arXiv subjects

Peter Filzmoser

Publications and source records attributed to Peter Filzmoser.

At least 37 records · Page 2Linked to original sources

arXiv2023

Spatially smoothed robust covariance estimation for local outlier detection

Most multivariate outlier detection procedures ignore the spatial dependency of observations, which is present in many real data sets from various application areas. This paper introduces a new outlier detection method that accounts for a (continuously) varying covariance structure, depending on the spatial neighborhood of the observations. The underlying estimator thus constitutes a compromise between a unified global covariance estimation, and local covariances estimated for individual neighborhoods. Theoretical properties of the estimator are presented, in particular related to robustness properties, and an efficient algorithm for its computation is introduced. The performance of the method is evaluated and compared based on simulated data and for a data set recorded from Austrian weather stations.

stat.ME↗

arXiv2022

Multivariate outlier explanations using Shapley values and Mahalanobis distances

For the purpose of explaining multivariate outlyingness, it is shown that the squared Mahalanobis distance of an observation can be decomposed into outlyingness contributions originating from single variables. The decomposition is obtained using the Shapley value, a well-known concept from game theory that became popular in the context of Explainable AI. In addition to outlier explanation, this concept also relates to the recent formulation of cellwise outlyingness, where Shapley values can be employed to obtain variable contributions for outlying observations with respect to their "expected" position given the multivariate data structure. In combination with squared Mahalanobis distances, Shapley values can be calculated at a low numerical cost, making them even more attractive for outlier interpretation. Simulations and real-world data examples demonstrate the usefulness of these concepts.

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arXiv2022

Robust and Sparse Multinomial Regression in High Dimensions

A robust and sparse estimator for multinomial regression is proposed for high dimensional data. Robustness of the estimator is achieved by trimming the observations, and sparsity of the estimator is obtained by the elastic net penalty, which is a mixture of $L_1$ and $L_2$ penalties. From this point of view, the proposed estimator is an extension of the enet-LTS estimator \citep{Kurnaz18} for linear and logistic regression to the multinomial regression setting. After introducing an algorithm for its computation, a simulation study is conducted to show the performance in comparison to the non-robust version of the multinomial regression estimator. Some real data examples underline the usefulness of this robust estimator.

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arXiv2022

Visual Parameter Selection for Spatial Blind Source Separation

Analysis of spatial multivariate data, i.e., measurements at irregularly-spaced locations, is a challenging topic in visualization and statistics alike. Such data are integral to many domains, e.g., indicators of valuable minerals are measured for mine prospecting. Popular analysis methods, like PCA, often by design do not account for the spatial nature of the data. Thus they, together with their spatial variants, must be employed very carefully. Clearly, it is preferable to use methods that were specifically designed for such data, like spatial blind source separation (SBSS). However, SBSS requires two tuning parameters, which are themselves complex spatial objects. Setting these parameters involves navigating two large and interdependent parameter spaces, while also taking into account prior knowledge of the physical reality represented by the data. To support analysts in this process, we developed a visual analytics prototype. We evaluated it with experts in visualization, SBSS, and geochemistry. Our evaluations show that our interactive prototype allows to define complex and realistic parameter settings efficiently, which was so far impractical. Settings identified by a non-expert led to remarkable and surprising insights for a domain expert. Therefore, this paper presents important first steps to enable the use of a promising analysis method for spatial multivariate data.

cs.HC↗

arXiv2022

Identifying the root cause of cable network problems with machine learning

Good quality network connectivity is ever more important. For hybrid fiber coaxial (HFC) networks, searching for upstream high noise in the past was cumbersome and time-consuming. Even with machine learning due to the heterogeneity of the network and its topological structure, the task remains challenging. We present the automation of a simple business rule (largest change of a specific value) and compare its performance with state-of-the-art machine-learning methods and conclude that the precision@1 can be improved by 2.3 times. As it is best when a fault does not occur in the first place, we secondly evaluate multiple approaches to forecast network faults, which would allow performing predictive maintenance on the network.

cs.NI↗

arXiv2022

TBSSvis: Visual Analytics for Temporal Blind Source Separation

Temporal Blind Source Separation (TBSS) is used to obtain the true underlying processes from noisy temporal multivariate data, such as electrocardiograms. TBSS has similarities to Principal Component Analysis (PCA) as it separates the input data into univariate components and is applicable to suitable datasets from various domains, such as medicine, finance, or civil engineering. Despite TBSS's broad applicability, the involved tasks are not well supported in current tools, which offer only text-based interactions and single static images. Analysts are limited in analyzing and comparing obtained results, which consist of diverse data such as matrices and sets of time series. Additionally, parameter settings have a big impact on separation performance, but as a consequence of improper tooling, analysts currently do not consider the whole parameter space. We propose to solve these problems by applying visual analytics (VA) principles. Our primary contribution is a design study for TBSS, which so far has not been explored by the visualization community. We developed a task abstraction and visualization design in a user-centered design process. Task-specific assembling of well-established visualization techniques and algorithms to gain insights in the TBSS processes is our secondary contribution. We present TBSSvis, an interactive web-based VA prototype, which we evaluated extensively in two interviews with five TBSS experts. Feedback and observations from these interviews show that TBSSvis supports the actual workflow and combination of interactive visualizations that facilitate the tasks involved in analyzing TBSS results.

cs.HC↗

arXiv2022

Compositional Cubes: A New Concept for Multi-factorial Compositions

Compositional data are commonly known as multivariate observations carrying relative information. Even though the case of vector or even two-factorial compositional data (compositional tables) is already well described in the literature, there is still a need for a comprehensive approach to the analysis of multi-factorial relative-valued data. Therefore, this contribution builds around the current knowledge about compositional data a general theory of work with k-factorial compositional data. As a main finding it turns out that similar to the case of compositional tables also the multi-factorial structures can be orthogonally decomposed into an independent and several interactive parts and, moreover, a coordinate representation allowing for their separate analysis by standard analytical methods can be constructed. For the sake of simplicity, these features are explained in detail for the case of three-factorial compositions (compositional cubes), followed by an outline covering the general case. The three-dimensional structure is analysed in depth in two practical examples, dealing with systems of spatial and time dependent compositional cubes. The methodology is implemented in the R package robCompositions.

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arXiv2022

Extending compositional data analysis from a graph signal processing perspective

Traditional methods for the analysis of compositional data consider the log-ratios between all different pairs of variables with equal weight, typically in the form of aggregated contributions. This is not meaningful in contexts where it is known that a relationship only exists between very specific variables (e.g.~for metabolomic pathways), while for other pairs a relationship does not exist. Modeling absence or presence of relationships is done in graph theory, where the vertices represent the variables, and the connections refer to relations. This paper links compositional data analysis with graph signal processing, and it extends the Aitchison geometry to a setting where only selected log-ratios can be considered. The presented framework retains the desirable properties of scale invariance and compositional coherence. An additional extension to include absolute information is readily made. Examples from bioinformatics and geochemistry underline the usefulness of thisapproach in comparison to standard methods for compositional data analysis.

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arXiv2021

Spatial Blind Source Separation in the Presence of a Drift

Multivariate measurements taken at different spatial locations occur frequently in practice. Proper analysis of such data needs to consider not only dependencies on-sight but also dependencies in and in-between variables as a function of spatial separation. Spatial Blind Source Separation (SBSS) is a recently developed unsupervised statistical tool that deals with such data by assuming that the observable data is formed by a linear latent variable model. In SBSS the latent variable is assumed to be constituted by weakly stationary random fields which are uncorrelated. Such a model is appealing as further analysis can be carried out on the marginal distributions of the latent variables, interpretations are straightforward as the model is assumed to be linear, and not all components of the latent field might be of interest which acts as a form of dimension reduction. The weakly stationarity assumption of SBSS implies that the mean of the data is constant for all sample locations, which might be too restricting in practical applications. Therefore, an adaptation of SBSS that uses scatter matrices based on differences was recently suggested in the literature. In our contribution we formalize these ideas, suggest an adapted SBSS method and show its usefulness on synthetic and real data.

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arXiv2020

The impact of COVID-19 on relative changes in aggregated mobility using mobile-phone data

Evaluating relative changes leads to additional insights which would remain hidden when only evaluating absolute changes. We analyze a dataset describing mobility of mobile phones in Austria before, during COVID-19 lock-down measures until recent. By applying compositional data analysis we show that formerly hidden information becomes available: we see that the elderly population groups increase relative mobility and that the younger groups especially on weekends also do not decrease their mobility as much as the others.

physics.soc-ph↗

arXiv2020

A Robust Adaptive Modified Maximum Likelihood Estimator for the Linear Regression Model

In linear regression, the least squares (LS) estimator has certain optimality properties if the errors are normally distributed. This assumption is often violated in practice, partly caused by data outliers. Robust estimators can cope with this situation and thus they are widely used in practice. One example of robust estimators for regression are adaptive modified maximum likelihood (AMML) estimators (Donmez, 2010). However, they are not robust to $x$ outliers, so-called leverage points. In this study, we propose a new regression estimator by employing an appropriate weighting scheme in the AMML estimation method. The resulting estimator is called robust AMML (RAMML) since it is not only robust to y outliers but also to x outliers. A simulation study is carried out to compare the performance of the RAMML estimator with some existing robust estimators such as MM, least trimmed squares (LTS) and S. The results show that the RAMML estimator is preferable in most settings according to the mean squared error (MSE) criterion. Two data sets taken from the literature are also analyzed to show the implementation of the RAMML estimation methodology.

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arXiv2020

Robust multivariate methods in Chemometrics

This chapter presents an introduction to robust statistics with applications of a chemometric nature. Following a description of the basic ideas and concepts behind robust statistics, including how robust estimators can be conceived, the chapter builds up to the construction (and use) of robust alternatives for some methods for multivariate analysis frequently used in chemometrics, such as principal component analysis and partial least squares. The chapter then provides an insight into how these robust methods can be used or extended to classification. To conclude, the issue of validation of the results is being addressed: it is shown how uncertainty statements associated with robust estimates, can be obtained.

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arXiv2020

A method to identify geochemical mineralization on linear transect

Mineral exploration in biogeochemistry is related to the detection of anomalies in soil, which is driven by many factors and thus a complex problem. Mikšová, Rieser, and Filzmoser (2019) have introduced a method for the identification of spatial patterns with increased element concentrations in samples along a linear sampling transect. This procedure is based on fitting Generalized Additive Models (GAMs) to the concentration data, and computing a curvature measure from the pairwise log-ratios of these fits. The higher the curvature, the more likely one or both elements of the pair indicate local mineralization. This method is applied on two geochemical data sets which have been collected specifically for the purpose of mineral exploration. The aim is to test the technique for its ability to identify pathfinder elements to detect mineralized zones, and to verify whether the method can indicate which sampling material is best suited for this purpose. Reference: Mikšová D., Rieser C., Filzmoser P. (2019). "Identification of mineralization in geochemistry along a transect based on the spatial curvature of log-ratios." arXiv, (1912.02867).

stat.AP↗

arXiv2020

Cellwise Robust M Regression

The cellwise robust M regression estimator is introduced as the first estimator of its kind that intrinsically yields both a map of cellwise outliers consistent with the linear model, and a vector of regression coefficients that is robust against vertical outliers and leverage points. As a by-product, the method yields a weighted and imputed data set that contains estimates of what the values in cellwise outliers would need to amount to if they had fit the model. The method is illustrated to be equally robust as its casewise counterpart, MM regression. The cellwise regression method discards less information than any casewise robust estimator. Therefore, predictive power can be expected to be at least as good as casewise alternatives. These results are corroborated in a simulation study. Moreover, while the simulations show that predictive performance is at least on par with casewise methods if not better, an application to a data set consisting of compositions of Swiss nutrients, shows that in individual cases, CRM can achieve a significantly higher predictive accuracy compared to MM regression.

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arXiv2019

Identification of mineralization in geochemistry along a transect based on the spatial curvature of log-ratios

Detecting subcropping mineralizations but also deeply buried mineralizations is one important goal in geochemical exploration. The identification of useful indicators for mineralization is a difficult task as mineralization might be influenced by many factors, such as location, investigated media, depth, etc. We propose a statistical method which indicates chemical elements related to mineralization along a transect. Moreover, the method determines along a transect the potential area of the deposit. The identification is based on General Additive Models (GAMs) for the element concentrations across the spatial coordinate(s). The log-ratios of the GAM fits are taken to compute the curvature, where high and narrow curvature is supposed to indicate the mineralization area. By defining a measure for the quantification of high curvature, the log-ratios can be ranked, and elements can be identified that are indicative of the anomaly patterns.

stat.AP↗

arXiv2019

Robust Principal Component Analysis for Compositional Tables

A data table which is arranged according to two factors can often be considered as a compositional table. An example is the number of unemployed people, split according to gender and age classes. Analyzed as compositions, the relevant information would consist of ratios between different cells of such a table. This is particularly useful when analyzing several compositional tables jointly, where the absolute numbers are in very different ranges, e.g. if unemployment data are considered from different countries. Within the framework of the logratio methodology, compositional tables can be decomposed into independent and interactive parts, and orthonormal coordinates can be assigned to these parts. However, these coordinates usually require some prior knowledge about the data, and they are not easy to handle for exploring the relationships between the given factors. Here we propose a special choice of coordinates with a direct relation to centered logratio (clr) coefficients, which are particularly useful for an interpretation in terms of the original cells of the tables. With these coordinates, robust principal component analysis (PCA) is performed for dimension reduction, allowing to investigate the relationships between the factors. The link between orthonormal coordinates and clr coefficients enables to apply robust PCA, which would otherwise suffer from the singularity of clr coefficients.

stat.ME↗

arXiv2017

Variable selection with genetic algorithms using repeated cross-validation of PLS regression models as fitness measure

Genetic algorithms are a widely used method in chemometrics for extracting variable subsets with high prediction power. Most fitness measures used by these genetic algorithms are based on the ordinary least-squares fit of the resulting model to the entire data or a subset thereof. Due to multicollinearity, partial least squares regression is often more appropriate, but rarely considered in genetic algorithms due to the additional cost for estimating the optimal number of components. We introduce two novel fitness measures for genetic algorithms, explicitly designed to estimate the internal prediction performance of partial least squares regression models built from the variable subsets. Both measures estimate the optimal number of components using cross-validation and subsequently estimate the prediction performance by predicting the response of observations not included in model-fitting. This is repeated multiple times to estimate the measures' variations due to different random splits. Moreover, one measure was optimized for speed and more accurate estimation of the prediction performance for observations not included during variable selection. This leads to variable subsets with high internal and external prediction power. Results on high-dimensional chemical-analytical data show that the variable subsets acquired by this approach have competitive internal prediction power and superior external prediction power compared to variable subsets extracted with other fitness measures.

stat.CO↗

arXiv2017

Clustering of imbalanced high-dimensional media data

Media content in large repositories usually exhibits multiple groups of strongly varying sizes. Media of potential interest often form notably smaller groups. Such media groups differ so much from the remaining data that it may be worthy to look at them in more detail. In contrast, media with popular content appear in larger groups. Identifying groups of varying sizes is addressed by clustering of imbalanced data. Clustering highly imbalanced media groups is additionally challenged by the high dimensionality of the underlying features. In this paper, we present the Imbalanced Clustering (IClust) algorithm designed to reveal group structures in high-dimensional media data. IClust employs an existing clustering method in order to find an initial set of a large number of potentially highly pure clusters which are then successively merged. The main advantage of IClust is that the number of clusters does not have to be pre-specified and that no specific assumptions about the cluster or data characteristics need to be made. Experiments on real-world media data demonstrate that in comparison to existing methods, IClust is able to better identify media groups, especially groups of small sizes.

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