A robust nonlinear projection method using the neural gas network

A robust nonlinear projection method based on self-organizing neural networks is proposed. The neural gas algorithm along with the competitive Hebbian learning rule are used to quantize the data samples and construct a neighborhood graph in input space. The resulting graph is used to estimate geodesic distances. The proposed projection method minimizes a cost function that depends on the interpoint distances, and favors local topologies. The projection is done in two steps to avoid errors due to shortcuts in the neighborhood graph when dealing with noisy and/or non-uniformly distributed data sets. The proposed nonlinear projection method outperformed alternative methods such as curvilinear distance analysis and geodesic nonlinear projection in terms of trustworthiness, continuity and topology preservation measurements, using two benchmark data sets: noisy Swiss Roll and Iris.