Embedding Tangent Space Extreme Learning Machine for EEG Decoding in Brain Computer Interface Systems

Algorithm 1

Embedding tangent space extreme learning machine (ETS + ELM).

	Input: given SPD matrix set with samples , dimensions of embedding , iterative number , stop threshold , and ELM parameter , and ;
(1)	Construct a Riemannian graph over all samples based on Riemannian geodesic distance (Section 3.1);
(2)	Initialize: ;
(3)	Fort = 1 : 1:(), do;
	Calculate the matrices (Section 3.2);
	Obtain mapping matrix by (12);
	If
	break;
	end if;
	end for;
(4)	Construct -dimensional embedding , where is convergent matrix in step 4;
(5)	Calculate the Riemannian mean of all data on embedding:
(6)	Project embedding point onto tangent space on Riemannian mean by (6) ;
(7)	Apply a three-layer ELM in the tangent space, learning the weight from (14), using the training data;
(8)	The label of the testing data may be obtained by , where is the mapping matrix of the testing data;
	Output: the label of the testing data.