By Omran M. G. H.
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Extra info for Particle Swarm Optimization Methods for Pattern Recognition and Image Processing
While the lbest approach results in a larger diversity, it is still slower than the gbest approach. 3 PSO Neighborhood topologies Different neighborhood topologies have been investigated [Kennedy 1999; Kennedy and Mendes 2002]. Two common neighborhood topologies are the star (or wheel) and ring (or circle) topologies. For the star topology one particle is selected as a hub, which is connected to all other particles in the swarm. However, all the other particles are only connected to the hub. For the ring topology, particles are arranged in a ring.
Algorithms that use splitting to generate the cluster tree are called divisive. On the other hand, the more popular algorithms that use merging to generate the cluster tree are called agglomerative. Divisive hierarchical algorithms start with all the patterns assigned to a single cluster. Then, splitting is applied to a cluster in each stage until each cluster consists of one pattern. Contrary to divisive hierarchical algorithms, agglomerative hierarchical algorithms start with each pattern assigned to one cluster.
All the particles in the swarm will be affected by the best solution found in iteration t, immediately in iteration t + 1 ). 6. However, using the ring and Von Neumann topologies will slow down the convergence rate because the best solution found has to propagate through several neighborhoods before affecting all particles in the swarm. This slow propagation will enable the particles to explore more areas in the search space and thus decreases the chance of premature convergence. 4 The Binary PSO Kennedy and Eberhart  have adapted the PSO to search in binary spaces.