Anti-alignments in conformance checking: the dark side of process models

Conformance checking techniques asses the suitability of a process model in representing an underlying process, observed through a collection of real executions. These techniques suffer from the wellknown state space explosion problem, hence handling process models exhibiting large or even infinite state spaces remains a challenge. One important metric in conformance checking is to asses the precision of the model with respect to the observed executions, i.e., characterize the ability of the model to produce behavior unrelated to the one observed. By avoiding the computation of the full state space of a model, current techniques only provide estimations of the precision metric, which in some situations tend to be very optimistic, thus hiding real problems a process model may have. In this paper we present the notion of antialignment as a concept to help unveiling traces in the model that may deviate significantly from the observed behavior. Using anti-alignments, current estimations can be improved, e.g., in precision checking. We show how to express the problem of finding anti-alignments as the satisfiability of a Boolean formula, and provide a tool which can deal with large models efficiently.Peer ReviewedPostprint (author's final draft

What Automated Planning Can Do for Business Process Management

Business Process Management (BPM) is a central element of today organizations. Despite over the years its main focus has been the support of processes in highly controlled domains, nowadays many domains of interest to the BPM community are characterized by ever-changing requirements, unpredictable environments and increasing amounts of data that influence the execution of process instances. Under such dynamic conditions, BPM systems must increase their level of automation to provide the reactivity and flexibility necessary for process management. On the other hand, the Artificial Intelligence (AI) community has concentrated its efforts on investigating dynamic domains that involve active control of computational entities and physical devices (e.g., robots, software agents, etc.). In this context, Automated Planning, which is one of the oldest areas in AI, is conceived as a model-based approach to synthesize autonomous behaviours in automated way from a model. In this paper, we discuss how automated planning techniques can be leveraged to enable new levels of automation and support for business processing, and we show some concrete examples of their successful application to the different stages of the BPM life cycle

A Tool for Aligning Event Logs and Prescriptive Process Models through Automated Planning

In Conformance Checking, alignment is the problem of detecting and repairing nonconformity between the actual execution of a business process, as recorded in an event log, and the model of the same process. Literature proposes solutions for the alignment problem that are implementations of planning algorithms built ad-hoc for the specific problem. Unfortunately, in the era of big data, these ad-hoc implementations do not scale sufficiently compared with well-established planning systems. In this paper, we tackle the above issue by presenting a tool, also available in ProM, to represent instances of the alignment problem as automated planning problems in PDDL (Planning Domain Definition Language) for which state-of-the-art planners can find a correct solution in a finite amount of time. If alignment problems are converted into planning problems, one can seamlessly update to the recent versions of the best performing automated planners, with advantages in term of versatility and customization. Furthermore, by employing several processes and event logs of different sizes, we show how our tool outperforms existing approaches of several order of magnitude and, in certain cases, carries out the task while existing approaches run out of memory

The Quaternion-Based Spatial Coordinate and Orientation Frame Alignment Problems

We review the general problem of finding a global rotation that transforms a given set of points and/or coordinate frames (the "test" data) into the best possible alignment with a corresponding set (the "reference" data). For 3D point data, this "orthogonal Procrustes problem" is often phrased in terms of minimizing a root-mean-square deviation or RMSD corresponding to a Euclidean distance measure relating the two sets of matched coordinates. We focus on quaternion eigensystem methods that have been exploited to solve this problem for at least five decades in several different bodies of scientific literature where they were discovered independently. While numerical methods for the eigenvalue solutions dominate much of this literature, it has long been realized that the quaternion-based RMSD optimization problem can also be solved using exact algebraic expressions based on the form of the quartic equation solution published by Cardano in 1545; we focus on these exact solutions to expose the structure of the entire eigensystem for the traditional 3D spatial alignment problem. We then explore the structure of the less-studied orientation data context, investigating how quaternion methods can be extended to solve the corresponding 3D quaternion orientation frame alignment (QFA) problem, noting the interesting equivalence of this problem to the rotation-averaging problem, which also has been the subject of independent literature threads. We conclude with a brief discussion of the combined 3D translation-orientation data alignment problem. Appendices are devoted to a tutorial on quaternion frames, a related quaternion technique for extracting quaternions from rotation matrices, and a review of quaternion rotation-averaging methods relevant to the orientation-frame alignment problem. Supplementary Material covers extensions of quaternion methods to the 4D problem.Comment: This replaces an early draft that lacked a number of important references to previous work. There are also additional graphics elements. The extensions to 4D data and additional details are worked out in the Supplementary Material appended to the main tex

Bayesian matching of unlabeled marked point sets using random fields, with an application to molecular alignment

Statistical methodology is proposed for comparing unlabeled marked point sets, with an application to aligning steroid molecules in chemoinformatics. Methods from statistical shape analysis are combined with techniques for predicting random fields in spatial statistics in order to define a suitable measure of similarity between two marked point sets. Bayesian modeling of the predicted field overlap between pairs of point sets is proposed, and posterior inference of the alignment is carried out using Markov chain Monte Carlo simulation. By representing the fields in reproducing kernel Hilbert spaces, the degree of overlap can be computed without expensive numerical integration. Superimposing entire fields rather than the configuration matrices of point coordinates thereby avoids the problem that there is usually no clear one-to-one correspondence between the points. In addition, mask parameters are introduced in the model, so that partial matching of the marked point sets can be carried out. We also propose an adaptation of the generalized Procrustes analysis algorithm for the simultaneous alignment of multiple point sets. The methodology is illustrated with a simulation study and then applied to a data set of 31 steroid molecules, where the relationship between shape and binding activity to the corticosteroid binding globulin receptor is explored.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS486 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Learning Discriminative Stein Kernel for SPD Matrices and Its Applications

Stein kernel has recently shown promising performance on classifying images represented by symmetric positive definite (SPD) matrices. It evaluates the similarity between two SPD matrices through their eigenvalues. In this paper, we argue that directly using the original eigenvalues may be problematic because: i) Eigenvalue estimation becomes biased when the number of samples is inadequate, which may lead to unreliable kernel evaluation; ii) More importantly, eigenvalues only reflect the property of an individual SPD matrix. They are not necessarily optimal for computing Stein kernel when the goal is to discriminate different sets of SPD matrices. To address the two issues in one shot, we propose a discriminative Stein kernel, in which an extra parameter vector is defined to adjust the eigenvalues of the input SPD matrices. The optimal parameter values are sought by optimizing a proxy of classification performance. To show the generality of the proposed method, three different kernel learning criteria that are commonly used in the literature are employed respectively as a proxy. A comprehensive experimental study is conducted on a variety of image classification tasks to compare our proposed discriminative Stein kernel with the original Stein kernel and other commonly used methods for evaluating the similarity between SPD matrices. The experimental results demonstrate that, the discriminative Stein kernel can attain greater discrimination and better align with classification tasks by altering the eigenvalues. This makes it produce higher classification performance than the original Stein kernel and other commonly used methods.Comment: 13 page

Process-oriented Iterative Multiple Alignment for Medical Process Mining

Adapted from biological sequence alignment, trace alignment is a process mining technique used to visualize and analyze workflow data. Any analysis done with this method, however, is affected by the alignment quality. The best existing trace alignment techniques use progressive guide-trees to heuristically approximate the optimal alignment in O(N2L2) time. These algorithms are heavily dependent on the selected guide-tree metric, often return sum-of-pairs-score-reducing errors that interfere with interpretation, and are computationally intensive for large datasets. To alleviate these issues, we propose process-oriented iterative multiple alignment (PIMA), which contains specialized optimizations to better handle workflow data. We demonstrate that PIMA is a flexible framework capable of achieving better sum-of-pairs score than existing trace alignment algorithms in only O(NL2) time. We applied PIMA to analyzing medical workflow data, showing how iterative alignment can better represent the data and facilitate the extraction of insights from data visualization.Comment: accepted at ICDMW 201