Federated Multitask Learning with Manifold Regularization for Face Spoof Attack Detection

Table 1

Definitions of notations.

Name	Type	Definition
	Function	Loss function in multitask learning
	Function	Regularization function in multitask learning
	Function	Conjugate dual functions of and
	Function	Local subproblem in federated learning
	Function	Trace of the matrix
	Function	The exp function
	Matrix	Image data
	Matrix	Weighted matrix of samples within tasks
	Matrix	Identity matrix
	Matrix	Image feature matrix
	Matrix	Weighted matrix among tasks
	Matrix	Affinity matrix among tasks
	Matrix	Symmetric positive definite matrix defined as
	Vector	The dual variables
	Vector	Primal variables
	Vector	Information transferred among devices
	Scalar	Parameter to control the updating speed of the federated model
	Scalar	Parameter to control the global and local weights.
	Scalar	Parameter to control the contribution of task relationships
	Scalar	The number of nearest neighbors
	Scalar	The number of local nodes