Can Eigen value and Eigen vector be explained in terms of its use in Data Science. How it can be described in layman's terms to normal amateur in this field?
Any help in terms of applications, use, concepts, real world examples in the field of Data Science and Machine Learning would be appreciated.
Please share your experience of real world research in this area, explain and discuss over here instead providing links to papers and articles. Really appreciate it.
Thanks in advance!
https://www.amazon.com/s/ref=nb_sb_noss_2?url=search-alias%3Daps&field-keywords=Linear+algebra+for+statistics
The above link shows 2 books that may be helpful. Best wishes, David Booth
https://www.google.com/search?source=hp&ei=H0ZUW-noMoajjwSjw5ywCA&q=application+of+eigenvalues+and+eigenvectors+in+statistics+&oq=application+of+eigenvalues+and+eigenvectors+in+statistics+&gs_l=mobile-gws-wiz-hp.12..0i22i30.16865.60369..65754...0.0...143.1873.18j4......0....1j5.......0..0j46j0i131j46i131j0i70i249j0i22i10i30j33i160.U-GVX0C5Xew
See the above link as a starting point. Then look for a linear algebra book that emphasizes statistical application.
Best wishes, David Booth
The concepts of eigenvalue and eigenvector of square matrices are very important. For instance principal component analysis is based on them. Every eigenvalue has a corresponding eigenvector. Principal component analysis of a system of variables is done by calculating he eigenvalue of the dispersion matrix or the correlation matrix of the variables. A principal component is a linear combinations of items of the corresponding eigenvector.
They are important concepts in PCA which is one of the techniques in statistical learning.
Eigenvalues describe the proportion of variance contributed by each of the eigenvectors derived from transformations (rotations) of the original set of variables to orthogonal variables (uncorrelated). This generally results in a reduction of the number of variables (eigenvectors) needed to explain the majority of the total variance among the origanal variables. The contribution of each original variable to the direction of the eigenvectors means that the most important of all the variables can be summarized in just a few vectors.
Eigen values and eigen vectors play significant role in data analysis.
Several analysis like principal component analysis, factor analysis, canonical analysis etc. are based on eigen values and eigen vectors.
In Statistics, we collect data, which often can be structured in the form of a numerical data matrix, the question is what information this numerical body conveys to us, in Statistics, the total variation of the data-set (data matrix) is the squared Frobenius norm of the matrix, and one is interested in different ways the total variation can be decomposed into smaller variation components, one such natural way is provided from the relationship which states that the squared frobenius norm of the data matrix, denoted by D, is equal to sum of eigenvalues of D'*D matrix, which is a positive semi-definite/positive definite matrix, here, each eigenvalue, which is real and non-negative by virtue of Positive Definiteness/Semi-Definiteness, represent a component of variation resulting from a pair of 1 Dimensional sub-spaces of the Row space and Column space of the Data Matrix D.
I do agree with Debopam Ghosh.
He has given an elaborate answer.
Thanks to him.
And yet I'm pretty sure that someone who does not know what an eigenvector is would not understand positive definite or the Froebenius norm. Plain language please.
https://www.analyticsvidhya.com/blog/2017/05/comprehensive-guide-to-linear-algebra/
https://math.stackexchange.com/questions/1946959/how-can-eigenvectors-and-eigenvalues-possibly-be-so-useful
https://www.quora.com/What-is-usage-of-eigenvectors-and-eigenvalues-in-machine-learning
https://towardsdatascience.com/boost-your-data-sciences-skills-learn-linear-algebra-2c30fdd008cf
The resources mentioned by Mohamed AbdElAziz Khamis will be helpful.
Appreciation to him.
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