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## What is principal component analysis?

Principal component analysis is a mathematical procedure that would use an orthogonal transformation to covert a series of observations that have correlated values of a series of values that comprises of uncorrelated variables, which are known as principal components. The first principal component would be getting the highest variance. The subsequent components would be getting the highest variance, but within the constraint that is orthogonal to the before component. If you are distributing the data together or normally, then you can make sure to keep the principal components independent. The principal component analysis is highly sensitive to the scaling of the original variables. Karl Pearson is the person who has coined out the concept of Principal Component Analysis in the year 1901. This is widely used in exploratory data analysis and to make the right predictive models. The mathematical definition that is given for Principal Component Analysis is that it transforms the orthogonal linear transformation data to a coordinate system. The highest variance in the data would be resting on the first coordinate, which is also known as a first principal component.

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This principal component analysis is a dimension reduction tool that is used to cut down the large set of variables into smaller sets provided the smaller sets contains all the information that is in the larger sets. This is also a mathematical procedure that would transform correlated variables into a small number of uncorrelated variables, which are known as principal components. You can observe the variance in the data in the first principal component and the subsequent principal components would have the remaining variability. Principal components are alike to that of multivariate procedure, i.e. factor analysis. There are many people who could not understand the difference between both these analyses. Generally, this type of analysis is carried out on square symmetric matrix. The matrix can be SSCP matrix, covariance matrix and correlation matrix. The results that are obtained for the type SSCP and covariance would not differ as these objects will have differing only in the global scaling factor.

**Objectives of Principal component analysis**

• Principal component analysis will cut down the attribute space from a huge number of variables to a small number of variables using a non-dependent procedure

• Principal component analysis is also known as dimensionality reduction or data compression technique. The main aim is to reduce dimensions and there is no assurance that the dimensions would be interpretable.

• It is easy to pick a subset of variables from a huge set of variables depending on the original variables that have the highest number of correlations with the principal component

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Kaiser-Meyer-Olkin (KMO) Test | Cumulative Density Functions |

Multithreaded Procedures | CI Approach (AUC) |

Time Series Analysis | Linear And Logistic Regression Models |

Probability Density Function | Time Series & Forecasting |

Diagnostic Measures | An Sari-Bradley Tests |

Incorporating Covariates | Nonparametric Methods |

Histograms | Analysis Of Data From Longitudinal |

Fitting Distributions To Data | Nonlinear Mixed Models |

Sampling Statistical Power | Right-Censored Data Analysis |

Normality Testing Of PK Parameters (AUC, Cmax) | Multilevel & Longitudinal Modeling |

Bootstrap Confidence Interval For t1/2 | Communalities |

R Code And S-Plus | Life Distributions |

Descriptive Statistics And T-Tests | Completeness |

Quartile Regression Models | Illustrative Statistical Analysis Of Clinical Trial Data |

Jacque Bear Tests | Autocorrelation |

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