Multi-Modal Learning-Based Equipment Fault Prediction in the Internet of Things

. 2022 Sep 6;22(18):6722. doi: 10.3390/s22186722

Algorithm 1 Multi-modal Learning Algorithm

1:
Input: Two block matrices V and W.
2:
Output: The projection matrix B.
3:
Initialize $B^{0}$ to any column orthogonal matrix.
4:
repeat
5:
Calculate $θ^{n}$ using Equation (13).
6:
Construct the trace difference problem based on Equation (14).
7:
Solve the trace difference problem using Equation (15).
8:
Reconstruct the projection matrix $B^{n} = [b_{1}^{n}, b_{2}^{n}, b_{3}^{n}, \dots, b_{d}^{n}]$ .
9:
Perform singular value decomposition $S^{(b)} = B^{n} {(B^{n})}^{T} V^{(u)} B^{n} {(B^{n})}^{T}$ .
10:
Update the projection matrix using Equation (16).
11:
until $| | B^{n} - B^{n - 1} | | < \sqrt{C d} ε$ .
12:
$B = B^{n}$ .