Functions that preserve families of positive semidefinite matrices

By C. FitzGerald, Charles A. Micchelli, Allan Pinkus. 1995

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Francis R. Bach
2. Haizhang Zhang
3. Ulrich Bodenhofer
4. Bharath K. Sriperumbudur
5. Yoshua Bengio
6. Bernhard Schölkopf
7. Andreas Kothmeier
8. Sepp Hochreiter

Citations in the corpus

• Kernel methods in machine learning (2007, neutral): “[50] for (conditionally) positive definite matrices; by Proposition 5, it also applies for (conditionally) positive definite kernels, and for functions of dot products.”
• Universal Kernels (2006, background): “For an extensive discussion of dot product kernels see FitzGerald et al. (1995).”
• Strictly Positive Definite Functions on a Real Inner Product Space (2004, background): “159], FitzGerald, Micchelli, Pinkus [4]) that if for all positive definite matrices (aij) n i,j=1 (and for all n) the matrix (f(aij)) n i,j=1 is positive definite, then f is necessarily of the form f(t) = ∞ ∑”
• APCluster: an R package for affinity propagation clustering (2011, methodology): “1 [4,] 0.”