Обсуждение: GSoC 2014 proposal

On 03/30/2014 11:50 PM, Иван Парфилов wrote:
> The implementation of this algorithm would be for data type cube and based
> on GiST.
>
> The key concept of BIRCH algorithm is clustering feature. Given a set of N
> d-dimensional data points, the clustering feature CF of the set is defined
> as the triple CF = (N,LS,SS), where LS is the linear sum and SS is the
> square sum of data points. Clustering features are organized in a CF tree,
> which is a height balanced tree with two parameters: branching factor B and
> threshold T.
>
> Because the structure of CF tree is similar to B+-tree we can use GiST for
> implementation [2].
> The GiST is a balanced tree structure like a B-tree, containing <key,
> pointer> pairs. GiST key is a member of a user-defined class, and
> represents some property that is true of all data items reachable from the
> pointer associated with the key. The GiST provides a possibility to create
> custom data types with indexed access methods and extensible set of
> queries.

The BIRCH algorithm as described in the paper describes building a tree 
in memory. If I understood correctly, you're suggesting to use a 
pre-built GiST index instead. Interesting idea!

There are a couple of signifcant differences between the CF tree 
described in the paper and GiST:

1. In GiST, a leaf item always represents one heap tuple. In the CF 
tree, a leaf item represents a cluster, which consists of one or more 
tuples. So the CF tree doesn't store an entry for every input tuple, 
which makes it possible to keep it in memory.

2. In the CF tree, "all entries in a leaf node must satisfy a threshold 
requirement, with respect to a threshold value T: the diameter (or 
radius) has to be less than T". GiST imposes no such restrictions. An 
item can legally be placed anywhere in the tree; placing it badly will 
just lead to degraded search performance, but it's still a legal GiST tree.

3. A GiST index, like any other index in PostgreSQL, holds entries also 
for deleted tuples, until the index is vacuumed. So you cannot just use 
information from a non-leaf node and use it in the result, as the 
information summarized at a non-leaf level includes noise from the dead 
tuples.

Can you elaborate how you are planning to use a GiST index to implement 
BIRCH? You might also want to take a look at SP-GiST; SP-GiST is more 
strict in where in the tree an item can be stored, and lets the operator 
class to specify exactly when a node is split etc.

> We need to implement it to create GiST-based CF-tree to use it in BIRCH
> algorithm.
>
>
> *Example of usage(approximate):*
>
> create table cube_test (v cube);
>
+> insert into cube_test values (cube(array[1.2, 0.4]), cube(array[0.5, 
-0.2]),
>
>    cube(array[0.6, 1.0]),cube(array[1.0, 0.6]) );
>
> create index gist_cf on cube_test using gist(v);
>
> --Prototype(approximate)
>
> --birch(maxNodeEntries, distThreshold, distFunction)
>
> SELECT birch(4.1, 0.2, 1) FROM cube_test;
>
>   cluster | val1 | val2
>
> ---------+------+--------
>
>        1  |  1.2 |  0.4
>
>        0  |  0.5 | -0.2
>
>        1  |  0.6 |  1.0
>
>        1  |  1.0 |  0.6
>
> Accordingly, in this GSoC project BIRCH algorithm for data type cube would
> be implemented.
From the example, it seems that birch(...) would be an aggregate 
function. Aggregates in PostgreSQL currently work by scanning all the 
input data. That would certainly be a pretty straightforward way to 
implement BIRCH too. Every input tuple would be passed to the the 
so-called "transition function" (which you would write), which would 
construct a CF tree on-the-fly. At the end, the result would be 
constructed from the CF tree. With this approach, the CF tree would be 
kept in memory, and thrown away after the query.

That would be straightforward, but wouldn't involve GiST at all. To use 
an index to implement an aggregate would require planner/executor 
changes. That would be interesting, but offhand I have no idea what that 
would look like. We'll need more details on that.

- Heikki

On 03/30/2014 11:50 PM, Иван Парфилов wrote:
> * Quantifiable results*
>
>   Adding support of BIRCH algorithm for data type cube

Aside from the details of *how* that would work, the other question is:

Do we want this in contrib/cube? There are currently no clustering 
functions, or any other statistical functions or similar, in 
contrib/cube. Just basic contains/contained/overlaps operators. And 
B-tree comparison operators which are pretty useless for cube.

Do we want to start adding such features to cube, in contrib? Or should 
that live outside the PostgreSQL source tree, in an separate extension, 
so that it could live on its own release schedule, etc. If BIRCH goes 
into contrib/cube, that's an invitation to add all kinds of functions to it.

We received another GSoC application to add another clustering algorithm 
to the MADlib project. MADlib is an extension to PostgreSQL with a lot 
of different statistical tools, so MADlib would be a natural home for 
BIRCH too. But if it requires backend changes (ie. changes to GiST), 
then that needs to be discussed on pgsql-hackers, and it probably would 
be better to do a reference implementation in contrib/cube. MADlib could 
later copy it from there.

- Heikki

On 04/03/2014 04:15 PM, Alexander Korotkov wrote:
> On Wed, Apr 2, 2014 at 2:22 PM, Alexander Korotkov <aekorotkov@gmail.com>wrote:
>
>> On Tue, Apr 1, 2014 at 2:23 PM, Heikki Linnakangas <
>> hlinnakangas@vmware.com> wrote:
>>
>>> The BIRCH algorithm as described in the paper describes building a tree
>>> in memory. If I understood correctly, you're suggesting to use a pre-built
>>> GiST index instead. Interesting idea!
>>>
>>> There are a couple of signifcant differences between the CF tree
>>> described in the paper and GiST:
>>>
>>> 1. In GiST, a leaf item always represents one heap tuple. In the CF tree,
>>> a leaf item represents a cluster, which consists of one or more tuples. So
>>> the CF tree doesn't store an entry for every input tuple, which makes it
>>> possible to keep it in memory.
>>>
>>> 2. In the CF tree, "all entries in a leaf node must satisfy a threshold
>>> requirement, with respect to a threshold value T: the diameter (or radius)
>>> has to be less than T". GiST imposes no such restrictions. An item can
>>> legally be placed anywhere in the tree; placing it badly will just lead to
>>> degraded search performance, but it's still a legal GiST tree.
>>>
>>> 3. A GiST index, like any other index in PostgreSQL, holds entries also
>>> for deleted tuples, until the index is vacuumed. So you cannot just use
>>> information from a non-leaf node and use it in the result, as the
>>> information summarized at a non-leaf level includes noise from the dead
>>> tuples.
>>>
>>> Can you elaborate how you are planning to use a GiST index to implement
>>> BIRCH? You might also want to take a look at SP-GiST; SP-GiST is more
>>> strict in where in the tree an item can be stored, and lets the operator
>>> class to specify exactly when a node is split etc.
>>>
>>
>> Hmmm, it's likely I've imagined something quite outside of this paper, and
>> even already suggested it to Ivan... :)
>> I need a little time to rethink it.
>>
>
> Using GiST we can implement BIRCH-like clustering like so:
> 1) Build a CF tree as GiST index without restriction of T threshold value.
> 2) Scan CF tree with threshold T with some auxiliary operator. If
> consistent method see CF entry which diameter is greater than T then it
> returns true. Otherwise it returns false and put this CF entry into output
> area (could be either in-memory or temporary table).
> 3) Process other steps of algorithm as usual.

I still don't understand how that would work. You can't trust the 
non-leaf entries, because their CF value can contain deleted entries. So 
you have to scan every tuple anyway. Once you do that, what's the point 
of the index?

- Heikki