Multidimensional Scaling Using Artificial Neural Networks

Abstract

Manifold Learning has been widely exploited in the arena of data analysis, machine learning and pattern recognition. The main assumption behind manifold learning is that the input high-dimensional data lies intrinsically on a low-dimensional manifold. This technique is to be used for non-linear dimensionality reduction. Although there are very well known dimensionality reduction techniques are already designed such as Principal Component Analysis (PCA), Independent Component Analysis, Linear Discriminant Analysis, and others but they are unable to capture the non linear structure of the data so that researchers are interested in this area. After that many manifold learning algorithms are developed such as Multidimensional Scaling (MDS), Locally linear embedding (LLE), Hessian Eigenmapping, t-distributed Stochastic Neighbor Embedding (t-SNE) etc. Multidimensional Scaling is one of them that seeks vectorial representation of the data points given the pairwise distance between the data points.There are two variant of Multidimensional Scaling one is metric Multidimensional Scaling and other is non-metric Multidimensional Scaling. Our interest on metric Multidimensional Scaling. The methodologies that are available to implement classical metric-MDS boil down to finding eigen values and eigen vectors of some matrix and which is computationally difficult for large dimensional matrix that motivate us to implement it using neural network setup. We are implementing it using Artificial Neural Networks and experiment it on famous Iris and Wine datasets and compare our results with some existing methods on few other datasets also.