Nonlinear Intrinsic Dimensionality Computations

In pattern recognition, the raw data and dimensionality of the measurement space is usually very large. Therefore, some form of dimensionality reduction has been commonly considered as a practical preprocessing method for feature selection. Based on a method that increases the variance while maintaining local structure, a technique is developed to determine intrinsic dimensionality. A cost function is introduced to guide the maintenance of the rank order and therefore local structure. Two criteria of using the cost function to increase the variance have been introduced. Several methods of defining the local regions are suggested. A program is implemented and tested to find the intrinsic dimensionality of a variety of experimental data.