Abstract: This paper highlights a new approach to look at online
principle components analysis (OPCA). Given a data matrix X ā
R,^m x n we characterise the online updates of its covariance as a
matrix perturbation problem. Up to the principle components, it
turns out that online updates of the batch PCA can be captured
by symmetric matrix perturbation of the batch covariance matrix.
We have shown that as nā n0 >> 1, the batch covariance and
its update become almost similar. Finally, utilize our new setup of
online updates to find a bound on the angle distance of the principle
components of X and its update.
Abstract: Earthquake is an unpredictable natural disaster and intensive earthquakes have caused serious impacts on social-economic system, environmental and social resilience. Conventional ways to mitigate earthquake disaster are to enhance building codes and advance structural engineering measures. However, earthquake-induced ground damage such as liquefaction, land subsidence, landslide happen on places nearby earthquake prone or poor soil condition areas. Therefore, this study uses spatial statistical analysis to explore the spatial pattern of damaged buildings. Afterwards, principle components analysis (PCA) is applied to categorize the similar features in different kinds of clustered patterns. The results show that serious landslide prone area, close to fault, vegetated ground surface and mudslide prone area are common in those highly damaged buildings. In addition, the oldest building might not be directly referred to the most vulnerable one. In fact, it seems that buildings built between 1974 and 1989 become more fragile during the earthquake. The incorporation of both spatial statistical analyses and PCA can provide more accurate information to subsidize retrofit programs to enhance earthquake resistance in particular areas.
Abstract: The common bean is the most important grain legume for direct human consumption in the world and BCMV is one of the world's most serious bean diseases that can reduce yield and quality of harvested product. To determine the best tolerance index to BCMV and recognize tolerant genotypes, 2 experiments were conducted in field conditions. Twenty five common bean genotypes were sown in 2 separate RCB design with 3 replications under contamination and non-contamination conditions. On the basis of the results of indices correlations GMP, MP and HARM were determined as the most suitable tolerance indices. The results of principle components analysis indicated 2 first components totally explained 98.52% of variations among data. The first and second components were named potential yield and stress susceptible respectively. Based on the results of BCMV tolerance indices assessment and biplot analysis WA8563-4, WA8563-2 and Cardinal were the genotypes that exhibited potential seed yield under contamination and noncontamination conditions.