	US 12,425,564 B2
	Incomplete multi-view fuzzy system modeling method based on visible and hidden view collaborative learning
Zhaohong Deng, Wuxi (CN); Wei Zhang, Wuxi (CN); and Shitong Wang, Wuxi (CN)
Assigned to JIANGNAN UNIVERSITY, Wuxi (CN)
Filed by JIANGNAN UNIVERSITY, Wuxi (CN)
Filed on Jul. 31, 2023, as Appl. No. 18/362,613.
Claims priority of application No. 202310071513.0 (CN), filed on Feb. 3, 2023.
Prior Publication US 2024/0267506 A1, Aug. 8, 2024
Int. Cl. H04N 13/351 (2018.01); G06V 10/764 (2022.01)

CPC H04N 13/351 (2018.05) [G06V 10/764 (2022.01)]

8 Claims

1. An incomplete multi-view fuzzy system modeling method based on visible and hidden view collaborative learning, comprising the following steps:

step one: identifying the number c of classes of incomplete multi-view data {x^ν∈R^N×d^{^ν}, ν=1, 2, . . . , V} for training, the number V of views, the size N of samples, and the feature dimension d^ν of each view;

step two: constructing an objective function to extract a common view, and to impute missing views;

(2.1) determining an identification matrix E^ν∈R^N×Nand a sample weight matrix W^ν∈R^N×Naccording to input incomplete multi-view data, which are defined as follows:

where w indicates the weight of imputed instance, which is defined as the percentage of the number of available instances to the total number of instances; and at the same time, a common hidden view H∈R^N×c, a basis matrix B^ν∈R^d^{^ν}^×cof each view and an error matrix U^ν∈R^N×d^{^ν} of each view are initialized, respectively;

(2.2) constructing the common hidden view learning objective function and computing the objective function value; the objective function is defined as follows:

where L^ν=D^ν−S^νis a Laplacian matrix, D^νis a diagonal matrix, and the ith diagonal element d_i^ν thereof is equal to E_j=1^NS_i,j^ν; the first two terms of the formula (3) are used for solving the common hidden view and imputing the missing views; and the second item

is used for enabling a reconstructed error matrix to be closer to a real value;

(2.3) solving H, B^ν and U^νin the formula (3) by using an iterative solution method, wherein an update function is as follows:

obtaining a locally optimal solution by iterative optimizations (4), (5), and (6) until convergence, and obtaining the optimal optimal U^ν;

step three: imputing the missing views according to the optimal error matrix acquired in step two;

step four: mapping imputed multi-view data into fuzzy space, and constructing an objective function of an incomplete multi-view fuzzy system and solving; and

step five: obtaining final classification results.