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* KIND, either express or implied. See the License for the
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*
* @file path.sql_in
*
* @brief SQL functions for pathing functions
* @date Sep 2015
*
*/
/* ----------------------------------------------------------------------- */
m4_include(`SQLCommon.m4')
/**
@addtogroup grp_path
<div class="toc"><b>Contents</b>
<ul>
<li><a href="#syntax">Function Syntax</a></li>
<li><a href="#examples">Examples</a></li>
<li><a href="#nomenclature">Nomenclature</a></li>
<li><a href="#literature">Literature</a></li>
</ul>
</div>
@brief A function to perform complex pattern matching across rows
and extract useful information about the matches.
@details The goal of the MADlib path function is to perform regular pattern
matching over a sequence of rows, and to extract useful information about
the pattern matches. The useful information could be a simple count of
matches or something more involved like aggregations or window functions.
Symbols are used to identify particular rows of interest. Then, standard
PostgreSQL pattern matching using symbols can be applied to identify
patterns across the rows of interest. (This is similar in concept to
regular expressions which match patterns within strings of text.)
For example, a symbol can be defined for purchase events by on-line
shoppers. Then, preceding events that led to the purchase can be
identified and operated on, perhaps to find the common actions that
resulted in a purchase. Or conversely, to find actions that resulted
in an exit without a purchase having been made.
Steps on how to use path functions:
1. Partition input rows.
2. Order the partitions.
3. Define symbols to match rows of interest.
4. Define regular expression of symbols and operators to define
patterns to match in your ordered partitions.
5. Define an aggregate function to compute for each pattern match.
6. If desired, output the pattern matches for inspection or to
operate on them with subsequent queries.
@anchor syntax
@par Function Syntax
<pre class="syntax">
path(
source_table,
output_table,
partition_expr,
order_expr,
symbol,
pattern,
aggregate_func,
persist_rows,
overlapping_patterns
)
</pre>
\b Arguments
<dl class="arglist">
<dt>source_table</dt>
<dd>VARCHAR. Name of the source table, containing data for path
analysis.</dd>
<dt>output_table</dt>
<dd>VARCHAR. Name of the result table.
<dt>partition_expr</dt>
<dd>VARCHAR. The 'partition_expr' can be a single column or a list of
comma-separated columns/expressions to divide all rows into groups,
or partitions. Matching is applied across the rows that fall into
the same partition. This can be NULL or '' to indicate the matching is
to be applied to the whole table.</dd>
<dt>order_expr</dt>
<dd>VARCHAR. This expression controls the order in which rows are
processed or matched in a partition. For example, time is a common way
to order partitions.
</dd>
<dt>symbol</dt>
<dd>VARCHAR. Symbols enable you to express patterns of interest in a
simple way (see definition of ‘pattern’ argument below). A symbol
identifies a row of a particular type that you’re searching for as
part of a pattern match. Symbol definition uses the standard
PostgreSQL assignment statement 'identifier := expression;' [1].
A given row can only match one symbol. If a row matches multiple
symbols, the symbol that comes first in the symbol definition list
will take precedence.
</dd>
<dt>pattern</dt>
<dd>VARCHAR. The 'pattern' clause defines the pattern that the path
algorithm searches for. You express the pattern using symbols and
operators following regular PostgreSQL pattern matching syntax and
rules [2].
@anchor note
@note
Symbols defined using more than one (1) character need to be
enclosed in parentheses '()' when referenced in the 'pattern'
argument. For example:
- a symbol defined as 'a' in the 'symbol' argument can be used directly
in the 'pattern' argument
- a symbol defined as 'abc' in the 'symbol' argument must be written as
'(abc)' in the 'pattern' argument
The following pattern matching metacharacters are supported:
<ul>
<li>| denotes alternation (either of two alternatives). </li>
<li>? denotes repetition of the previous item zero or one time. </li>
<li>* denotes repetition of the previous item zero or more times. </li>
<li>+ denotes repetition of the previous item one or more times. </li>
<li>{m} denotes repetition of the previous item exactly m times. </li>
<li>{m,} denotes repetition of the previous item m or more times. </li>
<li>{m,n} denotes repetition of the previous item at least m and not more than n times. </li>
<li>Parentheses () can be used to group items into a single logical item.</li>
</ul>
</dd>
<dt>aggregate_func (optional)</dt>
<dd>VARCHAR, default NULL. A comma-separated list of aggregates to be
applied to the pattern matches [3].
You can think of this input parameter as being like a SELECT clause.
Please note that window functions
cannot currently be used in the parameter 'aggregate_func'. If you want
to use a window function [4], output the pattern matches and write a SQL
query with a window function over the output tuples (see 'persist_rows'
parameter below).
If you just want to output the pattern matched rows and not compute any
aggregates, you can put NULL or '' in the 'aggregate_func' parameter.
</dd>
<dt>persist_rows (optional)</dt>
<dd>BOOLEAN, default FALSE. If TRUE the matched rows are persisted in a separate output
table. This table is named as <output_table>_tuples (the string
"_tuples" is added as suffix to the value of <em>output_table</em>).
</dd>
<dt>overlapping_patterns (optional)</dt>
<dd>BOOLEAN, default FALSE. If TRUE find every occurrence of the pattern in the partition, regardless of whether it might have been part of a previously found match.
</dd>
</dl>
@anchor examples
@examp
The data set describes shopper behavior on a notional web site that sells
beer and wine. A beacon fires an event to a log file when the shopper
visits different pages on the site: landing page, beer selection page,
wine selection page, and checkout. Other pages on the site like help
pages show up in the logs as well. Let’s assume that the log has been
sessionized.
-# Create the date table:
<pre class="example">
DROP TABLE IF EXISTS eventlog;
CREATE TABLE eventlog (event_timestamp TIMESTAMP,
user_id INT,
session_id INT,
page TEXT,
revenue FLOAT);
INSERT INTO eventlog VALUES
('04/15/2015 01:03:00', 100821, 100, 'LANDING', 0),
('04/15/2015 01:04:00', 100821, 100, 'WINE', 0),
('04/15/2015 01:05:00', 100821, 100, 'CHECKOUT', 39),
('04/15/2015 02:06:00', 100821, 101, 'WINE', 0),
('04/15/2015 02:09:00', 100821, 101, 'WINE', 0),
('04/15/2015 01:15:00', 101121, 102, 'LANDING', 0),
('04/15/2015 01:16:00', 101121, 102, 'WINE', 0),
('04/15/2015 01:17:00', 101121, 102, 'CHECKOUT', 15),
('04/15/2015 01:18:00', 101121, 102, 'LANDING', 0),
('04/15/2015 01:19:00', 101121, 102, 'HELP', 0),
('04/15/2015 01:21:00', 101121, 102, 'WINE', 0),
('04/15/2015 01:22:00', 101121, 102, 'CHECKOUT', 23),
('04/15/2015 02:15:00', 101331, 103, 'LANDING', 0),
('04/15/2015 02:16:00', 101331, 103, 'WINE', 0),
('04/15/2015 02:17:00', 101331, 103, 'HELP', 0),
('04/15/2015 02:18:00', 101331, 103, 'WINE', 0),
('04/15/2015 02:19:00', 101331, 103, 'CHECKOUT', 16),
('04/15/2015 02:22:00', 101443, 104, 'BEER', 0),
('04/15/2015 02:25:00', 101443, 104, 'CHECKOUT', 12),
('04/15/2015 02:29:00', 101881, 105, 'LANDING', 0),
('04/15/2015 02:30:00', 101881, 105, 'BEER', 0),
('04/15/2015 01:05:00', 102201, 106, 'LANDING', 0),
('04/15/2015 01:06:00', 102201, 106, 'HELP', 0),
('04/15/2015 01:09:00', 102201, 106, 'LANDING', 0),
('04/15/2015 02:15:00', 102201, 107, 'WINE', 0),
('04/15/2015 02:16:00', 102201, 107, 'BEER', 0),
('04/15/2015 02:17:00', 102201, 107, 'WINE', 0),
('04/15/2015 02:18:00', 102871, 108, 'BEER', 0),
('04/15/2015 02:19:00', 102871, 108, 'WINE', 0),
('04/15/2015 02:22:00', 102871, 108, 'CHECKOUT', 21),
('04/15/2015 02:25:00', 102871, 108, 'LANDING', 0),
('04/15/2015 02:17:00', 103711, 109, 'BEER', 0),
('04/15/2015 02:18:00', 103711, 109, 'LANDING', 0),
('04/15/2015 02:19:00', 103711, 109, 'WINE', 0);
</pre>
-# Calculate the revenue by checkout:
<pre class="example">
DROP TABLE IF EXISTS path_output, path_output_tuples;
SELECT madlib.path(
'eventlog', -- Name of input table
'path_output', -- Table name to store path results
'session_id', -- Partition input table by session
'event_timestamp ASC', -- Order partitions in input table by time
'buy:=page=''CHECKOUT''', -- Define a symbol for checkout events
'(buy)', -- Pattern search: purchase
'sum(revenue) as checkout_rev', -- Aggregate: sum revenue by checkout
TRUE -- Persist matches
);
SELECT * FROM path_output ORDER BY session_id, match_id;
</pre>
Result:
<pre class="result">
session_id | match_id | checkout_rev
------------+----------+--------------
100 | 1 | 39
102 | 1 | 15
102 | 2 | 23
103 | 1 | 16
104 | 1 | 12
108 | 1 | 21
(6 rows)
</pre>
Note that there are 2 checkouts within session 102, which is apparent
from the 'match_id' column. This serves to illustrate that the
'aggregate_func' operates on a <em>per pattern match</em> basis,
not on a <em>per partition</em> basis. If in fact we wanted revenue
by partition ('session_id' in this example), then we could do:
<pre class="example">
SELECT session_id, sum(checkout_rev) FROM path_output GROUP BY session_id ORDER BY session_id;
</pre>
Result:
<pre class="result">
session_id | sum
------------+-----
100 | 39
102 | 38
103 | 16
104 | 12
108 | 21
(5 rows)
</pre>
Since we set TRUE for 'persist_rows', we can view the associated
pattern matches:
<pre class="example">
SELECT * FROM path_output_tuples ORDER BY session_id ASC, event_timestamp ASC;
</pre>
Result:
<pre class="result">
event_timestamp | user_id | session_id | page | revenue | symbol | match_id
---------------------+---------+------------+----------+---------+--------+----------
2015-04-15 01:05:00 | 100821 | 100 | CHECKOUT | 39 | buy | 1
2015-04-15 01:17:00 | 101121 | 102 | CHECKOUT | 15 | buy | 1
2015-04-15 01:22:00 | 101121 | 102 | CHECKOUT | 23 | buy | 2
2015-04-15 02:19:00 | 101331 | 103 | CHECKOUT | 16 | buy | 1
2015-04-15 02:25:00 | 101443 | 104 | CHECKOUT | 12 | buy | 1
2015-04-15 02:22:00 | 102871 | 108 | CHECKOUT | 21 | buy | 1
(6 rows)
</pre>
Notice that the 'symbol' and 'match_id' columns are added to the
right of the matched rows.
-# We are interested in sessions with an order placed within 4 pages of
entering the shopping site via the landing page. We represent this by the
regular expression: '(land)[^(land)(buy)]{0,2}(buy)'. In other words, visit
to the landing page followed by from 0 to 2 non-entry, non-sale pages,
followed by a purchase. The SQL is as follows:
<pre class="example">
DROP TABLE IF EXISTS path_output, path_output_tuples;
SELECT madlib.path(
'eventlog', -- Name of input table
'path_output', -- Table name to store path results
'session_id', -- Partition input table by session
'event_timestamp ASC', -- Order partitions in input table by time
'land:=page=''LANDING'',
wine:=page=''WINE'',
beer:=page=''BEER'',
buy:=page=''CHECKOUT'',
other:=page<>''LANDING'' AND page<>''WINE'' AND page<>''BEER'' AND page<>''CHECKOUT''', -- Symbols for page types
'(land)[^(land)(buy)]{0,2}(buy)', -- Purchase within 4 pages entering site
'sum(revenue) as checkout_rev', -- Aggregate: sum revenue by checkout
TRUE -- Persist matches
);
SELECT * FROM path_output ORDER BY session_id, match_id;
</pre>
Result:
<pre class="result">
session_id | match_id | session_rev
------------+----------+-------------
100 | 1 | 39
102 | 1 | 15
102 | 2 | 23
(3 rows)
</pre>
Now view the associated pattern matches:
<pre class="example">
SELECT * FROM path_output_tuples ORDER BY session_id ASC, event_timestamp ASC;
</pre>
Result:
<pre class="result">
event_timestamp | user_id | session_id | page | revenue | symbol | match_id
---------------------+---------+------------+----------+---------+--------+----------
2015-04-15 01:03:00 | 100821 | 100 | LANDING | 0 | land | 1
2015-04-15 01:04:00 | 100821 | 100 | WINE | 0 | wine | 1
2015-04-15 01:05:00 | 100821 | 100 | CHECKOUT | 39 | buy | 1
2015-04-15 01:15:00 | 101121 | 102 | LANDING | 0 | land | 1
2015-04-15 01:16:00 | 101121 | 102 | WINE | 0 | wine | 1
2015-04-15 01:17:00 | 101121 | 102 | CHECKOUT | 15 | buy | 1
2015-04-15 01:18:00 | 101121 | 102 | LANDING | 0 | land | 2
2015-04-15 01:19:00 | 101121 | 102 | HELP | 0 | other | 2
2015-04-15 01:21:00 | 101121 | 102 | WINE | 0 | wine | 2
2015-04-15 01:22:00 | 101121 | 102 | CHECKOUT | 23 | buy | 2
(10 rows)
</pre>
-# We may want to use a window function instead of an aggregate.
Currently, only aggregates are supported in the core path function
in the parameter 'aggregate_func'. However, you can write
window functions on the output tuples to achieve the desired result.
&nbsp;
Continuing the previous example, let’s say we want to compute average
revenue for checkouts within 4 pages of entering the shopping site
via the landing page:
<pre class="example">
SELECT DATE(event_timestamp), user_id, session_id, revenue,
avg(revenue) OVER (PARTITION BY DATE(event_timestamp)) as avg_checkout_rev
FROM path_output_tuples
WHERE page='CHECKOUT'
ORDER BY user_id, session_id;
</pre>
Result:
<pre class="result">
date | user_id | session_id | revenue | avg_checkout_rev
------------+---------+------------+---------+------------------
2015-04-15 | 100821 | 100 | 39 | 25.6666666666667
2015-04-15 | 101121 | 102 | 15 | 25.6666666666667
2015-04-15 | 101121 | 102 | 23 | 25.6666666666667
(3 rows)
</pre>
Here we are partitioning the window function by day because we want
daily averages, although our sample data set only has a single day.
-# Now we want to do a golden path analysis to find the most successful
shopper paths through the site. Since our data set is small, we decide
this means the most frequently viewed page just before a checkout is made:
<pre class="example">
DROP TABLE IF EXISTS path_output, path_output_tuples;
SELECT madlib.path(
'eventlog', -- Name of input table
'path_output', -- Table name to store path results
'session_id', -- Partition input table by session
'event_timestamp ASC', -- Order partitions in input table by time
'land:=page=''LANDING'',
wine:=page=''WINE'',
beer:=page=''BEER'',
buy:=page=''CHECKOUT'',
other:=page<>''LANDING'' AND page<>''WINE'' AND page<>''BEER'' AND page<>''CHECKOUT''', -- Symbols for page types
'[^(buy)](buy)', -- Pattern to match
'array_agg(page ORDER BY session_id ASC, event_timestamp ASC) as page_path', -- Build array with shopper paths
FALSE -- Don't persist matches
);
</pre>
Now count the common paths and print the most frequent:
<pre class="example">
SELECT count(*), page_path from
(SELECT * FROM path_output) q
GROUP BY page_path
ORDER BY count(*) DESC
LIMIT 10;
</pre>
Result:
<pre class="result">
count | page_path
-------+-----------------
5 | {WINE,CHECKOUT}
1 | {BEER,CHECKOUT}
(2 rows)
</pre>
There are only 2 different paths. The wine page is viewed more frequently
than the beer page just before checkout.
-# To demonstrate the use of 'overlapping_patterns', consider
a pattern with at least one page followed by and ending with a checkout:
<pre class="example">
DROP TABLE IF EXISTS path_output, path_output_tuples;
SELECT madlib.path(
'eventlog', -- Name of the table
'path_output', -- Table name to store the path results
'session_id', -- Partition by session
'event_timestamp ASC', -- Order partitions in input table by time
$$ nobuy:=page<>'CHECKOUT',
buy:=page='CHECKOUT'
$$, -- Definition of symbols used in the pattern definition
'(nobuy)+(buy)', -- At least one page followed by and ending with a CHECKOUT.
'array_agg(page ORDER BY session_id ASC, event_timestamp ASC) as page_path',
FALSE, -- Don't persist matches
TRUE -- Turn on overlapping patterns
);
SELECT * FROM path_output ORDER BY session_id, match_id;
</pre>
Result with overlap turned on:
<pre class="result">
session_id | match_id | page_path
------------+----------+-----------------------------------
100 | 1 | {LANDING,WINE,CHECKOUT}
100 | 2 | {WINE,CHECKOUT}
102 | 1 | {LANDING,WINE,CHECKOUT}
102 | 2 | {WINE,CHECKOUT}
102 | 3 | {LANDING,HELP,WINE,CHECKOUT}
102 | 4 | {HELP,WINE,CHECKOUT}
102 | 5 | {WINE,CHECKOUT}
103 | 1 | {LANDING,WINE,HELP,WINE,CHECKOUT}
103 | 2 | {WINE,HELP,WINE,CHECKOUT}
103 | 3 | {HELP,WINE,CHECKOUT}
103 | 4 | {WINE,CHECKOUT}
104 | 1 | {BEER,CHECKOUT}
108 | 1 | {BEER,WINE,CHECKOUT}
108 | 2 | {WINE,CHECKOUT}
(14 rows)
</pre>
With overlap turned off, the result would be:
<pre class="result">
session_id | match_id | page_path
------------+----------+-----------------------------------
100 | 1 | {LANDING,WINE,CHECKOUT}
102 | 1 | {LANDING,WINE,CHECKOUT}
102 | 2 | {LANDING,HELP,WINE,CHECKOUT}
103 | 1 | {LANDING,WINE,HELP,WINE,CHECKOUT}
104 | 1 | {BEER,CHECKOUT}
108 | 1 | {BEER,WINE,CHECKOUT}
(6 rows)
</pre>
@anchor note
@note
Please note some current limitations of the path algorithm.
- Window functions cannot currently be used in the parameter
'aggregate_func'. Instead, output the pattern matches and write
a SQL query with a window function over the output tuples.
- A given row can only match one symbol. If a row matches
multiple symbols, the symbol that comes <em>first</em> in the symbol
definition list will take precedence.
- Maximum number of symbols that can be defined is 35.
- The columns 'match_id' and 'symbol' are generated by the path
algorithm. If coincidently you have columns in your input data
named 'match_id' or 'symbol', the system generated column names
will be changed to "__madlib_path_match_id__" and "__madlib_path_symbol__"
@anchor nomenclature
@par Nomenclature
Partition
- scope of rows to be searched for pattern match
- typical examples: user id, session id, portfolio id
Order
- sort order of input rows in partition
- typical example: time
Symbol
- a row of a particular type that you’re searching for, that you want to
include in a pattern
Pattern
- regular PostgreSQL pattern match expression of symbols and operators
that you want to match across rows
Pattern match
- rows that result from a pattern match expression of symbols
- can be multiple matches per partition
@anchor literature
@par Literature
NOTE: The following links refer to documentation resources for the
current PostgreSQL database version. Depending upon your database
platform version, you may need to change "current" references in the
links to your database version.
If your database platform uses the Greenplum Database (or related
variants), please check with the project community and/or your
database vendor to identify the PostgreSQL version it is based on.
[1] PostgreSQL basic statements/assignment operator,
http://www.postgresql.org/docs/current/static/plpgsql-statements.html
[2] PostgreSQL pattern matching,
http://www.postgresql.org/docs/current/static/functions-matching.html
[3] PostgreSQL aggregate functions,
http://www.postgresql.org/docs/current/static/tutorial-agg.html
[4] PostgreSQL window functions,
http://www.postgresql.org/docs/current/static/tutorial-window.html
*/
-------------------------------------------------------------------------
DROP TYPE IF EXISTS MADLIB_SCHEMA.path_match_result CASCADE;
CREATE TYPE MADLIB_SCHEMA.path_match_result AS (
id FLOAT8[],
row_id FLOAT8[]
);
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.path_pattern_match
(
symbols TEXT,
pattern TEXT,
row_id FLOAT8[],
overlapping_patterns BOOLEAN
) RETURNS MADLIB_SCHEMA.path_match_result
AS 'MODULE_PATHNAME', 'path_pattern_match'
LANGUAGE C STRICT
m4_ifdef(`__HAS_FUNCTION_PROPERTIES__', `NO SQL', `');
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.path(
source_table VARCHAR,
output_table VARCHAR,
partition_expr VARCHAR,
order_expr VARCHAR,
symbol_expr VARCHAR,
pattern_expr VARCHAR,
agg_func VARCHAR,
persist_rows BOOLEAN,
overlapping_patterns BOOLEAN
) RETURNS TEXT AS $$
PythonFunction(utilities, path, path)
$$ LANGUAGE plpythonu
m4_ifdef(`__HAS_FUNCTION_PROPERTIES__', `MODIFIES SQL DATA', `');
-------------------------------------------------------------------------
-- Overloaded functions for default arguments ---------------
-- Do not allow overlapping by default
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.path(
source_table VARCHAR,
output_table VARCHAR,
partition_expr VARCHAR,
order_expr VARCHAR,
symbol_expr VARCHAR,
pattern_expr VARCHAR,
agg_func VARCHAR,
persist_rows BOOLEAN
) RETURNS TEXT AS $$
SELECT MADLIB_SCHEMA.path($1, $2, $3, $4, $5, $6, $7, $8, False)
$$ LANGUAGE SQL
m4_ifdef(`__HAS_FUNCTION_PROPERTIES__', `MODIFIES SQL DATA', `');
-- Do not output matched rows by default
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.path(
source_table VARCHAR,
output_table VARCHAR,
partition_expr VARCHAR,
order_expr VARCHAR,
symbol_expr VARCHAR,
pattern_expr VARCHAR,
agg_func VARCHAR
) RETURNS TEXT AS $$
SELECT MADLIB_SCHEMA.path($1, $2, $3, $4, $5, $6, $7, False, False)
$$ LANGUAGE SQL
m4_ifdef(`__HAS_FUNCTION_PROPERTIES__', `MODIFIES SQL DATA', `');
-- if no agg func provided then output the matched rows only
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.path(
source_table VARCHAR,
output_table VARCHAR,
partition_expr VARCHAR,
order_expr VARCHAR,
symbol_expr VARCHAR,
pattern_expr VARCHAR
) RETURNS TEXT AS $$
SELECT MADLIB_SCHEMA.path($1, $2, $3, $4, $5, $6, NULL, False, False)
$$ LANGUAGE SQL
m4_ifdef(`__HAS_FUNCTION_PROPERTIES__', `MODIFIES SQL DATA', `');
-------------------------------------------------------------------------
-- To Implement -----------------------------------------------------------
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.path(message TEXT)
RETURNS text AS $$
PythonFunction(utilities, path, path_help_message)
$$ language plpythonu
m4_ifdef(`__HAS_FUNCTION_PROPERTIES__', `CONTAINS SQL', `');
CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.path()
RETURNS text AS $$
SELECT MADLIB_SCHEMA.path('');
$$ language SQL
m4_ifdef(`__HAS_FUNCTION_PROPERTIES__', `CONTAINS SQL', `');