The invention relates to a gradient perturbation optimization method for implicit
matrix decomposition based on
differential privacy, and belongs to the field of computer recommendation systems and the field of
information security. An implicit feedback matrix composed of 0 and 1 is used for representing feedback data of a user to an item, 0 represents
negative feedback, and 1 represents
positive feedback. Randomly initializing a user implicit
factor matrix W and a project implicit
factor matrix H; a
data set and a target function L (W, H) are constructed, W and H are optimized and solved by adopting a
matrix decomposition method based on Bayesian personalized sorting, and a result W is stored. Randomly initializing a
noise adding item implicit
factor matrix # imgabs0 # and an initial
record matrix # imgabs1 # by using the trained W, substituting the W into L (W, H), constructing a target function # imgabs3 # about # imgabs2 #, calculating a gradient # imgabs6 # of # imgabs4 # about # imgabs5 #,
cutting the gradient by using a
cutting threshold C, and obtaining an optimal privacy budget size
lambda t in each round of training by using an overall mse calculation formula, then, the gradient is disturbed by using
lambda t and the sensitivity of the gradient to obtain # imgabs7, the # imgabs8 is aggregated to obtain a cumulative gradient, and # imgabs9 is used for updating an item implicit factor matrix by using the cumulative gradient and # imgabs10; # imgabs11 is repeatedly updated to obtain a final item implicit factor matrix # imgabs12, and the final item implicit factor matrix # imgabs12 is distributed to each user; and the user u calculates a predicted value # imgabs13 on the equipment of the user u according to the predicted value, sorts unobserved interaction items in a descending order, and finally selects the first K items from the interaction items to recommend to the user u. The method has good
privacy protection and model accuracy.