To cluster the 6-digit postal codes into homogeneous lifestyle groups, Manifold combined the projective adaptive resonance theory with an enhanced K-means clustering and fuzzy logic and incorporated them into a hierarchical clustering technique. The fuzzy clustering evaluates the probabilities of an object belonging to one or more clusters, which reflects the behavior of many consumers, particularly those similar to the average Canadian.

Using principal component analysis, Manifold reduced dimension of the input data from 10,000+ to a few dozen and ran a fuzzy K-means method for a series of number of clusters iteratively. At each step, the initial seeds of clusters were carefully selected so that outliers and small clusters are separated in the clustering process.

To determine the optimal number of clusters, Manifold examined the local peaks of the pseudo F-statistics: the ratio of between cluster variance and within cluster variance. Manifold also looked at peaks of the cubic clustering criterion (CCC) and developed proprietary statistical measures which have been published in scientific journals and conference proceedings.

Manifold validated the clusters with both in-time and out-time surveys and historical Census data.

More details on Manifold’s initial framework for clustering analysis is available in the following scientific publications:

1. A Fuzzy Clustering Based Algorithm for Feature Selection.Machine Learning and Cybernetics. Page(s): 1993 – 1998 Vol.4 4-5 Nov. 2002
2. A New Validation Index for Determining the Number of Clusters in a Data Set Proceeding of INNS-IEEE Conference on Neural Networks (Washington DC). Page(s): 1852-1857, 2001.
3. FCM-based Model Selection Algorithms for Determining the Number of Clusters Pattern Recognition, vol. 37, no. 10, pp. 2027-3037, October 2004.
4. Measurement Based Traffic Prediction Using Fuzzy Logic IEEE CCECE2002. Canadian Conference on Electrical and Computer Engineering. Conference Proceedings (Cat. No.02CH37373), Winnipeg, Manitoba, Canada, 2002, pp. 834-840 vol.2.
5. A Fuzzy Dynamic Bandwidth Re-allocator IEEE CCECE2002. Canadian Conference on Electrical and Computer Engineering. Conference Proceedings (Cat. No.02CH37373), Winnipeg, Manitoba, Canada, 2002, pp. 815-822 vol.2.