Eleisha's Segment 48: Principal Component Analysis (PCA)

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To Compute 1. Suppose that only one principal component is large (that is, there is a single dominant value s_i). In terms of the matrix $\displaystyle \mathbf V$ (and anything else relevant), what are the constants $\displaystyle a_j$ and $\displaystyle b_j$ that make a one-dimensional model of the data? This would be a model where $\displaystyle x_{ij} \approx a_j \lambda_i + b_j$ with each of the data points (rows) having its own value of an independent variable $\displaystyle \lambda_i$ and each of the responses (columns) having it's own constants a_j,b_j.