or overall ontology managing through Physics of Open Systems (POS) paradigm. The question is: Is it possible to cope with the complexity by integrating dimension reduction steps with basic POS concepts on the Large Data Objects (LDOs) holding the structure and behavior of the complex system. The intended mission of this chapter is to formulate a starting System of Systems (SoS) based configurable hyper framework model that may be dynamically improved to better suit the static structure and dynamic behavior of complex SoS configurations. That is the reason why the reflexive integration of POS and different dimensional reduction methods, through an interoperability framework, have been proposed as the main contribution of this research chapter.

Evaluation and Analysis of the Impact of Coastal Urban Impervious Surfaces on Ecological Environments

“…The principle component analysis (PCA) method, which is based on the idea of dimension reduction, can turn a collection of correlated variables into a group of uncorrelated variables by matrix transformation in order to simplify more complex situations [56]. After integrating four ecological indicators, the multivariate analysis method of spatial analysis was used in this paper to achieve spatial principal component analysis, and the contribution rate of each ecological indicator in the synthesized image to RSEI was calculated to obtain the first component of PCA, which was then standardized and normalized Spatial principal component analysis can achieve objective and automatic selection of ecological indicators, and to a certain extent, avoid the impact of subjective factors on the evaluation results of indicator selection and weight uncertainty differences.…”

A systematic study on composition and antioxidant of 15 varieties of wild Idesia polycarpa fruits in China

“…A total of 46 different components from 15 wild Idesia polycarpa samples were analyzed. When performing multivariate large sample analysis with certain correlations among variables, principal component analysis converts the measured variables into several uncorrelated but integrated indicators containing information from the original data for multivariate statistical analysis by dimensionality reduction (Naik, 2018).…”

Unconventional Water Use Allocation in Harbin, China

“…Because each indicator has a different level of influence, this study uses the PCA method [40,41] and the Spearman algorithm [42] to select the features of complex parameters and screen out the important parameters that have the greatest impact on the amount of unconventional water use in Harbin. Principal component analysis (PCA) is a widely used data dimensionality reduction algorithm that determines the significant influence of the correlation coefficient of the factors.…”