Abstract
A multivariate outlier detection method for interval data is proposed that makes use of a parametric approach to model the interval data. The trimmed maximum likelihood principle is adapted in order to robustly estimate the model parameters. A simulation study demonstrates the usefulness of the robust estimates for outlier detection, and new diagnostic plots allow gaining deeper insight into the structure of real world interval data.

Abstract
Interval time series occur when real intervals of some variable of interest are registered as an ordered sequence along time. We address the problem of clustering interval time series (ITS), for which different approaches are proposed. First, clustering is performed based on point-to-point comparisons. Time-domain and wavelet features also serve as clustering variables in alternative approaches. Furthermore, autocorrelation matrix functions, gathering the autocorrelation and cross-correlation functions of the ITS upper and lower bounds, may be compared using adequate distances (e.g. the Frobenius distance) and used for clustering ITS. An improved procedure to determine the autocorrelation function of ITS is proposed, which also serves as a basis for clustering. The different alternative approaches are explored and their performances compared for ITS simulated under different setups. An application to sea level daily ranges, observed at different locations in Australia, illustrates the proposed methods.

Abstract
In this work we seek clusters of genomic words in human DNA by studying their inter-word lag distributions. Due to the particularly spiked nature of these histograms, a clustering procedure is proposed that first decomposes each distribution into a baseline and a peak distribution. An outlier-robust fitting method is used to estimate the baseline distribution (the 'trend'), and a sparse vector of detrended data captures the peak structure. A simulation study demonstrates the effectiveness of the clustering procedure in grouping distributions with similar peak behavior and/or baseline features. The procedure is applied to investigate similarities between the distribution patterns of genomic words of lengths 3 and 5 in the human genome. These experiments demonstrate the potential of the new method for identifying words with similar distance patterns.

Abstract
Community detection techniques use only the information about the network topology to find communities in networks Similarly, classic clustering techniques for vector data consider only the information about the values of the attributes describing the objects to find clusters. In real-world networks, however, in addition to the information about the network topology, usually there is information about the attributes describing the vertices that can also be used to find communities. Using both the information about the network topology and about the attributes describing the vertices can improve the algorithms' results. Therefore, authors started investigating methods for community detection in attributed networks. In the past years, several methods were proposed to uncover this task, partitioning a graph into sub-graphs of vertices that are densely connected and similar in terms of their descriptions. This article focuses on the analysis and comparison of some of the proposed methods for community detection in attributed networks. For that purpose, several applications to both synthetic and real networks are conducted. Experiments are performed on both weighted and unweighted graphs. The objective is to establish which methods perform generally better according to the validation measures and to investigate their sensitivity to changes in the networks' structure and homogeneity.

Abstract
We address classification of distributional data, where units are described by histogram or interval-valued variables. The proposed approach uses a linear discriminant function where distributions or intervals are represented by quantile functions, under specific assumptions. This discriminant function allows defining a score for each unit, in the form of a quantile function, which is used to classify the units in two a priori groups, using the Mallows distance. There is a diversity of application areas for the proposed linear discriminant method. In this work we classify the airline companies operating in NY airports based on air time and arrival/departure delays, using a full year flights.

Abstract
We compare two interval time series (ITS) by testing whether their underlying distributions are significantly different or not. To perform hypothesis testing, we make use of the discrete wavelet transform (DWT) which decomposes a time series into a set of coefficients over a number of frequency bands or scales. We obtain the DWT of the radius and centre of each of the two ITS at different scales, and perform randomisation tests. In order to use a randomisation test, the observations must be uncorrelated; this condition is more or less satisfied since at each scale, the DWT coefficients are approximately uncorrelated with each other. Our proposed test statistic is the ratio of the determinants of the covariance matrix of radius and centre DWTs of the two ITS, at each scale. This test statistic ensures that the variability between the upper and lower bounds of each ITS is encompassed. Simulation studies conducted to evaluate the performance of the test show reasonably good estimates of size and power under most conditions, and applications to real interval time series reveal the practical usefulness of this test.