Multi-dimensional scaling with non-repeating random paths

Triadic comparisons can be used to create similarity or dissimilarity matrices for multi-dimensional scaling. The number of judgments to be performed grows rapidly with increasing numbers of input items or stimuli. Balanced incomplete block designs have been used to specify the number of times a given pair of items occurs in order to reduce the overall number of judgments. This paper proposes using a set of non-repeating random paths to sample a given set of samples. This sampling scheme can be used to efficiently distribute the total number of dissimilarity judgments among a large number of observers. This paper applies the non-repeating random path sampling, a special form of random walks sampling to a web-based color name similarity experiment. The results are then compared to a parallel laboratory study using a complete set of triads and a smaller number of observers.