Principal Component Analysis
Principal component analysis is a mathematical procedure that transforms a number of correlated variables into a smaller number of variables that are not correlated. The aim of applying this procedure is to help in the discovery or reduction of the dimensionality of the data set. Besides, it can also aid the identification of new meaningful underlying variables. Just as the name suggests, this concepts aims to measure data in terms of principal elements instead of the usual x-y axis that is applied in most occasions.
When studying about the Principal Component analysis, it is important to note that there are important concepts that can help you understand the subject better. One of them is referred to as principal component. This is a linear combination of the original variables. Another concept is known as Eigenvectors that refers to the coefficients of the original variables used in the construction of factors. Eigenvalue is also another important concept in PCA that refers to a corresponding scalar value for every eigenvector of a linear transformation.
The first invention of the Principal component analysis was done by Karl Pearson in 1901, as an analogue of the theorem of principal axes in mechanics. However, it was later on developed and named in the 1930s by Harold Hotelling. This method has today become ideal for the construction of predictive models. Principal component analysis can be conducted by eigenvalue decomposition or a data correlation.
The strength and setback of the principal component analysis is that it is a way of analysis that is non-parametric. With it, there are no parameters to tweak, neither are there coefficients that can be adjusted based on the experience of the user. That is the reason why every user is able to come up with an independent and unique answer. However, this strength can also be viewed as a weakness. In case one is aware of some features of the dynamics of a system in advance, it is senseless to incorporate these assumptions into an algorithm with selected parameter.
According to the argument of Shlens (2009), there are three basic assumptions of the Principal Component Analysis that should be noted during the calculation and interpretation of principal components. One of these assumptions is that linearity defines the problem as a change of basis. Another assumption is that large variances have got important structure. It bears the belief that the data consists of a high SNR. Thus, principal components with larger associated variances are representative of an interesting structure unlike those with lower variances.
Principal component analysis is a standard tool that is used for the analysis of data in various fields today. In fact, it has been a valuable tool in disciplines like computer graphics, neuroscience among several others. The reason why it has proved to be an essential tool is because it is a non-parametric and simple method for the extraction of relevant information from data sets that may be confusing.
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