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Indexes are useful for summarizing multivariate information into single metrics for monitoring, communicating, and decision-making. While most work has focused on defining new indexes for specific purposes, more attention needs to be directed towards making it possible to understand index behavior in different data conditions, and to determine how their structure affects their values and variation in values. Here we discuss a modular data pipeline recommendation to assemble indexes. It is universally applicable to index computation and allows investigation of index behavior as part of the development procedure. One can compute indexes with different parameter choices, adjust steps in the index definition by adding, removing, and swapping them to experiment with various index designs, calculate uncertainty measures, and assess indexes robustness. The paper presents three examples to illustrate the pipeline framework usage: comparison of two different indexes designed to monitor the spatio-temporal distribution of drought in Queensland, Australia; the effect of dimension reduction choices on the Global Gender Gap Index (GGGI) on countries ranking; and how to calculate bootstrap confidence intervals for the Standardized Precipitation Index (SPI). The methods are supported by a new R package, called tidyindex.

The woylier package implements tour interpolation paths between frames using Givens rotations. This provides an alternative to the geodesic interpolation between planes currently available in the tourr package. Tours are used to visualise high-dimensional data and models, to detect clustering, anomalies and non-linear relationships. Frame-to-frame interpolation can be useful for projection pursuit guided tours when the index is not rotationally invariant. It also provides a way to specifically reach a given target frame. We demonstrate the method for exploring non-linear relationships between currency cross-rates.

We describe the applications of clustering and visualization tools using the so-called neutral B anomalies as an example. Clustering permits parameter space partitioning into regions that can be separated with some given measurements. It provides a visualization of the collective dependence of all the observables on the parameters of the problem. These methods highlight the relative importance of different observables, and the effect of correlations, and help to understand tensions in global fits. The tools we describe also permit a visual inspection of high dimensional observable and parameter spaces through both linear projections and slicing., Comment: Talk presented at Corfu Summer Institute 2022 "School and Workshops on Elementary Particle Physics and Gravity" based on e-Print: 2103.07937, Animations as mp4 ancillary files

This paper describes new user controls for examining high-dimensional data using low-dimensional linear projections and slices. A user can interactively change the contribution of a given variable to a low-dimensional projection, which is useful for exploring the sensitivity of structure to particular variables. The user can also interactively shift the center of a slice, for example, to explore how structure changes in local subspaces. The Mathematica package as well as example notebooks are provided, which contain functions enabling the user to experiment with these new manual controls, with one specifically for exploring regions and boundaries produced by classification models. The advantage of Mathematica is its linear algebra capabilities, and interactive cursor location controls. Some limited implementation has also been made available in the R package tourr., Comment: 16 pages, 9 figures

Multivariate spatio-temporal data refers to multiple measurements taken across space and time. For many analyses, spatial and time components can be separately studied: for example, to explore the temporal trend of one variable for a single spatial location, or to model the spatial distribution of one variable at a given time. However for some studies, it is important to analyse different aspects of the spatio-temporal data simultaneouly, like for instance, temporal trends of multiple variables across locations. In order to facilitate the study of different portions or combinations of spatio-temporal data, we introduce a new data structure, cubble, with a suite of functions enabling easy slicing and dicing on the different components spatio-temporal components. The proposed cubble structure ensures that all the components of the data are easy to access and manipulate while providing flexibility for data analysis. In addition, cubble facilitates visual and numerical explorations of the data while easing data wrangling and modelling. The cubble structure and the functions provided in the cubble R package equip users with the capability to handle hierarchical spatial and temporal structures. The cubble structure and the tools implemented in the package are illustrated with different examples of Australian climate data.

This article discusses a high-dimensional visualization technique called the tour, which can be used to view data in more than three dimensions. We review the theory and history behind the technique, as well as modern software developments and applications of the tour that are being found across the sciences and machine learning.

A guided tour helps to visualise high-dimensional data by showing low-dimensional projections along a projection pursuit optimisation path. Projection pursuit is a generalisation of principal component analysis, in the sense that different indexes are used to define the interestingness of the projected data. While much work has been done in developing new indexes in the literature, less has been done on understanding the optimisation. Index functions can be noisy, might have multiple local maxima as well as an optimal maximum, and are constrained to generate orthonormal projection frames, which complicates the optimization. In addition, projection pursuit is primarily used for exploratory data analysis, and finding the local maxima is also useful. The guided tour is especially useful for exploration, because it conducts geodesic interpolation connecting steps in the optimisation and shows how the projected data changes as a maxima is approached. This work provides new visual diagnostics for examining a choice of optimisation procedure, based on the provision of a new data object which collects information throughout the optimisation. It has helped to diagnose and fix several problems with projection pursuit guided tour. This work might be useful more broadly for diagnosing optimisers, and comparing their performance. The diagnostics are implemented in the R package, ferrn.

We introduce the interactive tool pandemonium to cluster model predictions that depend on a set of parameters. The model predictions are used to define the coordinates in observable space which go into the clustering. The results of this partitioning are then visualized in both observable and parameter space to study correlations between them. The tool offers multiple choices for coordinates, distance functions and linkage methods within hierarchical clustering. It provides a set of diagnostic statistics and visualization methods to study the clustering results in order to interpret the outcome. The methods are most useful in an interactive environment that enables exploration, and we have implemented them with a graphical user interface in R. We demonstrate the concepts with an application to phenomenological studies in flavor physics in the context of the so-called B anomalies., Comment: 48 pages, 30 figures, version to appear in EPJ Plus

Non-linear dimensionality reduction (NLDR) methods such as t-distributed stochastic neighbour embedding (t-SNE) are ubiquitous in the natural sciences, however, the appropriate use of these methods is difficult because of their complex parameterisations; analysts must make trade-offs in order to identify structure in the visualisation of an NLDR technique. We present visual diagnostics for the pragmatic usage of NLDR methods by combining them with a technique called the tour. A tour is a sequence of interpolated linear projections of multivariate data onto a lower dimensional space. The sequence is displayed as a dynamic visualisation, allowing a user to see the shadows the high-dimensional data casts in a lower dimensional view. By linking the tour to an NLDR view, we can preserve global structure and through user interactions like linked brushing observe where the NLDR view may be misleading. We display several case studies from both simulations and single cell transcriptomics, that shows our approach is useful for cluster orientation tasks., Comment: 25 pages, 7 figures, submitted to JDSSV

In high-dimensional data analysis the curse of dimensionality reasons that points tend to be far away from the center of the distribution and on the edge of high-dimensional space. Contrary to this, is that projected data tends to clump at the center. This gives a sense that any structure near the center of the projection is obscured, whether this is true or not. A transformation to reverse the curse, is defined in this paper, which uses radial transformations on the projected data. It is integrated seamlessly into the grand tour algorithm, and we have called it a burning sage tour, to indicate that it reverses the curse. The work is implemented into the tourr package in R. Several case studies are included that show how the sage visualizations enhance exploratory clustering and classification problems.

Multivariate data is often visualized using linear projections, produced by techniques such as principal component analysis, linear discriminant analysis, and projection pursuit. A problem with projections is that they obscure low and high density regions near the center of the distribution. Sections, or slices, can help to reveal them. This paper develops a section pursuit method, building on the extensive work in projection pursuit, to search for interesting slices of the data. Linear projections are used to define sections of the parameter space, and to calculate interestingness by comparing the distribution of observations, inside and outside a section. By optimizing this index, it is possible to reveal features such as holes (low density) or grains (high density). The optimization is incorporated into a guided tour so that the search for structure can be dynamic. The approach can be useful for problems when data distributions depart from uniform or normal, as in visually exploring nonlinear manifolds, and functions in multivariate space. Two applications of section pursuit are shown: exploring decision boundaries from classification models, and exploring subspaces induced by complex inequality conditions from multiple parameter model. The new methods are available in R, in the tourr package., Comment: v3 is accepted for publication in JCGS and contains the appendix

Taking projections of high-dimensional data is a common analytical and visualisation technique in statistics for working with high-dimensional problems. Sectioning, or slicing, through high dimensions is less common, but can be useful for visualising data with concavities, or non-linear structure. It is associated with conditional distributions in statistics, and also linked brushing between plots in interactive data visualisation. This short technical note describes a simple approach for slicing in the orthogonal space of projections obtained when running a tour, thus presenting the viewer with an interpolated sequence of sliced projections. The method has been implemented in R as an extension to the tourr package, and can be used to explore for concave and non-linear structures in multivariate distributions., Comment: 13 pages, 6 figures

New results in processes with an underlying quark transition $b\to s \ell^+\ell^-$ have been recently reported by the LHCb and Belle II collaborations. In this note we show how the main implications of a handful of new measurements can be understood with the tools introduced in our recent paper, arXiv:1811.10793, without the need to redo the global fits. We find that the main impact of the new results, due to $R_K^{[1.1,6]}$ from LHCb, is a decrease in $C_{10\mu}^{NP}$ with a reduced uncertainty. We validate this conclusion by presenting the result of a new global fit., Comment: 11 pages, 2 figures

Projection pursuit is used to find interesting low-dimensional projections of high-dimensional data by optimizing an index over all possible projections. Most indexes have been developed to detect departure from known distributions, such as normality, or to find separations between known groups. Here, we are interested in finding projections revealing potentially complex bivariate patterns, using new indexes constructed from scagnostics and a maximum information coefficient, with a purpose to detect unusual relationships between model parameters describing physics phenomena. The performance of these indexes is examined with respect to ideal behaviour, using simulated data, and then applied to problems from gravitational wave astronomy. The implementation builds upon the projection pursuit tools available in the R package, tourr, with indexes constructed from code in the R packages, scagnostics, minerva and mbgraphic., Comment: 39 pages, 13 figures

SModelS is an automatised tool enabling the fast interpretation of simplified model results from the LHC within any model of new physics respecting a $\mathbb{Z}_2$ symmetry. With the version 1.2 we announce several new features. First, previous versions were restricted to missing energy signatures and assumed prompt decays within each decay chain. SModelS v1.2 considers the lifetime of each $\mathbb{Z}_2$-odd particle and appropriately takes into account missing energy, heavy stable charge particle and R-hadron signatures. Second, the current version allows for a combination of signal regions in efficiency map results whenever a covariance matrix is available from the experiment. This is an important step towards fully exploiting the constraining power of efficiency map results. Several other improvements increase the user-friendliness, such as the use of wildcards in the selection of experimental results, and a faster database which can be given as a URL. Finally, smodelsTools provides an interactive plots maker to conveniently visualize the results of a model scan., Comment: 24 pages, 4 figures

Discrepancies between measurements of decay modes with an underlying quark level transition $b\to s \ell^+\ell^-$ and standard model (SM) predictions have persisted for several years, particularly for the muon channels. The inadequacy of the SM becomes more compelling in a global fit. For example, Ref. [1] described 175 observables by six parameters encoding new physics and quantified the disagreement with the SM at about the $5\sigma$ level. While certain one and two parameter fits have previously been considered in detail, we establish a framework for the detailed discussion of the full 6d fit. We visualize and quantify the 6d $1\sigma$ region around the best fit point and define fit uncertainties for both current and future observables. We then define metrics quantifying the deviations between measurements and both SM and best fit predictions. These metrics relate observables to directions in parameter space, revealing their precise role in the fit, thus providing guidance for future theoretical and experimental work. Some metrics further quantify the role of correlated uncertainties, which turns out to be significant. For example the relevance of angular observables such as $P_5^\prime$ is reduced in this context. Finally, studying the space of observables allows us to discuss the internal tensions in the fit., Comment: 39 pages, 14 figures, journal version, animations referenced in the text are available at https://uschilaa.github.io/animations/

A recent paper on visualizing the sensitivity of hadronic experiments to nucleon structure [1] introduces the tool PDFSense which defines measures to allow the user to judge the sensitivity of PDF fits to a given experiment. The sensitivity is characterized by high-dimensional data residuals that are visualized in a 3-d subspace of the 10 first principal components or using t-SNE [2]. We show how a tour, a dynamic visualisation of high dimensional data, can extend this tool beyond 3-d relationships. This approach enables resolving structure orthogonal to the 2-d viewing plane used so far, and hence finer tuned assessment of the sensitivity., Comment: Format of the animations changed for easier viewing

ATLAS and CMS have been performing a large number of searches for physics beyond the Standard Model (BSM). In particular results of supersymmetry (SUSY) searches are typically interpreted in the context of simplified models. While mass limits obtained in this manner are highly model dependent, cross section upper limits (or efficiency maps) may be used to obtain constraints on generic BSM scenarios without any further event and detector simulation. This procedure has been automatised in the public tool SModelS, which first decomposes the generic scenario into its simplified model components which can then be tested directly against the experimental constraints in the SModelS database. We briefly introduce SModelS and then discuss how the coverage by simplified model results compares to what can be obtained in a full simulation study for the example of the 19 parameter phenomenological MSSM (pMSSM). Considering all parameter points that ATLAS has tested in a comprehensive study [1], we find that about 60 % of the points excluded by ATLAS can be excluded from simplified model constraints. This fraction could be improved by considering currently `missing' simplified model topologies. We show that in particular topologies with asymmetric branches are often important, while long cascade decays with more than one intermediate particle are less relevant. A particularly interesting asymmetric branch topology is a 3 jet + $E_T^{\mathrm{miss}}$ signature arising from gluino-squark production., Comment: 5 pages. To appear in the proceedings of the European Physical Society Conference on High Energy Physics 2017 (EPS-HEP 2017)

We investigate to which extent the SUSY search results published by ATLAS and CMS in the context of simplified models actually cover the more realistic scenarios of a full model. Concretely, we work within the phenomenological MSSM (pMSSM) with 19 free parameters and compare the constraints obtained from SModelSv1.1.1 with those from the ATLAS pMSSM study in arXiv:1508.06608. We find that about 40-45% of the points excluded by ATLAS escape the currently available simplified model constraints. For these points we identify the most relevant topologies which are not tested by the current simplified model results. In particular, we find that topologies with asymmetric branches, including 3-jet signatures from gluino-squark associated production, could be important for improving the current constraining power of simplified models results. Furthermore, for a better coverage of light stops and sbottoms, constraints for decays via heavier neutralinos and charginos, which subsequently decay visibly to the lightest neutralino are also needed., Comment: 29 pages, 13 figures, 5 tables, journal version

We consider simplified dark matter models where a dark matter candidate couples to the standard model (SM) particles via an $s$-channel spin-2 mediator, and study constraints on the model parameter space from the current LHC data. Our focus lies on the complementarity among different searches, in particular monojet and multijet plus missing energy searches and resonance searches. For universal couplings of the mediator to SM particles, missing-energy searches can give stronger constraints than $WW$, $ZZ$, dijet, dihiggs, $t\bar t$, $b\bar b$ resonance searches in the low-mass region and/or when the coupling of the mediator to dark matter is much larger than its couplings to SM particles. The strongest constraints however come from diphoton and dilepton resonance searches. Only if these modes are suppressed, missing-energy searches can be competitive in constraining dark matter models with a spin-2 mediator., Comment: 14 pages, 12 figures, 2 tables. Supplemental material for this paper can be downloaded from http://lpsc.in2p3.fr/projects-th/recasting/spin2mediator/ ; v2: Constraints from LHC 8TeV resonance searches added, version accepted by EPJC

SModelS is an automatised tool for the interpretation of simplified model results from the LHC. It allows to decompose models of new physics obeying a Z2 symmetry into simplified model components, and to compare these against a large database of experimental results. The first release of SModelS, v1.0, used only cross section upper limit maps provided by the experimental collaborations. In this new release, v1.1, we extend the functionality of SModelS to efficiency maps. This increases the constraining power of the software, as efficiency maps allow to combine contributions to the same signal region from different simplified models. Other new features of version 1.1 include likelihood and chi-square calculations, extended information on the topology coverage, an extended database of experimental results as well as major speed upgrades for both the code and the database. We describe in detail the concepts and procedures used in SModelS, explaining in particular how upper limits and efficiency map results are dealt with in parallel. Detailed instructions for code usage are also provided., Comment: The manual is compatible with SModelS version 1.1.1. v4: Version to appear in Computer Physics Communications

We assess how different ATLAS and CMS searches for supersymmetry in the $t\bar t + E_T^{\rm miss}$ final state at Run 1 of the LHC constrain scenarios with a fermionic top partner and a dark matter candidate. We find that the efficiencies of these searches in all-hadronic, 1-lepton and 2-lepton channels are quite similar for scalar and fermionic top partners. Therefore, in general, efficiency maps for stop-neutralino simplified models can also be applied to fermionic top-partner models, provided the narrow width approximation holds in the latter. Owing to the much higher production cross-sections of heavy top quarks as compared to stops, masses up to $m_T\approx 850$ GeV can be excluded from the Run 1 stop searches. Since the simplified-model results published by ATLAS and CMS do not extend to such high masses, we provide our own efficiency maps obtained with CheckMATE and MadAnalysis 5 for these searches. Finally, we also discuss how generic gluino/squark searches in multi-jet final states constrain heavy top partner production., Comment: 39 pages, 8 figures, 17 tables. Version accepted by JHEP. Efficiency maps derived for this paper can be downloaded from http://lpsc.in2p3.fr/projects-th/recasting/susy-vs-vlq/ttbarMET

ATLAS and CMS have performed a large number of searches for physics beyond the Standard Model (BSM). The results are typically presented in the context of Simplified Model Spectra (SMS), containing only a few new particles with fixed decay branching ratios, yielding generic upper limits on the cross section as a function of particle masses. The interpretation of these limits within realistic BSM scenarios is non-trivial and best done by automated computational tools. To this end we have developed SModelS, a public tool that can test any given BSM model with a $\mathbb{Z}_2$ symmetry by decomposing it into its SMS components and confronting them with a large database of SMS results. This allows to easily evaluate the main LHC constraints on the model. Additionally, SModelS returns information on important signatures that are not covered by the existing SMS results. This may be used to improve the coverage of BSM searches and SMS interpretations. We present the working principle of SModelS, in particular the decomposition procedure, the database and matching of applicable experimental results. Moreover, we present applications of SModelS to different models: the MSSM, a model with a sneutrino as the lightest supersymmetric particle and the UMSSM. These results illustrate how SModelS can be used to identify important constraints, untested regions and interesting new signatures., Comment: 6 pages, 5 figures. To appear in the proceedings of the European Physical Society Conference on High Energy Physics 2015 (EPS-HEP 2015), Vienna, Austria, 22nd to 29th of July 2015

A mostly right-handed sneutrino as the lightest supersymmetric particle (LSP) is an interesting dark matter candidate, leading to LHC signatures which can be quite distinct from those of the conventional neutralino LSP. Using SModelSv1.0.1 for testing the model against the limits published by ATLAS and CMS in the context of so-called Simplified Model Spectra (SMS), we investigate to what extent the supersymmetry searches at Run 1 of the LHC constrain the sneutrino-LSP scenario. Moreover, we discuss the most relevant topologies for which no SMS results are provided by the experimental collaborations but which would allow to put more stringent constraints on sneutrino LSPs. These include, for instance, the mono-lepton signature which should be particularly interesting to consider at Run 2 of the LHC., Comment: 30 pages, 23 figures, matches published version

SModelS is a tool for the automatic interpretation of simplified-model results from the LHC. Version 1.0 of the code is now publicly available. This document provides a quick user guide for installing and running SModelS v1.0., Comment: The code is available for download at http://smodels.hephy.at/

We present a general procedure to decompose Beyond the Standard Model (BSM) collider signatures presenting a Z2 symmetry into Simplified Model Spectrum (SMS) topologies. Our method provides a way to cast BSM predictions for the LHC in a model independent framework, which can be directly confronted with the relevant experimental constraints. Our concrete implementation currently focusses on supersymmetry searches with missing energy, for which a large variety of SMS results from ATLAS and CMS are available. As show-case examples we apply our procedure to two scans of the minimal supersymmetric standard model. We discuss how the SMS limits constrain various particle masses and which regions of parameter space remain unchallenged by the current SMS interpretations of the LHC results., Comment: v3: Version published in EPJC