3.4. Principle Component Analysis (PCA)

Principle component analysis, also referred to as eigenvector transformation, Hotelling transformation and Karhunen Loeve transformation in remote sensing, is a multivariate technique [66] that is used to decrease dataset dimensionality. In this technique, the original remote sensing dataset, which is a correlated variable, is distorted into a simpler dataset for analysis. This permits the dataset to be uncorrelated variables representing the most significant information from the novel [21]. The computation of the variance covariance matrix (C) of multiband images is expressed as: Where M and X are the multiband image mean and individual pixel value vectors respectively, and n is the number of pixels.

In change detection, there are two ways to relate PCA. The first method is counting two image dates to a single file, and the second methods is subtracting the second image date from the corresponding image of the first date after performing PCA individually. The disadvantages of PCA can
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For example, Baronti, Carla [39] concerned PCA to examine the changes occurring in multi-temporal polarimetric synthetic aperture radar (SAR) images. They used association instead of a covariance matrix in the transformation to condense gain variations that are introduced by the imaging system and that provide weight to each polarization. In another example, Liu, Nishiyama [49] evaluated four techniques, including image differencing, image ratioing, image regression and PCA, from a mathematical perspective. They distinguished that standardized PCA achieved the greatest performance for change detection. Standardized PCA is better than unstandardized PCA for change detection because, if the images subjected to PCA are not calculated in the same scale, the correlation matrix normalizes the data onto the same scale

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