Performance Comparison of Nonlinear Dimensionality Reduction Methods for Image Data Using Different Distance Measures

During recent years a special class of nonlinear dimensionality reduction (NLDR) methods known as manifold learning methods, obtain a lot of attention for low dimension representation of high dimensional data. Most commonly used NLDR methods like Isomap, locally linear embedding, local tangent space alignment, Hessian locally linear embedding, Laplacian eigenmaps and diffusion maps, construct their logic on finding neighborhood points of every data point in high dimension space. These algorithms use Euclidean distance as measurement metric for distance between two data points. In literature different (dis)similarity measures are available for measuring distances between two data points/images. In this paper the authors made a systematic comparative analysis for performance of different NLDR algorithms in reducing high dimensional image data into a low dimensional 2D data using different distance measures. The performance of an algorithm is measured by the fact that how successfully it preserves intrinsic geometry of high dimensional manifold. Visualization of low dimensional data reveals the original structure of high dimensional data.