Factor Analysis Vs. Principle Component Analysis
PCA components explain the maximum amount of variance while factor analysis
explains the covariance in data.
PCA components are fully orthogonal to each other whereas factor analysis does not
require factors to be orthogonal.
PCA component is a linear combination of the observed variable while in FA, the
observed variables are linear combinations of the unobserved variable or factor.
PCA components are uninterpretable. In FA, underlying factors are labelable and
interpretable.
PCA is a kind of dimensionality reduction method whereas factor analysis is the latent
variable method.
PCA is a type of factor analysis. PCA is observational whereas FA is a modeling
technique.
3.3 Multidimensional Scaling
Multidimensional scaling is a visual representation of distances or dissimilarities between sets of objects.
“Objects” can be colors, faces, map coordinates etc.

Objects that are more similar (or have shorter distances) are closer together on the graph than objects
that are less similar (or have longer distances).
As well as interpreting dissimilarities as distances on a graph, MDS can also serve as a dimension
reduction technique for high-dimensional data. MDS is now used over a wide variety of disciplines.
When to use MDS? :- For example you were give a list of city location and task is to make a map that
includes distances between cities. For this procedure is quite simple i.e taking ruler and measuring
distance of both city end (Location). But what If you were given distance between cities (Similarity) and
not location. This could need a fair amount of geometric knowledge to complete it. Hence this type of
problem is suitable for multidimensional scaling. You’re basically given a set of differences, and the goal
is to create a map that will also tell you what the original distances where and where they were located.
Pitfalls of MDS: - 2d graph is easiest graph to figure out but it might get distorted because of poor
representation of distances. If this happens you can switch to 3d graph, but 3d graph is difficult to plot
on sheet of paper in addition to it is difficult to comprehend
Multidimensional scaling is similar to Principal Components Analysis (PCA) and dendrograms. All are
tools to visualize relationships, but they differ in how the data is presented. In some cases, MDS can be
used as an alternative to a dendrogram. However, unlike dendrograms, MDS is not plotted in “clusters,”
nor are they hierarchical structures. PCA is another similar tool, but while MDS uses a similarity matrix to
plot the graph, PCA uses the original data.
Multidimensional scaling vs factor analysis
Both Multidimensional scaling (MDS) and Factor Analysis (FA) uncover hidden patterns or relationships in
data. Both techniques require a matrix of measures of associations.

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- Multivariate statistics