tag:blogger.com,1999:blog-6555947.post3949393483333088144..comments2024-03-14T01:32:43.610-06:00Comments on The Geomblog: Data, Dimensions and Geometry oh my !Suresh Venkatasubramanianhttp://www.blogger.com/profile/15898357513326041822noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-6555947.post-34567666871235216102012-11-12T09:17:23.629-07:002012-11-12T09:17:23.629-07:00Fixed. thanks Fixed. thanks Suresh Venkatasubramanianhttps://www.blogger.com/profile/15898357513326041822noreply@blogger.comtag:blogger.com,1999:blog-6555947.post-38338113798569945522012-11-12T06:48:15.162-07:002012-11-12T06:48:15.162-07:00Minor typo: it's "René Descartes", n...Minor typo: it's "René Descartes", not "Réne Descartes".Rodnoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-71150046788314852612012-11-09T00:04:32.552-07:002012-11-09T00:04:32.552-07:00Steve,
Another way to deal with complex objects r...Steve,<br />Another way to deal with complex objects related to kernel methods is dissimilarity. Instead of kernels, which represent inner products between objects and which can be turned into distances, you quantify how similar or dissimilar objects are. The dissimilarities don't even have to satisfy triangle inequality. You can then go to vector representation by embedding methods (such as multidimensional scaling) or try to do learning using dissimilarities themselves.Sancarhttps://www.blogger.com/profile/15401658059885149957noreply@blogger.comtag:blogger.com,1999:blog-6555947.post-79184140179564429972012-11-08T07:41:10.018-07:002012-11-08T07:41:10.018-07:00This is definitely a problem. There's no speci...This is definitely a problem. There's no specific answer just yet: what people do is a mixture of careful validation, trying to find low dimensional structures that explain the phenomenon, and other ad hoc methods. Suresh Venkatasubramanianhttps://www.blogger.com/profile/15898357513326041822noreply@blogger.comtag:blogger.com,1999:blog-6555947.post-8221022741569752042012-11-08T02:46:37.436-07:002012-11-08T02:46:37.436-07:00Just a curiousity of a person from outside.
When i...Just a curiousity of a person from outside.<br />When it comes to data mining (in the broad sense, i.e. also pattern recognition, for example), the following point always seemed to me problematic. If we are to find out things more complicated than the hand written digit, or if we simply do not have the time or resources to research the small set of features which characterize a given problem, we should probably have to deal with high dimensional spaces, as you note. But shouldn't then the concentration of measure effect interfere somehow with our efforts to separate class A from class B? In case you may have some indications: what really happens in regards to this in real world problems (especially the ones off the beaten track)?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-28512010779779428522012-11-07T23:50:26.426-07:002012-11-07T23:50:26.426-07:00Point taken. I intended the converse as you indica...Point taken. I intended the converse as you indicate Suresh Venkatasubramanianhttps://www.blogger.com/profile/15898357513326041822noreply@blogger.comtag:blogger.com,1999:blog-6555947.post-76880726352785597472012-11-07T23:43:02.411-07:002012-11-07T23:43:02.411-07:00This is very clear, but to nitpick:
And yet like m...This is very clear, but to nitpick:<br /><i>And yet like most simple ideas, it was revolutionary […]</i><br /><br />Really? I find it easy to believe the converse, that most revolutionary ideas are simple, but believing that most simple ideas are revolutionary seems hard.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-36815354442123697422012-11-07T20:51:54.824-07:002012-11-07T20:51:54.824-07:00Hi Steve
One answer to your question is that we...Hi Steve <br /> One answer to your question is that we do try to find a higher dimensional vector space to represent the complex objects. Roughly speaking, if there is some way to measure distance between objects, and this distance has some nice properties, then there is a vector space in which Euclidean distance is exactly the object distance. This method is called "the kernel approach". Suresh Venkatasubramanianhttps://www.blogger.com/profile/15898357513326041822noreply@blogger.comtag:blogger.com,1999:blog-6555947.post-29595208081381703652012-11-07T19:40:37.980-07:002012-11-07T19:40:37.980-07:00This talk reminds me of my high school teacher who...This talk reminds me of my high school teacher who always taught us to imagine geometrical objects as live objects in our minds with our eyes closed. This kind of analogy and imagination is a wonderful way of illustration to a layperson.南杏春暖https://www.blogger.com/profile/13474081704164173755noreply@blogger.comtag:blogger.com,1999:blog-6555947.post-73553340132062869842012-11-07T17:48:25.551-07:002012-11-07T17:48:25.551-07:00Thanks for the explanation. It's helpful to th...Thanks for the explanation. It's helpful to think of it this way.<br /><br />I'm no theoretician, but I've applied data mining algorithms for years. One thing that has always been counterintuitive to me is that objects can't always be well represented by a vector of values. Or maybe I'm just thinking of it in the wrong way. For example, let's say your object is a house and you want to compare it against other house objects. Some features might be simple, like the height, width, square footage, exterior paint color, etc. But some features might be complex like the configuration of the power wiring in the fourth bedroom. I guess you could find a way to represent such a complex feature with numerical values, but the point I'm trying to make is that some features are nested and complex while others are straightforward. So I guess my question is whether there are data-mining approaches designed to handle complex objects rather than vectors? Or is the field more about finding ways to convert complex objects to vectors?Stevehttps://www.blogger.com/profile/06952466893128017717noreply@blogger.com