Algorithm 1.

TGP Regression to Map Features from Visual Space to BIS [31]

Input: N training data represented by visual features as: X = (x1,x2,…,xN), with xi = (xi,1, xi,2,…,xi,d1) and represented by BIS features as: Y = (y1,y2,…,yN), with yi = (yi,1, yi,2,…, yi,d2);

A test data with only visual features, xN+1.

Output: Predicted BIS features of the test data, yN+1.

Step1: Compute the kernel matrix KX and KY, where

$${({\mathbf{K}}_X)}_{i,j}=\varphi {({\mathbf{x}}_i)}^T\varphi ({\mathbf{x}}_j)=K_X({\mathbf{x}}_i,{\mathbf{x}}_j)=exp(-{\theta }_x{\Vert {\mathbf{x}}_i-{\mathbf{x}}_j\Vert }^2)+{\lambda }_x{\delta }_{i,j}$$

Here, θx ≥ 0 is the kernel width parameter, λx ≥ 0 is the noise variance, and δi,j is the Kronecker delta function. KY is defined in the same way;

Step2: For xN+1, predict yN+1 by optimizing the following function [31]:

$$F({\mathbf{y}}_{N+1})=K_Y({\mathbf{y}}_{N+1},{\mathbf{y}}_{N+1})-2{\mu }^T{\mathbf{K}}_Y^{{\mathbf{y}}_{N+1}}-\nu log[K_Y({\mathbf{y}}_{N+1},{\mathbf{y}}_{N+1})-{({\mathbf{K}}_Y^{{\mathbf{y}}_{N+1}})}^T{\mathbf{K}}_Y^{-1}{\mathbf{K}}_Y^{{\mathbf{y}}_{N+1}}]$$

where $\mu ={\mathbf{K}}_X^{-1}{\mathbf{K}}_X^{{\mathbf{x}}_{N+1}}$ and Equation. $\nu =K_X({\mathbf{x}}_{N+1},{\mathbf{x}}_{N+1})-{({\mathbf{K}}_X^{{\mathbf{x}}_{N+1}})}^T{\mathbf{K}}_X^{-1}{\mathbf{K}}_X^{{\mathbf{x}}_{N+1}}.{\mathbf{K}}_X^{{\mathbf{x}}_{N+1}}$ is a N × 1 column vector with ${({\mathbf{K}}_X^{{\mathbf{x}}_{N+1}})}_i=K_X({\mathbf{x}}_i,{\mathbf{x}}_{N+1})$;

Return: yN+1.