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# principal component analysis (PCA)

Are you working with large datasets that contain a high number of dimensions per observation? Principal Component Analysis (PCA) can help.

This statistical technique allows you to reduce the dimensionality of your data while preserving the maximum amount of information.

With PCA, you can analyze your data more effectively, make predictive models, and visualize multidimensional data.

By transforming your data into a new coordinate system, PCA can help you identify clusters of related data points and increase the interpretability of your data.

applications of Principal Component Analysis (PCA):

In Genetics, PCA is used to identify genetic variations and understand the genetic structure of populations.

In Paleontology, it is used to analyze the chemical composition of fossils and identify differences between samples.

In Atmospheric Science, it helps analyze the spatial and temporal patterns of atmospheric variables like temperature, humidity, and pressure.

Recently, researchers used PCA in a study published in Nature to distinguish nearby soil samples in a 78,000-year-old burial.

The results showed a clear distinction between samples from the burial pit and samples from outside the pit at the same level of excavation.

Maths behind PCA:

Transforming complex data into a simpler form is the backbone of data analysis. Principal Component Analysis (PCA) is a linear algebra technique that does just that.

By transforming a dataset into a new coordinate system, PCA allows data to be represented in terms of its principal components.

These components are a sequence of unit vectors that describe the directions of maximum variance in the data.

difference between PCA and factor analysis:

While both techniques are used to reduce the dimensionality of a dataset, they differ in their underlying assumptions and goals.

PCA aims to identify the directions of maximum variance in the data and represent the data in terms of these directions, called principal components.

These components are linear combinations of the original variables that are uncorrelated with each other and account for as much of the total variance in the data as possible.

PCA is often used for exploratory data analysis and for making predictive models.

FA, on the other hand, aims to identify the underlying latent factors that are responsible for the observed correlations between the variables.

The factors are unobserved variables that are assumed to cause the observed variables. FA seeks to estimate the factor loadings,

which represent the strength of the relationship between each variable and each factor, as well as the factor scores, which represent the values of each factor for each observation.

FA is often used in psychology and social sciences to construct multi-scale tests.