tag:blogger.com,1999:blog-6555947.post6850625428870671055..comments2022-08-11T22:36:54.530-06:00Comments on The Geomblog: Negative-type distances and kernelsSuresh Venkatasubramanianhttp://www.blogger.com/profile/15898357513326041822noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-6555947.post-71321614516347174192009-09-08T02:17:06.086-06:002009-09-08T02:17:06.086-06:00I knew that there was a connection from kernels to...I knew that there was a connection from kernels to Euclidean distances but didn't know that it was other way around too.. Good post. Thanks.Arvind Agarwal, PhDhttps://www.blogger.com/profile/14954541942563312788noreply@blogger.comtag:blogger.com,1999:blog-6555947.post-86130746122855001532009-08-12T22:48:35.749-06:002009-08-12T22:48:35.749-06:00Indeed. maybe I should have made it clear. the cor...Indeed. maybe I should have made it clear. the correspondence is well known: it's just that I hadn't put it together till now (and reading Deza and Laurent, it's not explicit unless you're already familiar with kernels)Suresh Venkatasubramanianhttps://www.blogger.com/profile/15898357513326041822noreply@blogger.comtag:blogger.com,1999:blog-6555947.post-37265372231666635332009-08-11T23:23:45.467-06:002009-08-11T23:23:45.467-06:00This correspondence is known at least since Schoen...This correspondence is known at least since Schoenberg (1938), "Metric Spaces and Positive Definite Functions". It is presented in detail in the book Harmonic Analysis on Semigroups, by Berg, Christensen, and Ressel (1984), where the "squared distances" are called "negative definite kernels." This is also well known in the literature on kernel methods, e.g. Schoelkopf and Smola's Learning With Kernels (2001), where the negative of these squared distances appear under the name "conditionally positive definite kernels."AndrĂ© Martinshttps://www.blogger.com/profile/07656348479195514232noreply@blogger.comtag:blogger.com,1999:blog-6555947.post-45574949967457013312009-08-11T01:39:43.431-06:002009-08-11T01:39:43.431-06:00Just a little comment to say that I really like yo...Just a little comment to say that I really like your Blog!! It's always a pleasure to read your posts and thanks for that!!Valehttp://berlin49.denoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-85210213881577353572009-08-10T10:29:08.878-06:002009-08-10T10:29:08.878-06:00Thanks; that's nice!Thanks; that's nice!AChttps://www.blogger.com/profile/14911233583375020356noreply@blogger.com