Brief Explanation of the Basic Framework of the Principal Componant Analysis and Fuzzy Logic

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This section expands a brief explanation of the basic frame-work of the principal component analysis and fuzzy logic, along with some of the key basic concepts.
A. The principal component analysis (PCA)
The Principal component analysis (PCA) is an essential technique in data compression and feature reduction [13] and it is a statistical technique applied to reduce a set of correlated variables to smaller uncorrelated variables to each other. PCA is considered as special transformation which produces the principal components (PCs) Known as eigenvectors. PCs are sorted decreasing i.e. the first prin-cipal component (PC
) has largest of the variance. That is meanvar(PC1 );var(PC2
), where var(PCi )
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PCA is considered as special transformation which pro-duces the principal components (PCs) Known as eigenvectors
.PCs are sorted decreasing i.e. the first principal component
1) has largest of the variance; That is mean var (PC
) var (PC
2) var (PC
3) ... var (PC
p), where var(PC i ) expresses the variance of(PC i ) [14]. The PCA has characteristics and ability to reduce redundancy and uncertainty. So this paper used the PCA as the preprocessing step on the multispectral images to reduce the redundancy information and focus on the component; that have a significant impact on the data.
B. Fuzzy logic
Zadeh [15] introduced the concept of fuzzy logic to present vagueness in linguistics, and to implement and express human knowledge and inference capability in a natural way. The fuzzy logic starts with the concept of fuzzy sets which is defined as a set without a crisp. It is clearly defined boundary and can contain elements with only a partial degree of member-ship.The main power of fuzzy logic image processing is in the middle step (membership function) [16] A membership function defines how each value in the input space is mapped to a membership value (or degree of membership) between the range of 0 and 1. LetXbe the input space andxbe a generic element ofX. A classical set Ais defined as a collection of elements or objectsx2X, such that each xcan either belong or not belong to the setA, AvX.
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