Incorporating visualisation quality measures to curvilinear component analysis

Curvilinear Component Analysis (CCA) is a useful data visualisation method. CCA has the technical property that its optimisation surface, as defined by its stress function, changes during the optimisation according to a decreasing parameter. CCA uses a variant of the stochastic gradient descent method to create a mapping of data. In the optimisation method of CCA, the stress function is only a general guide towards an acceptable mapping. In other multidimensional scaling methods such as Sammon's mapping, the best mapping among multiple runs from different initialisations can be chosen by selecting the mapping with the lowest stress, whereas in CCA the embedding is simply the result of one run, surely we can have multiple starts. As a consequence of the absence of an objective function to be used as a selection criterion, embedding made by CCA can be poorly optimised. In this paper we present a new way of improving the optimisation of CCA by integrating non-stress data visualisation quality measures into the existing algorithm. We first use data visualisation quality measures to select the best mapping from multiple runs of a standard stochastic gradient descent implementation; then we tune various parameters involved to achieve further enhancement. A brief comparison with other dimensionality reduction methods is included.