INTERPOLATION USING MATRIX COMPLETION

1 . A computer-implemented method of obtaining an interpolated matrix of customer data, the method comprising:

generating a matrix identifying customers along a first axis and customer attributes along a second axis;

entering initially available data into the matrix;

interpolating based on the initially available data to fill the matrix;

imposing constraints on the interpolating; and

using the matrix, after the matrix is filled, to manage assets or target customers.

2 . The computer-implemented method according to claim 1 , further comprising obtaining the initially available data from surveys and market research.

3 . The computer-implemented method according to claim 1 , wherein the interpolating includes minimizing f(d-S(X)), where d is the initially available data, X is the matrix, S is a read-out of values in the matrix X, and f is an interpolation function.

4 . The computer-implemented method according to claim 1 , wherein the imposing the constraints includes imposing one or more of customer variance constraints, average market constraints, and attribute similarity constraints.

5 . The computer-implemented method according to claim 4 , wherein the imposing customer variance constraints includes imposing

g ( X )≦ t 1, where

g(X) is a convex function that approximates a rank constraint and t 1 is a column vector indicating sample variance of each of the customer attributes.

6 . The computer-implemented method according to claim 4 , wherein the imposing the average market constraints includes imposing

AX≦b, where

A is an aggregation matrix, X is the matrix, and b defines known market caps for each of the customer attributes.

7 . The computer-implemented method according to claim 4 , wherein the imposing the attribute similarity constraints includes imposing

k ( X )≦ t 2, where

k is a correlation function or a covariance matrix that maps a correlation among the customer attributes, X is the matrix, and t 2 represents information from market surveys.