Geodesic distances in the maximum likelihood estimator of intrinsic dimensionality

While analyzing multidimensional data, we often have to reduce their dimensionality so that to preserve as much information on the analyzed data set as possible. To this end, it is reasonable to find out the intrinsic dimensionality of the data. In this paper, two techniques for the intrinsic dimensionality are analyzed and compared, i.e., the maximum likelihood estimator (MLE) and ISOMAP method. We also propose the way how to get good estimates of the intrinsic dimensionality by the MLE method

Geodesic distances in the intrinsic dimensionality estimation using packing numbers

Dimensionality reduction is a very important tool in data mining. An intrinsic dimensionality of a data set is a key parameter in many dimensionality reduction algorithms. When the intrinsic dimensionality of a data set is known, it is possible to reduce the dimensionality of the data without losing much information. To this end, it is reasonable to find out the intrinsic dimensionality of the data. In this paper, one of the global estimators of intrinsic dimensionality, the packing numbers estimator (PNE), is explored experimentally. We propose the modification of the PNE method that uses geodesic distances in order to improve the estimates of the intrinsic dimensionality by the PNE method

Using topology preservation measures for high-dimensional data analysis in a reduced feature space

This paper deals with high-dimensional data analysis accomplished through supplementing standard feature extraction procedures with topology preservation measures. This approach is based on an observation that not all elements of an initial dataset are equally preserved in its low-dimensional embedding space representation. The contribution first overviews existing topology preservation measures, then their inclusion in the classical methods of exploratory data analysis is discussed. Finally, some illustrative examples of presented approach in the tasks of cluster analysis and classification are given

A methodology to compare dimensionality reduction algorithms in terms of loss of quality

Dimensionality Reduction (DR) is attracting more attention these days as a result of the increasing need to handle huge amounts of data effectively. DR methods allow the number of initial features to be reduced considerably until a set of them is found that allows the original properties of the data to be kept. However, their use entails an inherent loss of quality that is likely to affect the understanding of the data, in terms of data analysis. This loss of quality could be determinant when selecting a DR method, because of the nature of each method. In this paper, we propose a methodology that allows different DR methods to be analyzed and compared as regards the loss of quality produced by them. This methodology makes use of the concept of preservation of geometry (quality assessment criteria) to assess the loss of quality. Experiments have been carried out by using the most well-known DR algorithms and quality assessment criteria, based on the literature. These experiments have been applied on 12 real-world datasets. Results obtained so far show that it is possible to establish a method to select the most appropriate DR method, in terms of minimum loss of quality. Experiments have also highlighted some interesting relationships between the quality assessment criteria. Finally, the methodology allows the appropriate choice of dimensionality for reducing data to be established, whilst giving rise to a minimum loss of quality