Discussing the article: "MQL5 Wizard Techniques you should know (Part 16): Principal Component Analysis with Eigen Vectors"

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Check out the new article: MQL5 Wizard Techniques you should know (Part 16): Principal Component Analysis with Eigen Vectors.

Principal Component Analysis, a dimensionality reducing technique in data analysis, is looked at in this article, with how it could be implemented with Eigen values and vectors. As always, we aim to develop a prototype expert-signal-class usable in the MQL5 wizard.

SVD is able to achieve dimensionality reduction by splitting a matrix data set into 3 separate matrices, where one of these 3, the Σ matrix, identifies the most important directions of variance in the data. This matrix that is also known as the diagonal matrix contains the singular values, which represent the magnitudes of variance along each pre-identified direction (logged in another of the 3 matrices, often referred to as U). The larger the singular value, the more significant the corresponding direction in explaining the data's variability. This leads to the U column with the highest singular value being selected as representative of the entire matrix, which does amount to reduced dimensions. From a matrix to a single vector.

Conversely, the power method iteratively refines a vector estimate to converge towards the dominant eigenvector. This eigenvector captures the direction with the most significant variation in the data and amounts to a reduced dimension of the original matrix.

However, with eigen vectors & values our focus for this article, we are able to reduce an n x n matrix into n possible n sized vectors, with each of these vectors getting assigned an Eigenvalue. This eigenvalue then informs the selection of the one eigenvector to best represent the matrix, with again a higher value indicating higher positive correlation in explaining the data variability.

Author: Stephen Njuki