Dimensionality Reduction Mappings

A wealth of powerful dimensionality reduction methods has been established which can be used for data visualization and preprocessing. These are accompanied by formal evaluation schemes, which allow a quantitative evaluation along general principles and which even lead to further visualization schemes based on these objectives. Most methods, however, provide a mapping of a priorly given finite set of points only, requiring additional steps for out-of-sample extensions. We propose a general view on dimensionality reduction based on the concept of cost functions, and, based on this general principle, extend dimensionality reduction to explicit mappings of the data manifold. This offers simple out-of-sample extensions. Further, it opens a way towards a theory of data visualization taking the perspective of its generalization ability to new data points. We demonstrate the approach based on a simple global linear mapping as well as prototype-based local linear mappings.

Some steps towards a general principle for dimensionality reduction mappings

In the past years, many dimensionality reduction methods have been established which allow to visualize high dimensional data sets. Recently, also formal evaluation schemes have been proposed for data visualization, which allow a quantitative evaluation along general principles. Most techniques provide a mapping of a priorly given finite set of points only, requiring additional steps for out-of-sample extensions. We propose a general view on dimensionality reduction based on the concept of cost functions, and, based on this general principle, extend dimensionality reduction to explicit mappings of the data manifold. This offers the possibility of simple out-of-sample extensions. Further, it opens a way towards a theory of data visualization taking the perspective of its generalization ability to new data points. We demonstrate the approach based in a simple example

Manifold Alignment Aware Ants:a Markovian process for manifold extraction

Dimensionality reduction and clustering are often used as preliminary steps for many complex machine learning tasks. The presence of noise and outliers can deteriorate the performance of such preprocessing and therefore impair the subsequent analysis tremendously. In manifold learning, several studies indicate solutions for removing background noise or noise close to the structure when the density is substantially higher than that exhibited by the noise. However, in many applications, including astronomical datasets, the density varies alongside manifolds that are buried in a noisy background. We propose a novel method to extract manifolds in the presence of noise based on the idea of Ant colony optimization. In contrast to the existing random walk solutions, our technique captures points which are locally aligned with major directions of the manifold. Moreover, we empirically show that the biologically inspired formulation of ant pheromone reinforces this behavior enabling it to recover multiple manifolds embedded in extremely noisy data clouds. The algorithm's performance is demonstrated in comparison to the state-of-the-art approaches, such as Markov Chain, LLPD, and Disperse, on several synthetic and real astronomical datasets stemming from an N-body simulation of a cosmological volum

Visualization and knowledge discovery from interpretable models

Increasing number of sectors which affect human lives, are using Machine Learning (ML) tools. Hence the need for understanding their working mechanism and evaluating their fairness in decision-making, are becoming paramount, ushering in the era of Explainable AI (XAI). So, in this contribution we introduced a few intrinsically interpretable models which are also capable of dealing with missing values, in addition to extracting knowledge from the dataset and about the problem, and visualisation of the classifier and decision boundaries: angle based variants of Learning Vector Quantization. The performance of the developed classifiers were comparable to those reported in literature for UCI’s heart disease dataset treated as a binary class problem. The newly developed classifiers also helped investigating the complexities of this dataset as a multiclass proble

Range-Only Bearing Estimator for Localization and Mapping

Navigation and exploration within unknown environments are typical examples in which simultaneous localization and mapping (SLAM) algorithms are applied. When mobile agents deploy only range sensors without bearing information, the agents must estimate the bearing using the online distance measurement for the localization and mapping purposes. In this paper, we propose a scalable dynamic bearing estimator to obtain the relative bearing of the static landmarks in the local coordinate frame of a moving agent in real-time. Using contraction theory, we provide convergence analysis of the proposed range-only bearing estimator and present upper and lower-bound for the estimator gain. Numerical simulations demonstrate the effectiveness of the proposed method