SVD

Computes singular values (the diagonal of the S matrix) and right singular vectors (the V matrix) of an SVD decomposition of the input relation.

Computes singular values (the diagonal of the S matrix) and right singular vectors (the V matrix) of an SVD decomposition of the input relation. The results are saved as an SVD model. The signs of all elements of a singular vector in SVD 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

Volatile

Syntax

SVD ( 'model-name', 'input-relation', 'input-columns'
     [ USING PARAMETERS
              [exclude_columns = 'excluded-columns']
              [, num_components = num-components]
              [, method = 'method'] ] )

Arguments

model-name: Identifies the model to create, where model-name conforms 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 SVD.
input-columns: Comma-separated list of columns to use from the input relation, or asterisk (*) to select all columns. Input columns must be a numeric data type.

Parameters

exclude_columns: Comma-separated list of column names from input-columns to exclude from processing.
num_components: The number of components to keep in the model. The maximum number of components is the number of non-zero singular values computed, which is less than or equal to min (number of columns, number of rows). If you omit this parameter, all components are kept.
method: The method used to calculate SVD, can be set to LAPACK.

Model attributes

columns

The information about columns from the input relation used for creating the SVD 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

right_singular_vectors

The right singular vectors corresponding to the singular values mentioned above:

index: indices of the elements in each vector
vector1
vector2
...

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 SVD
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 SVD ('svdmodel', 'small_svd', 'x1,x2,x3,x4');
SVD
--------------------------------------------------------------
Finished in 1 iterations.
Accepted Rows: 8  Rejected Rows: 0
(1 row)

=> CREATE TABLE transform_svd AS SELECT
     APPLY_SVD (id, x1, x2, x3, x4 USING PARAMETERS model_name='svdmodel', exclude_columns='id', key_columns='id')
     OVER () FROM small_svd;
CREATE TABLE

=> SELECT * FROM transform_svd;
id  |       col1        |        col2         |        col3         |        col4
----+-------------------+---------------------+---------------------+--------------------
4   |  0.44849499240202 |  -0.347260956311326 |   0.186958376368345 |  0.378561270493651
6   |  0.17652411036246 | -0.0753183783382909 |  -0.678196192333598 | 0.0567124770173372
1   | 0.494871802886819 |   0.161721379259287 |  0.0712816417153664 | -0.473145877877408
2   |  0.17652411036246 | -0.0753183783382909 |  -0.678196192333598 | 0.0567124770173372
3   | 0.150974762654569 |   0.589561842046029 | 0.00392654610109522 |  0.360011163271921
5   | 0.494871802886819 |   0.161721379259287 |  0.0712816417153664 | -0.473145877877408
8   |  0.44849499240202 |  -0.347260956311326 |   0.186958376368345 |  0.378561270493651
7   | 0.150974762654569 |   0.589561842046029 | 0.00392654610109522 |  0.360011163271921
(8 rows)

=> SELECT APPLY_INVERSE_SVD (* USING PARAMETERS model_name='svdmodel', exclude_columns='id',
key_columns='id') OVER () FROM transform_svd;
id  |        x1        |        x2        |        x3        |        x4
----+------------------+------------------+------------------+------------------
4 | 91.4056627665577 | 44.7629617207482 | 83.1704961993117 | 38.9274292265543
6 | 20.6468626294368 | 9.30974906868751 | 8.71006863405534 |  6.5855928603967
7 | 31.2494347777156 | 20.6336519003026 | 27.5668287751507 | 5.84427645886865
1 |  107.93376580719 | 51.6980548011917 | 97.9665796560552 | 40.4918236881051
2 | 20.6468626294368 | 9.30974906868751 | 8.71006863405534 |  6.5855928603967
3 | 31.2494347777156 | 20.6336519003026 | 27.5668287751507 | 5.84427645886865
5 |  107.93376580719 | 51.6980548011917 | 97.9665796560552 | 40.4918236881051
8 | 91.4056627665577 | 44.7629617207482 | 83.1704961993117 | 38.9274292265543
(8 rows)

SVD