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In general, good features will improve the performance of any model, and should require fewer steps / result in faster convergence. One nice example of this is whether you want to use the distance from the hole for modeling the golf putting probability of success, or whether you design a new feature based on the geometry (hole size, ball size, tolerance for ...


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Independent component analysis is suitable for separating non-orthogonal basis. Check out this paper. I guess figure 1 is what you want. Choi S. (2009) Independent Component Analysis. In: Li S.Z., Jain A. (eds) Encyclopedia of Biometrics. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-73003-5_305


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Not a perfect answer, but will push you in the right direction. Are you familiar with the PageRank algorithm? It leverages Eigenvector centrality, which is closely related to application of PCA to network analysis. In PageRank, we start with a set of webpages, S and the transition probability matrix, A. Now, if a bot were to start on a given page then ...


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The best thing to do here is really to get labeled data. It will do far more for you than any attempt to solve this problem. Especially in something as life-and-death crucial as COVID, deploying a poor model is unethical. What you’ve suggested is to take an unweighted average and threshold it: $\mathrm{COVID?} = \left[ 4 \geq \sum_{i=1}^6 f_i\right]$, using ...


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First, as @Fiodor1234 mentioned, "less information" does not imply "less noise", and certainly not a lower ratio of noise to signal. Additionally, I don't think it is even clear what you mean by noise. Therefore, I intended to mention that there is no reason to believe PCA will reduce noise. However, I realized that that is not always ...


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The projection of $x$ onto the span of $v$ is a vector $\frac{x^\top v}{v^\top v} v$, but this vector has length $\frac{x^\top v}{v^\top v} \|v\| = \frac{x^\top v}{\sqrt{v^\top v}}$, which is what you should be using in your definition of variance. This will lead to $\frac{v^\top S v}{v^\top v}$ as the expression for variance (notice that replacing $v$ by $...


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I am not familiar with the matlab counterpart (have not used it for some time), but I assume you are looking for the eigenvalues and eigenvectors of the covariance matrix from scikit-learn. Since you already have the pca object and have fitted it to the data R, the values you are looking for are retrievable as object attributes: For the loadings and ...


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If your spectra are from pure substances or well-defined mixtures (so that each mixture becomes a substance in your application): If you want to group your spectra into previously unknown groups or clusters, you want to do cluster analysis. If you already know what materials you want to detect, look into classification (including one-class classification). ...


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There is also a difference in how attribute explained_variance_ is calculated. Let the data matrix $\mathbf X$ be of $n \times p$ size, where $n$ is the number of samples and $p$ is the number of variables. And $\mathbf{X}_c$ is the centered data matrix, i.e. column means have been subtracted and are now equal to zero in this matrix. Assume that we are ...


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