We already discussed several times the significance of understanding the Platonic and Aristotelian ways of gaining knowledge. It can be of great help to researchers in the field of pattern recognition in the appreciation of contributions by others, in discussions with colleagues and in supervising students. This may hold for science in general, but it…
Foundation Archives
Aristotle and the ugly duckling theorem
Monday, November 24th, 2014 at
14:52
Why is the nearest neighbor rule so good?
Monday, October 13th, 2014 at
11:21
Just compare the the new observations with the ones stored in memory. Take the most similar one and use its label. What is wrong with that? It is simple, intuitive, implementation is straightforward (everybody will get the same result), there is no training involved and it has asymptotically a very nice guaranteed performance, the Cover…
The ten Aristotelian categories, features and dissimilarities
Thursday, August 14th, 2014 at
16:49
The founding fathers of philosophy, Plato and Aristotle, created two competing foundations for knowledge: the ideas and the categories. According to Plato reality is constituted by the non-materialistic ideas: they are the true objects of the world. In his view ideas can be grouped into more and more universal ideas. According to Aristotle there is…
Random Representations
Wednesday, January 8th, 2014 at
11:35
The goal of representation is in pattern recognition to map objects into a domain in which they can be compared. Usually, this domain is a vector space. It might also be a graph or a symbolic sequence or any other modality that allows the computation of distances between the represented objects. The quality of a…
Hume’s fork in pattern recognition
Sunday, November 24th, 2013 at
17:04
Some things are necessarily true, there is no escape: bachelors are unmarried, the set of prime numbers is infinitely large, the Pythagorean theorem. Other things just happen to be true: stones fall down to earth, birds fly, men are mortal. It could have been otherwise. These are manifestations of Hume’s fork. Are there examples of…
Pattern recognition and the art of naming
Monday, July 8th, 2013 at
23:15
If we really understand something, we are able to express it in words, at least for ourselves. Having the right words available may be essential. Language plays a basic role in thinking, If something new is found, if a new idea pops up the right word can crystallize it in language. By this, it can…
Platonic thinking
Monday, April 22nd, 2013 at
00:00
Everybody tries to understand his world. Some people, the scientists, try to do this in a systematic way. They report their findings in books, journals and at conferences. The starting student may think that there is a single way of doing this, of building knowledge and describing progress. He will be confused on what he…
Non-metric dissimilarities are all around
Monday, March 4th, 2013 at
00:00
A big advantage of the representation of objects by a dissimilarity space over the use of kernels is that it has no problems with the usage of non-Euclidean dissimilarity measures. More specifically, it can handle non-metric measures as well. Here, we will show common examples that such dissimilarities arise easily, both, in daily life as…
Metric learning, a problem in consciousness
Monday, February 25th, 2013 at
00:00
Pattern recognition studies the tools to learn from examples what is yet unknown. Distances (or dissimilarities) are a primary notion for learning in pattern recognition. What to do if no proper distance measure is known? Can it be learnt? On what basis? This seems to be a consciousness problem. There are three sources of scientific…
Kernel-induced space versus the dissimilarity space
Monday, February 18th, 2013 at
00:00
The dissimilarity representation has a strong resemblance to a kernel. There are, however, essential differences in assumptions and usage. Here they will be summarized and illustrated by some examples. Dissimilarities and kernels are both functions describing the pairwise relations between objects. Dissimilarities can be considered as a special type of kernel if kernels are understood…
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