TABLE II.

The Method of CGSSL and Out-of-Sample Extension

Input: Data matrix X ∈ RD×(l+u), label matrix Y ∈ R(c+1)×(l+u), the number of nearest neighbor k and other relative parameters.

Output: The predicted label matrix F ∈ R(c+1)×(l+u).

The Transductive Method of GCSSL:

1. Construct the neighborhood graph and calculate the weight matrix W as Table 1.

2. Symmetrize and normalize W as W̃ = WΔ−1WT in Eq. (3).

3. Calculate the predicted label matrix F as Eq. (5) and output F.

Out-of-sample Inductive Extension:

1. Search the k nearest neighbor of z in $z\cup X$.

2. Construct the weight vector following Eq. (8).

3. Extend the weight vector following Eq. (9).

4. Calculate the predicted label of z as Eq. (7) and output f(z).