No problem. I was able to download it from here: https://www.academia.edu/10031088/ORDINAL_FRACTIONS_-_the_algebra_of_data
Skip Cave Cave Consulting LLC On Wed, Feb 28, 2018 at 3:04 PM, Martin Kreuzer <[email protected]> wrote: > Skip - > > The paper can be downloaded from this link > https://www.academia.edu/people/search?utf8=%E2%9C%93&q=bo+ > jacoby+ordinal+fractions > provided you have an account to log into ... > > If that's not working out -and Bo agrees- I could send you the short paper > by PM. > > -M > > At 2018-02-28 14:25, you wrote: > > Bo, >> >> <https://www.academia.edu/>.edu >> Advanced Search found 9,227papers containing “ORDINAL FRACTIONS†>> Search within the full text of 20 million papers >> >> >> Skip Cave >> Cave Consulting LLC >> >> On Tue, Feb 20, 2018 at 4:20 PM, 'Bo Jacoby' via Programming < >> [email protected]> wrote: >> >> > ORDINAL FRACTIONS - the algebra of data >> >> > | >> > | >> > | >> > | | | >> >> > | >> >> > | >> > | >> > | | >> > ORDINAL FRACTIONS - the algebra of data >> > This paper was submitted to the 10th World Computer Congress, IFIP 1986 >> > conference, but rejected by the referee.... | | >> >> > | >> >> > | >> >> >> >> >> > Den 22:42 tirsdag den 20. februar 2018 skrev Skip Cave < >> > [email protected]>: >> >> >> > Very nice! Thanks Raul. >> >> > However, there is something wrong about the cosine similarity, >> > which should always be between 0 & 1 >> >> > prod=:+/ .* >> >> > 1 1 1 (prod % %:@*&prod) 0 3 3 >> >> > 1.41421 >> >> > ​Skip >> >> >> > On Tue, Feb 20, 2018 at 2:27 PM, Raul Miller <[email protected]> >> > wrote: >> >> > > I don't know about blog entries - I think there are probably some that >> > > partially cover this topic. >> > > >> > > But it shouldn't be hard to implement most of these operations: >> > > >> > > Euclidean distance: >> > > >> > > 1 0 0 +/&.:*:@:- 0 1 0 >> > > 1.41421 >> > > >> > > Manhattan distance: >> > > >> > > 1 0 0 +/@:|@:- 0 1 0 >> > > 2 >> > > >> > > Minkowski distances: >> > > >> > > minkowski=: 1 :'m %: [:+/ m ^~ [:| -' >> > > 1 0 0 (1 minkowski) 0 1 0 >> > > 2 >> > > 1 0 0 (2 minkowski) 0 1 0 >> > > 1.41421 >> > > >> > > Cosine similarity: >> > > >> > > prod=:+/ .* >> > > 1 0 0 (prod % %:@*&prod) 0 1 0 >> > > 0 >> > > >> > > Jacard Similarity: >> > > >> > > union=: ~.@, >> > > intersect=: [ ~.@:-. -. >> > > 1 0 0 (intersect %&# union) 0 1 0 >> > > 1 >> > > >> > > You'll probably want to use these at rank 1 ("1) if you're operating >> > > on collections of vectors. >> > > >> > > But, I'm a little dubious about the usefulness of Jacard Similarity, >> > > because of the assumptions it brings to bear (you're basically >> > > encoding sets as vectors, which means your multidimensional vector >> > > space is just a way of encoding a single unordered dimension). >> > > >> > > Anyways, I hope this helps, >> > > >> > > -- >> > > Raul >> > > >> > > >> > > >> > > On Tue, Feb 20, 2018 at 2:08 PM, Skip Cave <[email protected]> >> > > wrote: >> > > > One of the hottest topics in data science today is the >> representation >> > of >> > > > data characteristics using large multi-dimensional arrays. Each >> datum >> > is >> > > > represented as a data point or multi-element vector in an array that >> > can >> > > > have hundreds of dimensions. In these arrays, each dimension >> > represents a >> > > > different attribute of the data. >> > > > >> > > > Much useful information can be gleaned by examining the similarity, >> or >> > > > distance between vectors in the array. However, there are many >> > different >> > > > ways to measure the similarity of two or more vectors in a >> > > multidimensional >> > > > space. >> > > > >> > > > Some common similarity/distance measures: >> > > > >> > > > 1. Euclidean distance <https://en.wikipedia.org/> >> wiki/Euclidean_distance >> > > >: >> > > > The length of the line between two data points >> > > > >> > > > 2. Manhattan distance <https://en.wikipedia.org/wiki >> /Taxicab_geometry> >: >> > > Also >> > > > known as Manhattan length, rectilinear distance, L1 distance or L1 >> > norm, >> > > > city block distance, Minkowski’s L1 distance, taxi-cab metric, or >> city >> >> > > > block distance. >> > > > >> > > > 3. Minkowski distance: <https://en.wikipedia.org/> >> wiki/Minkowski_distance> >> > > a >> > > > generalized metric form of Euclidean distance and Manhattan >> distance. >> > > > >> > > > 4. Cosine similarity: <https://en.wikipedia.org/wiki >> /Cosine_similarity> > >> > > The >> > > > cosine of the angle between two vectors. The cosine will be between >> 0 >> > &1, >> > > > where 1 is alike, and 0 is not alike. >> > > > >> > > > 5 >> > > > <https://i2.wp.com/dataaspirant.com/wp-content/> > >> uploads/2015/04/minkowski.png>. >> > > > Jacard Similarity: <https://en.wikipedia.org/wiki/Jaccard_index> >> The >> > > > cardinality of >> > > > the intersection of sets divided by the cardinality of the union of >> the >> > > > sample sets. >> > > > >> > > > Each of these metrics is useful in specific data analysis >> situations. >> > > > >> > > > In many cases, one also wants to know the similarity between >> clusters >> > of >> > > > points, or a point and a cluster of points. In these cases, the >> > centroid >> > > of >> > > > a set of points is also a useful metric to have, which can then be >> used >> > > > with the various distance/similarity measurements. >> > > > >> > > > Is there any essay or blog covering these common metrics using the J >> > > > language? I would seem that J is perfectly suited for calculating >> these >> > > > metrics, but I haven't been able to find anything much on this >> topic on >> > > the >> > > > J software site. I thought I would ask on this forum, before I go >> off >> > to >> > > > see what my rather rudimentary J skills can come up with. >> > > > >> > > > Skip >> > > > ------------------------------------------------------------ >> ---------- >> > > > For information about J forums see http://www.jsoftware.com/forum >> s.htm >> > > ------------------------------------------------------------ >> ---------- >> > > For information about J forums see http://www.jsoftware.com/forum >> s.htm >> > ---------------------------------------------------------------------- >> > For information about J forums see http://www.jsoftware.com/forums.htm >> >> >> > ---------------------------------------------------------------------- >> > For information about J forums see http://www.jsoftware.com/forums.htm >> >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
