PCA
Computes principal components from the input table/view.
Computes principal components from the input table/view. The results are saved in a PCA model. Internally, PCA finds the components by using SVD on the co-variance matrix built from the input date. The singular values of this decomposition are also saved as part of the PCA model. The signs of all elements of a principal component could be flipped all together on different runs.
This is a meta-function. You must call meta-functions in a top-level SELECT statement.
Behavior type
VolatileSyntax
PCA ( 'model-name', 'input-relation', 'input-columns'
[ USING PARAMETERS
[exclude_columns = 'excluded-columns']
[, num_components = num-components]
[, scale = is-scaled]
[, method = 'method'] ] )
Arguments
model-name- Identifies the model to create, where
model-nameconforms to conventions described in Identifiers. It must also be unique among all names of sequences, tables, projections, views, and models within the same schema. input-relation- The table or view that contains the input data for PCA.
input-columns- Comma-separated list of columns to use from the input relation, or asterisk (*) to select all columns. All input columns must be a numeric data type.
Parameters
exclude_columnsComma-separated list of column names from
input-columnsto exclude from processing.num_components- The number of components to keep in the model. If this value is not provided, all components are kept. The maximum number of components is the number of non-zero singular values returned by the internal call to SVD. This number is less than or equal to SVD (number of columns, number of rows).
scale- A Boolean value that specifies whether to standardize the columns during the preparation step:
-
True: Use a correlation matrix instead of a covariance matrix. -
False(default)
-
method- The method used to calculate PCA, can be set to
LAPACK.
Model attributes
columns- The information about columns from the input relation used for creating the PCA model:
-
index
-
name
-
singular_values- The information about singular values found. They are sorted in descending order:
-
index
-
value
-
explained_variance : percentage of the variance in data that can be attributed to this singular value
-
accumulated_explained_variance : percentage of the variance in data that can be retained if we drop all singular values after this current one
-
principal_components- The principal components corresponding to the singular values mentioned above:
-
index: indies of the elements in each component
-
PC1
-
PC2
-
...
-
counters- The information collected during training the model, stored as name-value pairs:
-
counter_name
-
accepted_row_count: number of valid rows in the data
-
rejected_row_count: number of invalid rows (having NULL, INF or NaN) in the data
-
iteration_count: number of iterations, always 1 for the current implementation of PCA
-
-
counter_value
-
call_string- The function call that created the model.
Privileges
Non-superusers:
-
CREATE privileges on the schema where the model is created
-
SELECT privileges on the input relation
Examples
=> SELECT PCA ('pcamodel', 'world','country,HDI,em1970,em1971,em1972,em1973,em1974,em1975,em1976,em1977,
em1978,em1979,em1980,em1981,em1982,em1983,em1984 ,em1985,em1986,em1987,em1988,em1989,em1990,em1991,em1992,
em1993,em1994,em1995,em1996,em1997,em1998,em1999,em2000,em2001,em2002,em2003,em2004,em2005,em2006,em2007,
em2008,em2009,em2010,gdp1970,gdp1971,gdp1972,gdp1973,gdp1974,gdp1975,gdp1976,gdp1977,gdp1978,gdp1979,gdp1980,
gdp1981,gdp1982,gdp1983,gdp1984,gdp1985,gdp1986,gdp1987,gdp1988,gdp1989,gdp1990,gdp1991,gdp1992,gdp1993,
gdp1994,gdp1995,gdp1996,gdp1997,gdp1998,gdp1999,gdp2000,gdp2001,gdp2002,gdp2003,gdp2004,gdp2005,gdp2006,
gdp2007,gdp2008,gdp2009,gdp2010' USING PARAMETERS exclude_columns='HDI,country');
PCA
---------------------------------------------------------------
Finished in 1 iterations.
Accepted Rows: 96 Rejected Rows: 0
(1 row)
=> CREATE TABLE worldPCA AS SELECT
APPLY_PCA (HDI,country,em1970,em1971,em1972,em1973,em1974,em1975,em1976,em1977,em1978,em1979,
em1980,em1981,em1982,em1983,em1984 ,em1985,em1986,em1987,em1988,em1989,em1990,em1991,em1992,em1993,em1994,
em1995,em1996,em1997,em1998,em1999,em2000,em2001,em2002,em2003,em2004,em2005,em2006,em2007,em2008,em2009,
em2010,gdp1970,gdp1971,gdp1972,gdp1973,gdp1974,gdp1975,gdp1976,gdp1977,gdp1978,gdp1979,gdp1980,gdp1981,gdp1982,
gdp1983,gdp1984,gdp1985,gdp1986,gdp1987,gdp1988,gdp1989,gdp1990,gdp1991,gdp1992,gdp1993,gdp1994,gdp1995,
gdp1996,gdp1997,gdp1998,gdp1999,gdp2000,gdp2001,gdp2002,gdp2003,gdp2004,gdp2005,gdp2006,gdp2007,gdp2008,
gdp2009,gdp2010 USING PARAMETERS model_name='pcamodel', exclude_columns='HDI, country', key_columns='HDI,
country',cutoff=.3)OVER () FROM world;
CREATE TABLE
=> SELECT * FROM worldPCA;
HDI | country | col1
------+---------------------+-------------------
0.886 | Belgium | 79002.2946705704
0.699 | Belize | -25631.6670012556
0.427 | Benin | -40373.4104598122
0.805 | Chile | -16805.7940082156
0.687 | China | -37279.2893141103
0.744 | Costa Rica | -19505.5631231635
0.4 | Cote d'Ivoire | -38058.2060339272
0.776 | Cuba | -23724.5779612041
0.895 | Denmark | 117325.594028813
0.644 | Egypt | -34609.9941604549
...
(96 rows)
=> SELECT APPLY_INVERSE_PCA (HDI, country, col1
USING PARAMETERS model_name = 'pcamodel', exclude_columns='HDI,country',
key_columns = 'HDI, country') OVER () FROM worldPCA;
HDI | country | em1970 | em1971 | em1972 | em1973 |
em1974 | em1975 | em1976| em1977 | em1978 | em1979
| em1980 | em1981 | em1982 | em1983 | em1984 |em1985
| em1986 | em1987 | em1988 | em1989 | em1990 | em1991
| em1992 | em1993| em1994 | em1995 | em1996 | em1997
| em1998 | em1999 | em2000 | em2001 |em2002 |
em2003 | em2004 | em2005 | em2006 | em2007 | em2008
| em2009 | em2010 | gdp1970 | gdp1971 | gdp1972 | gdp1973
| gdp1974 | gdp1975 | gdp1976 | gdp1977 |gdp1978 | gdp1979
| gdp1980 | gdp1981 | gdp1982 | gdp1983 | gdp1984 | gdp1985
| gdp1986| gdp1987 | gdp1988 | gdp1989 | gdp1990 | gdp1991
| gdp1992 | gdp1993 | gdp1994 | gdp1995 | gdp1996 |
gdp1997 | gdp1998 | gdp1999 | gdp2000 | gdp2001 | gdp2002
| gdp2003 |gdp2004 | gdp2005 | gdp2006 | gdp2007 | gdp2008
| gdp2009 | gdp2010
-------+---------------------+-------------------+-------------------+------------------+------------------
+------------------+-------------------+------------------+------------------+-------------------+---------
----------+-------------------+------------------+-------------------+-------------------+-----------------
--+------------------+-------------------+-------------------+-------------------+------------------+-------
-----------+------------------+-------------------+-------------------+------------------+------------------
-+-------------------+------------------+-------------------+-------------------+-------------------+-------
------------+--------------------+------------------+-------------------+------------------+----------------
---+-------------------+-------------------+------------------+-------------------+------------------+------
------------+------------------+------------------+------------------+------------------+------------------+
------------------+------------------+------------------+------------------+------------------+-------------
-----+------------------+------------------+------------------+------------------+------------------+-------
-----------+------------------+------------------+------------------+------------------+------------------+-
-----------------+------------------+------------------+------------------+------------------+--------------
----+------------------+------------------+------------------+------------------+------------------+--------
----------+------------------+------------------+------------------+------------------+------------------
0.886 | Belgium | 18585.6613572407 | -16145.6374560074 | 26938.956253415 | 8094.30475779595 |
12073.5461203817 | -11069.0567600181 | 19133.8584911727| 5500.312894949 | -4227.94863799987 | 6265.77925410752
| -10884.749295608 | 30929.4669575201 | -7831.49439429977 | 3235.81760508742 | -22765.9285442662 | 27200
.6767714485 | -10554.9550160917 | 1169.4144482273 | -16783.7961289161 | 27932.2660829329 | 17227.9083196848
| 13956.0524012749 | -40175.6286481088 | -10889.4785920499 | 22703.6576872859 | -14635.5832197402 |
2857.12270512168 | 20473.5044214494 | -52199.4895696423 | -11038.7346460738 | 18466.7298633088 | -17410.4225137703 |
-3475.63826305462 | 29305.6753822341 | 1242.5724942049 | 17491.0096310849 | -12609.9984515902 | -17909.3603476248
| 6276.58431412381 | 21851.9475485178 | -2614.33738160397 | 3777.74134131349 | 4522.08854282736 | 4251.90446379366
| 4512.15101396876 | 4265.49424538129 | 5190.06845330997 | 4543.80444817989 | 5639.81122679089 | 4420.44705213467
| 5658.8820279283 | 5172.69025294376 | 5019.63640408663 | 5938.84979495903 | 4976.57073629812 | 4710.49525137591
| 6523.65700286465 | 5067.82520773578 | 6789.13070219317 | 5525.94643553563 | 6894.68336419297 | 5961.58442474331
| 5661.21093840818 | 7721.56088518218 | 5959.7301109143 | 6453.43604137202 | 6739.39384033096 | 7517.97645468455
| 6907.49136910647 | 7049.03921764209 | 7726.49091035527 | 8552.65909911844 | 7963.94487647115 | 7187.45827585515
| 7994.02955410523 | 9532.89844418041 | 7962.25713582666 | 7846.68238907624 | 10230.9878908643 | 8642.76044946519
| 8886.79860331866 | 8718.3731386891
...
(96 rows)