Table 2. Some notations for the partial derivative computation.

d	size of the input and output
h	size of the hidden units
xl, l∈{1,2,…,d}	value of the lth input
xl(j)	value of the lth j nearest neighbors of input
zl, l∈{1,2,…,d}	value of the lth output
yi, i∈{1,2,…,h}	value of the jth hidden unit
Wij	connecting weight between the ith hidden unit and jth input and connecting weight between the ith hidden unit and jth output
b	bias of the hidden layer
c	bias of the output layer
θ	any parameters to be estimated
λ	non-negative regularization hyper-parameter
n	size of each batch training
J(θ; X(i), S(i))	reconstruction error for given input X(i)