Nonlinear Dimensionality Reduction for Data Visualization: An Unsupervised Fuzzy Rule-based Approach

Here, we propose an unsupervised fuzzy rule-based dimensionality reduction method primarily for data visualization. It considers the following important issues relevant to dimensionality reduction-based data visualization: (i) preservation of neighborhood relationships, (ii) handling data on a non-linear manifold, (iii) the capability of predicting projections for new test data points, (iv) interpretability of the system, and (v) the ability to reject test points if required. For this, we use a first-order Takagi-Sugeno type model. We generate rule antecedents using clusters in the input data. In this context, we also propose a new variant of the Geodesic c-means clustering algorithm. We estimate the rule parameters by minimizing an error function that preserves the inter-point geodesic distances (distances over the manifold) as Euclidean distances on the projected space. We apply the proposed method on three synthetic and three real-world data sets and visually compare the results with four other standard data visualization methods. The obtained results show that the proposed method behaves desirably and performs better than or comparable to the methods compared with. The proposed method is found to be robust to the initial conditions. The predictability of the proposed method for test points is validated by experiments. We also assess the ability of our method to reject output points when it should. Then, we extend this concept to provide a general framework for learning an unsupervised fuzzy model for data projection with different objective functions. To the best of our knowledge, this is the first attempt to manifold learning using unsupervised fuzzy modeling

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

MEDVIR: 3D visual interface applied to gene profile analisys.

The origins for this work arise in response to the increasing need for biologists and doctors to obtain tools for visual analysis of data. When dealing with multidimensional data, such as medical data, the traditional data mining techniques can be a tedious and complex task, even to some medical experts. Therefore, it is necessary to develop useful visualization techniques that can complement the expert’s criterion, and at the same time visually stimulate and make easier the process of obtaining knowledge from a dataset. Thus, the process of interpretation and understanding of the data can be greatly enriched. Multidimensionality is inherent to any medical data, requiring a time-consuming effort to get a clinical useful outcome. Unfortunately, both clinicians and biologists are not trained in managing more than four dimensions. Specifically, we were aimed to design a 3D visual interface for gene profile analysis easy in order to be used both by medical and biologist experts. In this way, a new analysis method is proposed: MedVir. This is a simple and intuitive analysis mechanism based on the visualization of any multidimensional medical data in a three dimensional space that allows interaction with experts in order to collaborate and enrich this representation. In other words, MedVir makes a powerful reduction in data dimensionality in order to represent the original information into a three dimensional environment. The experts can interact with the data and draw conclusions in a visual and quickly way