Singular value decomposition (SVD)
Singular value decomposition (SVD) unsupervised generative method is considered an algebra-driven tool for decomposing a data matrix, X, to extract its singular values Σ. The singular values, Σ, and eigenvalues, Λ, play a substantial role in model reduction, where the reduced version of the data is the result of transforming the original data from one…
Book: Introduction to Scientific Programming with Python
This book introduces programming for scientific and computational applications using the Python programming language. The presentation style is compact and example-based, making it suitable for students and researchers with little or no prior experience in programming. The book uses relevant mathematics and natural science examples to present programming as a practical toolbox that can quickly…
Principal Component Analysis – PCA
𝐏𝐫𝐢𝐧𝐜𝐢𝐩𝐚𝐥 𝐂𝐨𝐦𝐩𝐨𝐧𝐞𝐧𝐭 𝐀𝐧𝐚𝐥𝐲𝐬𝐢𝐬 (𝐏𝐂𝐀), was one of the earliest methods used to 𝐝𝐞𝐭𝐞𝐫𝐦𝐢𝐧𝐞 𝐭𝐡𝐞 𝐜𝐨𝐫𝐫𝐞𝐥𝐚𝐭𝐢𝐨𝐧𝐬 among data and to reduce the dimensionality of the space, 𝑿, by projecting it into a lower dimensional space 𝒁. 𝐏𝐂𝐀 attempts to find a mapping 𝒇 that preserves, to the 𝐠𝐫𝐞𝐚𝐭𝐞𝐬𝐭 𝐞𝐱𝐭𝐞𝐧𝐭 𝐩𝐨𝐬𝐬𝐢𝐛𝐥𝐞, 𝐭𝐡𝐞 𝐯𝐚𝐫𝐢𝐚𝐧𝐜𝐞 of the data points…
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