Transformation of data, Applied Statistics

Assignment Help:

PCA is a linear transformation that transforms the data to a new coordinate system such that the greatest variance by any projection of the data comes to lie on the first coordinate (called the first principal component), the second greatest variance on the second coordinate, and so on. The PCA can be used for dimensionality reduction in a dataset while retaining those characteristics of the dataset that contribute most to its variance, by keeping lower-order principal components and ignoring higher-order ones. Such low-order components often contain the "most important" aspects of the data. But this is not necessarily the case, depending on the application. Let p and tn denote respectively the original and reduced number of variables. The original variables are denoted X. In the simplest case our measure of accuracy of reconstruction is the sum ofp squared multiple correlations between X-variables and the predictions of X made froin the factors. In the more general case we can weight each squared multiple correlation by the variance of the corresponding X-variable.

Since we can set those variances ourselves by multiplying scores on each variable,by any constant we choose, this amounts to the ability to assign any weights we choose to the different variables.


Related Discussions:- Transformation of data

X-bar charts, First we look at these charts assuming that we know both the ...

First we look at these charts assuming that we know both the mean and the standard deviation of the process, that is  μ and  σ . These values represent the acceptable values (bench

Arithmetic mean, Arithmetic Mean   The process of computing Arithmetic M...

Arithmetic Mean   The process of computing Arithmetic Mean in the case of individual observations is to take the sum of the values of the variable and then divide by the number

Bionomial, The Quality Manager of a battery manufacturing plant reviewed th...

The Quality Manager of a battery manufacturing plant reviewed the warranty records within his department and found that 4% of the low maintenance batteries produced at the plant ov

Analysis of covariance (ancova), Analysis of covariance (ANCOVA) It is ...

Analysis of covariance (ANCOVA) It is initially used for an expansion of the analysis of variance which permits to the possible effects of continuous concomitant variables (suc

Residual, regression line drawn as Y=C+1075x, when x was 2, and y was 239, ...

regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual

Calculate the damping ratio for each system, (i) Plot the step responses of...

(i) Plot the step responses of the following second order systems and state the nature of each system. For each case, find the poles and plot the location of the poles in the compl

Find the relation between two substance, Find the Relation between two subs...

Find the Relation between two substance: The following table shows the results obtained in experiments aimed to determine how solubility of water in benzene depends on tempera

STATISTICS, Ask 3. Precision Manufacturing has a government contract to pro...

Ask 3. Precision Manufacturing has a government contract to produce stainless steel rods for use in military aircraft. Each rod is required to be 20 millimeters in diameter. Each

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd