1. Problem definition
Given a data set X = {x1, x2, …, xn} Rm and a label set L = {1, 2, … , c}, some samples xi are labeled as yi  L and some are unlabeled as yi = 
The goal is to provide a label to these unlabeled samples
Define a graph G = (V,E), with V = {v1, v2, …, vn}
Each node vi corresponds to a sample xi
An affinity matrix W defines the weight between the edges in E as follows:

2. Model definition Set of particles
Each particle corresponds to a label in L
Particle variables:
Node being visited by the particle
Particle potential
Target node by the particle
Node variables:
Owner particle
Level of ownership

3. Variables Initialization

4. Deterministic Moving Probabilities Random Moving Probabilities
0.8 v2 v2 v3
0.8
Random Moving Probabilities v1 v3 v4
0.3 v2 v4 v3

5. Particle and Nodes Dynamics
Node dynamics
For each node vi selected by a particle ρj as its target
Particle dynamics

6. Simulation Results: Banana-Shaped data set
(a) Toy Data (Banana-Shaped)
(b) Classication results
Classification of the banana-shaped patterns. (a) toy data set with 2000
samples divided in two classes, 20 samples are pre-labeled (red circles and blue
squares) (b) classification achieved by the proposed method

7. Simulation Results: Iris data set (UCI)
Classification Accuracy in the Iris data set with different number of pre-labeled samples

8. Simulation Results: Wine data set (UCI)
Classification Accuracy in the Wine data set with different number of pre-labeled samples

9. Simulation Results: execution time
Time elapsed to reach 95% correct classification with data sets of different sizes.
* Banana-shaped classes, 10% pre-labeled samples