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As one of the oldest multivariate statistical methods of data reduction, Principal Component Analysis (PCA)simplifies a dataset by producing a small number of derived variables that are uncorrelated and that account for most of the variation in the original data set. Eventually, the derived variables are combinations of the original variables. For example, it might be ?hat students take 10 examinations and some students do well in one exam whilst other students do better in another. It is difficult to compare one student with another when we have marks from 10 examinations to consider. One obvious way of comparing students is to calculate tlie mean score. This is a constructed combination of the existing variables,. However. we may get a more useful comparison of overall performances by considering other constructed combinations of the 10 exam marks. The PCA is one way of constructing such combinations, doing so in such ewakas to account for as much as possible of the variation in the original data. One can then compare students' performance by considering this much sn~aller number of variables.
Geometric Mean is defined as the n th root of the product of numbers to be averaged. The geometric mean of numbers X 1 , X 2 , X 3 .....X n is given as
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Cluster Analysis could be also represented more formally as optimization procedure, which tries to minimize the Residual Sum of Squares objective function: where μ(ωk) - is a centr
Assume that the pulley at A is a small frictionless pulley. The cord AB is only allowed to support a maximum tension in Newtons as given in P4, and the cord supporting the block ca
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