MST-Pathfinder

Algorithm

A Pathfinder Network (or PFNET) is a scaled network (or graph, in the sense of the graph theory) in which weighted edges have been pruned in a specific way. Only those edges which do not violate the triangle inequality are kept. The triangle inequality states that the direct distance between a couple of nodes must be lesser than or equal to the distance between any other path linking these nodes. The corresponding algorithm, first devised by Schvaneveldt (1990) has two parameters: r, which define the Minkowski r-metric used to compute the mentioned distance, and q, which define the maximum length of the paths considered in the triangle inequality. Pathfinder Networks are very important in the field of social networks, in which it helps to exhibit a unique representation of the underlying structure of the domain. In this context, the weight of the edges often represents the similarity between the entities given by the nodes.

According to the litterature, the most used values for its parameters are r=∞, meaning that we keep the edges having a value higher that the maximum similarity given by all the other paths, and q=n-1, meaning that we consider the paths having any kind of lengths, including the maximal one, n-1.

MST-Pathfinder, up to our knowledge, is the fastest algorithm to obtain Pathfinder Networks for r=∞ and q=n-1.

Applications

These networks are used in a large variety of applications including:

• Co-citation analysis (Buzydlowski, 2002)
• Latent knowledge visualization (Chen et al., 2001)
• Scientific domain visualization (Chen, 1998a)
• Communication networks (Shope et al., 2004)
• Animated visualization models of toxins (Chen & Morris, 2003)
• Mental models (Kudikyala & Vaughn, 2005)
• Debugging multi-agent systems (Serrano, 2010)
• and more recently the co-firing of rules in fuzzy systems (Alonso, 2012)

Additional information on Pathfinder Networks can be found on the corresponding Wikipedia webpage: http://en.wikipedia.org/wiki/Pathfinder_networks

The following table shows a comparison of the variants of the Pathfinder algorithm, along with their performance in terms of time and memory, took from the paper [3]:

Source code

Mst-Pathfinder: download link

Fast-Pathfinder: download link

Example of maps: download link

[1] R. W. Schvaneveldt (Ed.); Pathfinder Associative Networks: Studies in Knowledge Organization; Norwood, NJ: Ablex (1990). 
RECEIVED: 16/4/2007; REVI

[2] A. Quirin, O. Cordon, J. Santamaria, B. Vargas-Quesada, F. Moya-Anegon; A new Variant of the Pathfinder Algorithm to Generate Large Visual Science Maps in Cubic Time; Information, Processing & Management Journal, 44(4): 1611-1623 (2008). 
RECEIVED: 16/4/2007; REVISED: 3/9/2007; ACCEPTED: 8/9/2007; IMPACT FACTOR 2007: 1.500.; CATEGORY: COMP. SCI., INF. SYST; ORDER: 27/92; DOI:10.1016/j.ipm.2007.09.005

[3] A. Quirin, O. Cordon, V. P. Guerrero-Bote, B. Vargas-Quesada, F. Moya-Anegon; A Quick MST-based Algorithm to Obtain Pathfinder Networks; Journal of the American Society for Information Science and Technology, 59(12): 1912-1924 (2008).

[4] E. Serrano, A. Quirin, J. Botia, O. Cordon; Debugging Complex Software Systems by Means of Pathfinder Networks; Information Sciences, 180(5): 561-583 (2010).
NOTIFICATION OF ACCEPTANCE: 3/11/2009; IMPACT FACTOR 2009: 3.291; DOI: 10.1016/j.ins.2009.11.007