Principal Component Analysis on Spatial Data: An Overview

Random projections in reducing the dimensionality of climate simulation data

“…Because of spatial orthogonality and temporal uncorrelation, the PCs do not necessarily correspond to any physical phenomena or patterns (Demsˇar et al, 2013). The constraint in PCA for the successive components to explain the maximum remaining variance may lead to a mixing of physical phenomena in the extracted PCs (Aires et al, 2000).…”

Revisiting the Past: Replicating Fifty-Year-Old Flow Analysis Using Contemporary Taxi Flow Data

“…Although less common, a number of studies also attempted to use it on flow data in transportation (Black 1973), telecommunications (Goddard 1973), and, as in this application, taxi journeys (Goddard 1970). Many further uses for PCA have since been found in a geographical context (see Demsar et al [2013] for an extensive review), but they are not relevant for our replication experiment.…”

“…A similar rotation of PCs is sometimes employed in atmospheric science (Jolliffe 2002), but its validity is debatable because PCs derived via the correlation or covariance matrices already maximize variance, whereas factors do not necessarily achieve that (see the further discussion later). Hence, not only does rotation of the axes in the PC space risk changing the ordering associated with eigenvalues (Daultrey 1976), but the criterion of each rotated PC to be as closely bound as possible to a single initial variable is not very meaningful (Harris 2001;Demsar et al 2013). The use of the varimax rotation therefore raises the question of which method Goddard employed: PCA or FA.…”

“…Understanding PCA Since its development at the beginning of the twentieth century, PCA has been used in a range of scientific disciplines, including geography (Demsar et al 2013) for dimensionality reduction, orthogonalization, and the exploration of data cloud structures. A full mathematical description of PCA can be found in Jolliffee (2002), whereas here we briefly review the aspects of the method that are relevant to the analysis and interpretation of our and Goddard's results.…”

The North Sea Bicycle Race ECG Project: Time-Domain Analysis

“…PCA is a statistical operation aimed at reduction of dimensionality of the clustering data [15], frequently applied prior to K-means clustering. It allows reducing computational effort by 1354 PROCEEDINGS OF THE FEDCSIS.…”