Pca analysis
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PCA is a technique used to simplify complex datasets by transforming correlated variables into a set of uncorrelated variables called principal components. It identifies patterns in high-dimensional data and expresses the data in a way that highlights similarities and differences. PCA is useful for analyzing data and reducing dimensionality without much loss of information. It works by rotating the existing axes to capture major variability in the data while ignoring smaller variations.
Pca analysis
- 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.