If a matrix undergoes singular value decomposition (SVD) resulting in clearer patterns in data for machine learning applications, what underlying property of the matrix is primarily responsible for this effect?

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Seekh · Accepted Answer

The effect comes from the matrix’s ability to be described mainly by a few large singular values, which means it has a low‑rank or “compressible” structure. In an SVD, the singular values tell how much each orthogonal direction contributes to the data; when most of the energy is in the first few values, the matrix can be approximated well by a small number of components. This low‑rank property lets machine‑learning algorithms focus on the strongest patterns and ignore noise. For example, a 100×100 image matrix whose first ten singular values capture 95 % of the total energy can be reduced to a 10‑dimensional representation that still preserves the image’s main features.

If a matrix undergoes singular value decomposition (SVD) resulting in clearer patterns in data for machine learning applications, what underlying property of the matrix is primarily responsible for this effect?

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