Principal Component Analysis(PCA) in multivariate data analysis.

It is difficult to visualize sets of data in space if the data variables are more than three. If the numbers of variables in the data set is very large, a lots of computation and lots of data plots are need.

In the analysis of weather data, we can use PCA, in which we can find variable which has most significant role for the weather change and the variables which has least role. For example which parameter plays major role for the precipitation either humidity or temperature or else. PCA could be the tool for the analysis.

Another application of PCA could be in the evaluation of scores in the examination as PCA considers not only data around which scores are centered but also considers how the scores are scattered. whereas classical methods of evaluation only considers the values around which data are centered.

Most recently searching engines are using PCA for the clustering of possible results found, dimension reduction is another use of PCA in data compression. 

Continuous Mathematics in Discrete Image processing

Because recently more expertise in continuous mathematics are interested in discrete image processing, images are treated as continuous object though they are discrete in both space and graylevel and time in case of video images. Continuous algorithms are developed according to continuous mathematics and numerical analysis is used to implement for the analysis of discrete images in discrete domain like computer.

Because of higher accuracy, computer becoming more and more powerful and relatively new area in the image processing, more people are being engaged in image processing with continuous mathematics.

Numerical analysis is the area that brings continuous algorithms to discrete domain with the iteration of infinitesimal operations for the analysis of discrete images.

One of the areas in continuous mathematics, partial differential equation (PDE) is used in image processing in object segmentation, denoising, edge detection, image inpainting and in motion analysis.