Frank Rehm

A Novel Approach to Noise Clustering for Outlier Detection

Noise clustering, as a robust clustering method, performs partitioning of data sets reducing errors caused by outliers. Noise clustering defines outliers in terms of a certain distance, which is called noise distance. The probability or membership degree of data points belonging to the noise cluster increases with their distance to regular clusters. The main purpose of noise clustering is to reduce the influence of outliers on the regular clusters. The emphasis is not put on exactly identifying outliers. However, in many applications outliers contain important information and their correct identification is crucial. In this paper we present a method to estimate the noise distance in noise clustering based on the preservation of the hypervolume of the feature space. Our examples will demonstrate the efficiency of this approach.

Clustering of Flight Tracks

Airports are experiencing heavy capacity utilization leading to increased airport congestion and delay. It is therefore of great interest to identify the source of deficiencies in order to apply mitigation measures at the right place. Regarding the airside airport capacity, it is of concern to estimate practicable (or unimpeded) arrival times for arriving aircraft. In this paper we describe how prevalent flight routes can be found automatically out of a comprehensive set of arrival flight trajectories. By means of the proposed procedure, mean arrival routes can be determined for different runway configurations and different airports, which can facilitate the airport performance assessment.

MDS polar : a new approach for dimension reduction to visualize high dimensional data

Many applications in science and business such as signal analysis or costumer segmentation deal with large amounts of data which are usually high dimensional in the feature space. As a part of preprocessing and exploratory data analysis, visualization of the data helps to decide which kind of method probably leads to good results. Since the visual assessment of a feature space that has more than three dimensions is not possible, it becomes necessary to find an appropriate visualization scheme for such datasets. In this paper we present a new approach for dimension reduction to visualize high dimensional data. Our algorithm transforms high dimensional feature vectors into two-dimensional feature vectors under the constraints that the length of each vector is preserved and that the angles between vectors approximate the corresponding angles in the high dimensional space as good as possible, enabling us to come up with an efficient computing scheme.

Learning methods for air traffic management

Weather is an important source of delay for aircraft. Recent studies have shown that certain weather factors have significant influence on air traffic. More than 50% of all delay accounts to weather and causes among others high costs to airlines and passengers. In this work we will show to what extent weather factors in the closer region of Frankfurt Airport have an impact on the delay of flights. Besides the results of a linear regression model we will also present the results of some modern data mining approaches, such as regression trees and fuzzy clustering techniques. With the clustering approach we will show that several weather conditions have a similar influence on the delay of flights. Our analyses focus on the delay that will be explicitly caused by weather factors in the vicinity of the airport, the so-called terminal management area (TMA). Thus, delay caused by weather at the departure airport or by other circumstances during the flight will not bias our results. With our methods it becomes possible to predict the delay of flights if certain weather factors are known. We will specify these factors and quantify their effects on delay.

POLARMAP - Efficient Visualisation of High Dimensional Data

Multidimensional scaling provides low-dimensional visualisation of high-dimensional feature vectors. This is a very important step in data preprocessing because it helps the user to appraise which methods to use for further data analysis. But a well known problem with conventional MDS is the quadratic need of space and time. Beside this, a transformation of MDS must be completely recomputed if additional feature vectors have to be considered. The POLARMAP algorithm, presented in this paper, learns a function, similar to NeuroScale, but with lower computational costs, that maps high-dimensional feature vectors to a 2-dimensional feature space. With the obtained function even new feature vectors can be mapped to the target space

Modern Data Visualization for Air Traffic Management

Air traffic at airports is affected by various factors. The capacity of an airport and the demand at a certain point in time are serious parameters that account for a big extent to aircraft delay and related variables. It has been proven that weather is another important impact in this regard. Although weather cannot be controlled, the knowledge of how weather affects the air traffic at an airport can be very helpful to optimize air traffic management. Data mining promises to gain that knowledge. Usually, the very first step in data mining is data visualization. In this paper we discuss two new visualization techniques that allow to visualize aviation data and weather data in order to contribute to the optimization process. These modern multi-dimensional scaling techniques provide mappings of high-dimensional data to low-dimensional feature spaces. We will show some results on a practical application of a major European airport.

Prediction of Aircraft Flight Duration

Abstract Weather is one of the most impacting sources of delay in terms of air traffic. Many applications have shown that the use of weather forecast enables the airport controllers to improve the efficiency and the safety of an airport. To date, it is still challenging to analyse a set of weather factors to predict the airports capacity or the travel time of single aircraft. Mostly, this is due to the high complexity of the data. In this paper the results of an application that visualises complex weather data and its impact on air traffic are shown. Support Vector Regression (SVR) is then applied to demonstrate the prediction of aircraft flight duration by means of a modern nonlinear statistical technique.

Clustering with Repulsive Prototypes

Although there is no exact definition for the term cluster, in the 2D case, it is fairly easy for human beings to decide which objects belong together. For machines on the other hand, it is hard to determine which objects form a cluster. Depending on the problem, the success of a clustering algorithm depends on the idea of their creators about what a cluster should be. Likewise, each clustering algorithm comprises a characteristic idea of the term cluster. For example the fuzzy c-means algorithm (Kruse et al., Advances in Fuzzy Clustering and Its Applications, Wiley, New York, 2007, pp. 3–30; Hoppner et al., Fuzzy Clustering, Wiley, Chichester, 1999) tends to find spherical clusters with equal numbers of objects. Noise clustering (Rehm et al., Soft Computing – A Fusion of Foundations, Methodologies and Applications 11(5):489–494) focuses on finding spherical clusters of user-defined diameter. In this paper, we present an extension to noise clustering that tries to maximize the distances between prototypes. For that purpose, the prototypes behave like repulsive magnets that have an inertia depending on their sum of membership values. Using this repulsive extension, it is possible to prevent that groups of objects are divided into more than one cluster. Due to the repulsion and inertia, we show that it is possible to determine the number and approximate position of clusters in a data set.

VISUALIZATION OF FUZZY CLASSIFIERS

This paper presents different techniques to visualize high-dimensional fuzzy rule bases in relation to the classified data. The degree of membership to influential rules can be visualized for an entire data set. This enables the observer to detect conflicting or error-prone rules as well as misclassified feature vectors. Results are shown on a benchmark data set and on a weather data set that is used to predict flight durations on a major European airport.

Visualization of single clusters

Evaluation of clustering partitions is a crucial step in data processing. A multitude of measures exists, which – unfortunately – give for one data set various results. In this paper we present a visualization technique to visualize single clusters of high-dimensional data. Our method maps single clusters to the plane trying to preserve membership degrees that describe a data points gradual membership to a certain cluster. The resulting scatter plot illustrates separation of the respecting cluster and the need of additional prototypes as well. Since clusters will be visualized individually, additional prototypes can be added locally where they are needed.