jitenderanduat@gmail.com

1. Concept of principal
component analysis
By
Sangeetha M S
DFK1302

2. PCA -Overview
• It is a simple, nonparametric method of extracting
relevant information from confusing datasets.
• Statistical procedure that uses an orthogonal
transformation to convert a set of observations of
possibly correlated variables into a set of values of
linearly uncorrelated variable called principal
components.
• PCA was invented in 1901 by Karl Pearson
• Independently developed (and named) by Harold
Hotelling in the 1930s.
• First applied in ecology by Goodall (1954) under the
name “factor analysis” (“principal factor analysis” is a
synonym of PCA).
Overview

3. • It is a way of identifying patterns in data, and
expressing the data in such a way as to highlight
their similarities and differences.
• Since patterns in data can be hard to find in data
of high dimension, where the luxury of graphical
representation is not available, PCA is a powerful
tool for analysing data.
• The other main advantage of PCA is that once you
have found these patterns in the data, and you
compress the data, ie. by reducing the number of
dimensions, without much loss of information.

4. • PCA is considered an exploratory technique that
can be used to gain a better understanding of the
interrelationships between variables.
• PCA is performed on a set of data with the hope
of simplifying the description of a set of
interrelated variables.
• Variables are treated equally and they are not
separated into dependent and independent
variables.
• In simplest terms, PCA transforms the original
interrelated variables into a new set of
uncorrelated variables call Principal Components.

5. • An advantage of principal components to
researchers is that the complexity in
interpretation that can be caused by having
a large number of interrelated variables
can be reduced by utilizing only the first
few principal components that explain a
large proportion of the total variation.
• PCA can be used to test for normality. If
the principal components are not normally
distributed, then the original data weren’t
either.

6. • An important concept of PCA is to reduce
the number of variables or reduce
dimensionality.
• An important decision that the researcher
must make when using PCA is to determine
the number of principal components to use.
• This decision has no hard-set rules, and
the decision may seem subjective at times.

7. ROLE OF PCA
• PCA captures major (principal) variability present
in the data set and ignores smaller variability.
• It helps in finding Eigen Values and Eigen
Vectors.
• Significant Eigen Values and Eigen Vectors are
taken for deciding PCs.
• PCA forms new coordinate system defined by the
significant Eigen vectors. (new coordinates will
have lower dimensions )
• Mapping data to the new space.

8. PRINCIPLE OF PCA
• It works on Linear projection method to
reduce the number of variables.
• Transfer a set of correlated variables
into a new set of uncorrelated variables.
• Map the data into a space of lower
dimensionality.
• PCA rotates existing axes to new
positions in the space defined by original
variable.

9. IMPORTANCE
• With data of high dimensions, where
graphical representation is difficult, PCA is
a powerful multivariate statistical tool for
analyzing data and finding patterns in it.
• Mapping of data compression is also
possible using PCA.

10. INTERPRETATION
 PCA plots should be interpreted by looking
at points relative to the origin.
– Points that are in similar directions or
closed positions are positively correlated.
– Points that are on opposite sides of the
origin are negatively correlated.
– Points that are far from the origin or
more perpendicular less correlated.

11. APPLICATIONS
1. Sensory evaluation and quality control in
post harvest technologies.
2. Applicable to Stock assessments in fisheries
resources.
3. Applicable in genetics (Genomics) and
related experiments.
4. To assess the nutritional status of fishes
and shellfishes with respect to biochemical
compositions, growth parameters and
dietary aspects (Nutrients, 2011).
5. Monitoring environmental studies and other
parameters in aquaculture.

12. ADVANTAGES
Both objective and subjective attributes can be used.
• It can be done accurately (only) with the help of
Statistical software.
• Direct inputs from treatments.
• There is flexibility in naming and using dimensions.
• PCA is useful for finding new, more informative
and uncorrelated components.
• It reduces dimensionality by rejecting lower
variance components.

13. DISADVANTAGES
• Usefulness depends on the researchers' ability
to develop a complete and accurate set of
attributes - If important attributes are
missed, precision of the procedure is reduced
accordingly.
• Naming of the factors (independent variables)
can be difficult - multiple attributes can be
highly correlated with no apparent reason.
• If the observed variables are completely
unrelated, PCA analysis is unable to produce a
meaningful pattern.