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CONLANG  January 2011, Week 2

CONLANG January 2011, Week 2

Subject:

Re: An interesting way to auto-generate vocabulary and morphology

From:

Gary Shannon <[log in to unmask]>

Reply-To:

Constructed Languages List <[log in to unmask]>

Date:

Mon, 10 Jan 2011 10:21:02 -0800

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

text/plain (63 lines)

Sounds good. But it depends on each cluster having at least two
members and being remote, relative to another cluster member. Take for
example, a linear arrangement of three points: A at (0), B at (10) and
C at (11). Using your steps:

For A, the nearest neighbor is B. Neither belongs to a set, so add A
and B to the new cluster X.
For B, the nearest neighbor is C. B belongs to X so add C to X.

There is now only one cluster.

It seems, intuitively, like it should be two clusters with A being the
sole member of one of those clusters. If the points are distributed
across the plane (or in the N-space) with uniform randomness then it
seems to me as if most of the cases will result in only one cluster.
(This is a strictly intuitive guess and I may be way off base.)

I wonder if a "Bounding Volume Hierarchy" could be used in a similar
way? Decide on some volume, such as a (hyper-)sphere or (hyper-)cube.
Slide that volume around in the state space until you find a place
where it encloses a maximum (or at least a local maximum) of nodes.
Then lock it down. Use a second volume of the same dimensions and find
a (non-overlapping) place for it. Repeat this process until you have
enclosed most or all of the nodes in their own non-overlapping
volumes.

Then find a larger bounding volume which encloses some PAIR of basic
volumes. Repeating that process until each of the basic volumes have
been included in its own non-overlapping bounding volume. Repeat with
a larger bounding volume, etc. until the whole state space is enclosed
in a single bounding volume. Now the single outermost volume is the
root of the tree, and the bare nodes are the leaves of the binary
tree, and the tree, a hierarchy of bounding volumes, represents the
taxonomic tree of the lexicon.

Just a crazy idea off the top of my head. :)

--gary

On Mon, Jan 10, 2011 at 8:48 AM, Peter Bleackley
<[log in to unmask]> wrote:

>
> OK, I've used this clustering method a few times for different purposes, and
> generally found it useful. Here's how it works in more detail.
>
> For each item in your dataset, find the most similar item.
> If neither of these belongs to an existing cluster, start a new cluster
> containing them.
> If one belongs to an existing cluster, add the other one to it.
> If both belong to different existing clusters, merge those clusters.
> If both belong to the same existing cluster, do nothing.
>
> This produces a discrete clusters, with no prior assumptions about the
> number and form of those clusters. The cluster boundaries are determined
> entirely by the properties of the data.
>
> If you had two triangles whose vertices were at (0,0) (0,3) and (4,0) and at
> (10,0) (10,3) and (14,0), they would form two clusters.
>
> Pete
>

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