What are the best multivariate dimension reduction techniques for your dataset?

1 Principal Component Analysis

Principal Component Analysis (PCA) is one of the most popular and widely used multivariate dimension reduction techniques. It transforms your original variables into new ones called principal components, which are linear combinations of the original variables that capture the maximum amount of variation in the data. The first principal component explains the most variation, the second one explains the most variation after removing the effect of the first one, and so on. You can then select a subset of principal components that explain a high proportion of the total variation and use them as your reduced variables. PCA is useful when you want to reduce the dimensionality of your data without losing much information, and when you want to find out which variables are most correlated or influential.

2 Factor Analysis

Factor Analysis (FA) is another multivariate dimension reduction technique that is similar to PCA, but with a different goal and assumption. FA aims to identify the underlying factors or latent variables that explain the common variation among the observed variables, while PCA focuses on explaining the total variation. FA assumes that the observed variables are influenced by some unobserved factors, and that the variation among the observed variables can be decomposed into common factors and unique factors. The common factors are shared by multiple variables, while the unique factors are specific to each variable. You can then use the common factors as your reduced variables. FA is useful when you want to explore the structure and meaning of your data, and when you want to test hypotheses about the relationships among the variables.

3 Multidimensional Scaling

Multidimensional Scaling (MDS) is a multivariate dimension reduction technique that is different from PCA and FA, because it does not use the original variables as the input, but rather the distances or dissimilarities between the observations. MDS tries to find a low-dimensional representation of the data that preserves the distances or dissimilarities as much as possible. In other words, it maps the observations from a high-dimensional space to a lower-dimensional space, such that the relative positions of the observations are maintained. You can then use the coordinates of the observations in the lower-dimensional space as your reduced variables. MDS is useful when you want to visualize your data, and when you want to compare different types of distances or dissimilarities.