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

Andrews ‘plots, Andrews ‘Plots A graphical display of multivariate da...

Andrews ‘Plots A graphical display of multivariate data in which an observation, x0 = [x1, x2, . . . , xq] is represented can be represented in the form of function A set

Business reporting and analysis, You are a business analyst working for a c...

You are a business analyst working for a company called Combined Computers Pty Ltd. You have been asked to prepare a business report with statistics in it for the managing director

Estimate the values of the dependent variable, 1. Suppose you are estimatin...

1. Suppose you are estimating the imports (from both the U.S. mainland and foreign countries) of fuels and petroleum products in Hawaii (the dependent variable). The values of the

The sum of mean and variance, the sum of mean and variance ofabinomia distr...

the sum of mean and variance ofabinomia distribution of 5 trials is 9/5, find the binomial distribution.

Confirmatory factor analysis, Confirmatory factor analysis (CFA) seeks to d...

Confirmatory factor analysis (CFA) seeks to determine whether the number of factors and the loadings of measured (indicator) variables on them conform to what is expected on the ba

Prediction interval, Prediction Inte rval We would like to construct a...

Prediction Inte rval We would like to construct a prediction interval around    which would contain the actual Y. If n  ≥  30,     ± Zs e  would be the interval, where Z

Circul;atory ststistics Lab, What statistics can be obtained from a circula...

What statistics can be obtained from a circulatory lab?

Research tool, what are the characteristics of research tool?

what are the characteristics of research tool?

Systematic random sampling, Systematic Random Sampling This method  is ...

Systematic Random Sampling This method  is generally used in such cases where a complete list of the population is available from which sample has to be selected. Under this

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