Fig 1. Illustrative diagram of the proposed method.

(a) For each data point x_i, we build a local graph ${\mathcal{G}}_i$ based on its multi-feature observations ${\left\{f_j\left(x_i\right)\right\}}_{j=1}^m$. (b) We construct a random walk with transition probabilities matrix P_i on ${\mathcal{G}}_i$. (c) We extract the SSD signature π_i from P_i. (e) We collect the SSDs of ${\left\{x_i\right\}}_{i=1}^n$ into an SSD representation matrix. (g) Subsequently, the matrix is subjected to a nonlinear dimensionality reduction using diffusion maps by the construction of the global graph G⁽²⁾ and the corresponding random walk with P⁽²⁾. (f) Via eigenvalue decomposition, we obtain a low-dimensional representation Ψ(x_i) for i = 1, …, n, which is used in the subsequent tasks (g).