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Therefore, the reconstruction weights can be computed by the kernel matrix's eigenvalues and eigenvectors.
This is because epigenetic similarities between individuals provided by the kernel matrix are based on a relative metric, instead of an absolute one.
The estimated variance components associated with the Gaussian kernel were very large when h was large, and the proportion of phenotypic variation explained by the kernel matrix seemed excessive (up to 0.85).
Note that the structure of the model described by (2) is that of the standard animal model (Quaas and Pollak 1980) with the pedigree-derived numerator relationship matrix (A) replaced by the kernel matrix (K).
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The kernel matrix of all instances in D is denoted by K, the kernel matrix of training instances by KS and the kernel matrix of training versus test instances by KU.
This can be done by substituting the kernel matrix K with: widehat{K}=K-{1}_NK-K{1}_N+{1}_NK{1}_N, (7).
For example, in [22], all weighted kernel matrices are combined by Hadamard product while the kernel matrix and its corresponding weight are powered by an identical number.
pcaSVM: we consider the first component from principle component analysis (PCA) to be most related to the side information, and then weaken the side-effect by removing it from the kernel matrix.
Suppose ⏟ U is a projection matrix, Z T = ⏟ U T Y, that fulfills the objective function (8) and Y is the kernel matrix produced by the Grassmann kernel.
Hence, the distance between molecules was newly defined using the descriptor and was converted into the kernel matrix loaded by general SVM programs.
Hereafter, we denote K as the kernel matrix indexed by the observed covariate; and K i, j) indicates particular elements of K; K is the infinite dimensional Gaussian kernel, or the 3 p ×3 p dimensional kernel for the diffusion kernel.
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