| Autor: |
Landa B; Program in Applied Mathematics, Yale University., Coifman RR; Program in Applied Mathematics, Yale University., Kluger Y; Program in Applied Mathematics, Yale University.; Interdepartmental Program in Computational Biology and Bioinformatics, Yale University.; Department of Pathology, Yale University School of Medicine. |
| Jazyk: |
angličtina |
| Zdroj: |
SIAM journal on mathematics of data science [SIAM J Math Data Sci] 2021; Vol. 3 (1), pp. 388-413. Date of Electronic Publication: 2021 Mar 23. |
| DOI: |
10.1137/20M1342124 |
| Abstrakt: |
A fundamental step in many data-analysis techniques is the construction of an affinity matrix describing similarities between data points. When the data points reside in Euclidean space, a widespread approach is to from an affinity matrix by the Gaussian kernel with pairwise distances, and to follow with a certain normalization (e.g. the row-stochastic normalization or its symmetric variant). We demonstrate that the doubly-stochastic normalization of the Gaussian kernel with zero main diagonal (i.e., no self loops) is robust to heteroskedastic noise. That is, the doubly-stochastic normalization is advantageous in that it automatically accounts for observations with different noise variances. Specifically, we prove that in a suitable high-dimensional setting where heteroskedastic noise does not concentrate too much in any particular direction in space, the resulting (doubly-stochastic) noisy affinity matrix converges to its clean counterpart with rate m -1/2 , where m is the ambient dimension. We demonstrate this result numerically, and show that in contrast, the popular row-stochastic and symmetric normalizations behave unfavorably under heteroskedastic noise. Furthermore, we provide examples of simulated and experimental single-cell RNA sequence data with intrinsic heteroskedasticity, where the advantage of the doubly-stochastic normalization for exploratory analysis is evident. |
| Databáze: |
MEDLINE |
| Externí odkaz: |
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