Thank you Skip! But I do not know how to make a
<https://www.academia.edu/>.eduAdvanced Search . /Bo.
Den 22:18 onsdag den 28. februar 2018 skrev Skip Cave
<[email protected]>:
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 FRACTIONSâ€
>> 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
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