CUR

class spalor.models.CUR(n_rows=10, n_cols=10, r=None)

Dimensionality reduction based on a low-rank matrix faactorization:

A=C*U*R

where C consists of columns sampled from A, R is rows sampled from A, and U=(C’*C)^-1 *C’ *A * R’*(R*R’)^-1.

Typically, the columns and rows are selected at random with probabilites proportional to the leverage scores.

n_rowsint, default=10

Number of rows to sample.

n_colsint, default=10

Number of columns to sample.

method{‘exact’, ‘approximate’, ‘random’}, default=’leverage_scores_QR’

method to selct rows.

• “exact”: randomly select by leverage scores

• “approximate” : randomly select columns by approximated leverage scores

• “random” : randomly select columns

d1int

number or rows in the original matrix

d2int

number of columns in the original matrix

colslist

list containing indices of columns sampled

Cndarray, shape = (d1,n_components)

Columns sampled

Xndarray, shape = (n_components, d2)

Score matrix, often used for classification. Coordinates in the lower dimensional column space

``` A=np.array([[1, 1, 2, 2],

[2, 1, 3, 5], [1, 2, 3, 1], [3, 1, 4, 8]], dtype=float)

cur=CUR(n_rows=2, n_cols=2) cur.fit(A)

print(“C:

“, cur.C)

print(“U:

“, cur.U)

print(“R:

“, cur.R)

print(“columns used:

“, cur.cols)

print(“rows used:

“, cur.rows)

```

fit(A, rows=None, cols=None)

fit matrix A to CUR model