1. Machine Learning for SQL Use Cases
  2. Concepts
  3. Machine Learning Algorithms
  4. About CUR Matrix Decomposition
  5. Statistical Leverage Score

Statistical Leverage Score

Statistical leverage scores highlight the most representative columns or rows, aiding in the selection of important data points.

Leverage scores are statistics that determine which column (or rows) are most representative with respect to a rank subspace of a matrix. The statistical leverage scores represent the column (or attribute) and row importance. The normalized statistical leverage scores for all columns are computed from the top k right singular vectors as follows:

Description of statistical_leverage_score.eps follows
Description of the illustration statistical_leverage_score.eps
where k is called rank parameter and j = 1,...,n. Given that πj>=0 and
Description of statistical_leverage_score_1.eps follows
Description of the illustration statistical_leverage_score_1.eps
, these scores form a probability distribution over the n columns.

Similarly, the normalized statistical leverage scores for all rows are computed from the top k left singular vectors as:

Description of statistical_leverage_score_2.eps follows
Description of the illustration statistical_leverage_score_2.eps

where i = 1,...,m.