Data-Analysis: Computing SVD

Mon, 01 Jan 0001 00:00:00 +0000

This SVD example uses a small data set named small_svd. The example shows you how to compute SVD using the given data set. The table is a matrix of numbers. The singular value decomposition is computed using the SVD function. This example computes the SVD of the table matrix and assigns it to a new object, which contains one vector, and two matrices, U and V. The vector contains the singular values. The first matrix, U contains the left singular vectors and V contains the right singular vectors.

Before you begin the example, load the Machine Learning sample data.

Create the SVD model, named svdmodel.

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

View the summary output of svdmodel.


=> SELECT GET_MODEL_SUMMARY(USING PARAMETERS model_name='svdmodel');
GET_MODEL_SUMMARY
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=======
columns
=======
index|name
-----+----
1    | x1
2    | x2
3    | x3
4    | x4
===============
singular_values
===============
index| value  |explained_variance|accumulated_explained_variance
-----+--------+------------------+------------------------------
1    |22.58748|      0.95542     |            0.95542
2    | 3.79176|      0.02692     |            0.98234
3    | 2.55864|      0.01226     |            0.99460
4    | 1.69756|      0.00540     |            1.00000
======================
right_singular_vectors
======================
index|vector1 |vector2 |vector3 |vector4
-----+--------+--------+--------+--------
1    | 0.58736| 0.08033| 0.74288|-0.31094
2    | 0.26661| 0.78275|-0.06148| 0.55896
3    | 0.71779|-0.13672|-0.64563|-0.22193
4    | 0.26211|-0.60179| 0.16587| 0.73596
========
counters
========
counter_name      |counter_value
------------------+-------------
accepted_row_count|      8
rejected_row_count|      0
iteration_count   |      1
===========
call_string
===========
SELECT SVD('public.svdmodel', 'small_svd', 'x1,x2,x3,x4');
(1 row)

Create a new table, named Umat to obtain the values for U.

=> CREATE TABLE Umat 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

View the results in the Umat table. This table transforms the matrix into a new coordinates system.

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

Then, we can optionally transform the data back by converting it from Umat to Xmat. First, we must create the Xmat table and then apply the APPLY_INVERSE_SVD function to the table:
```
=> CREATE TABLE Xmat AS SELECT APPLY_INVERSE_SVD(* USING PARAMETERS model_name='svdmodel',
exclude_columns='id', key_columns='id') OVER() FROM Umat;
CREATE TABLE
```

Then view the data from the Xmat table that was created:

=> SELECT id, x1::NUMERIC(5,1), x2::NUMERIC(5,1), x3::NUMERIC(5,1), x4::NUMERIC(5,1) FROM Xmat
ORDER BY id;
id | x1  | x2  | x3  | x4
---+-----+-----+-----+-----
1  | 7.0 | 3.0 | 8.0 | 2.0
2  | 1.0 | 1.0 | 4.0 | 1.0
3  | 2.0 | 3.0 | 2.0 | 0.0
4  | 6.0 | 2.0 | 7.0 | 4.0
5  | 7.0 | 3.0 | 8.0 | 2.0
6  | 1.0 | 1.0 | 4.0 | 1.0
7  | 2.0 | 3.0 | 2.0 | 0.0
8  | 6.0 | 2.0 | 7.0 | 4.0
(8 rows)

OpenText Analytics Database 26.2.x – SVD (singular value decomposition)

Data-Analysis: Computing SVD

See also