Evaluation of Temporal Datasets via Interval Temporal Logic Model Checking

The problem of {em temporal dataset evaluation} consists in establishing to what extent a set of temporal data (histories) complies with a given temporal condition. It presents a strong resemblance with the problem of model checking enhanced with the ability of emph{rating} the compliance degree of a model against a formula. In this paper, we solve the temporal dataset evaluation problem by suitably combining the outcomes of model checking an interval temporal logic formula against sets of histories (finite interval models), possibly taking into account domain-dependent measures/criteria, like, for instance, sensitivity, specificity, and accuracy. From a technical point of view, the main contribution of the paper is a (deterministic) polynomial time algorithm for interval temporal logic model checking over finite interval models. To the best of our knowledge, this is the first application of a (truly) interval temporal logic model checking in the area of temporal databases and data mining rather than in the formal verification setting

Extracting Interval Temporal Logic Rules: A First Approach

Discovering association rules is a classical data mining task with a wide range of applications that include the medical, the financial, and the planning domains, among others. Modern rule extraction algorithms focus on static rules, typically expressed in the language of Horn propositional logic, as opposed to temporal ones, which have received less attention in the literature. Since in many application domains temporal information is stored in form of intervals, extracting interval-based temporal rules seems the natural choice. In this paper we extend the well-known algorithm APRIORI for rule extraction to discover interval temporal rules written in the Horn fragment of Halpern and Shoham\u27s interval temporal logic

Crowd Modeling using Temporal Association Rules

Understanding crowd behavior has attracted tremendous attention from researchers over the years. In this work, we propose an unsupervised approach for crowd scene modeling and anomaly detection using association rules mining. Using object tracklets, we identify events occurring in the scene, demonstrated by the paths or routes objects take while traversing the scene. Allen\u27s interval-based temporal logic is used to extract frequent temporal patterns from the scene. Temporal association rules are generated from these frequent temporal patterns. Our goal is to understand the scene grammar, which is encoded in both the spatial and spatio-temporal patterns. We perform anomaly detection and test the method on a well-known public data

Constraining the Search Space in Temporal Pattern Mining

Agents in dynamic environments have to deal with complex situations including various temporal interrelations of actions and events. Discovering frequent patterns in such scenes can be useful in order to create prediction rules which can be used to predict future activities or situations. We present the algorithm MiTemP which learns frequent patterns based on a time intervalbased relational representation. Additionally the problem has also been transfered to a pure relational association rule mining task which can be handled by WARMR. The two approaches are compared in a number of experiments. The experiments show the advantage of avoiding the creation of impossible or redundant patterns with MiTemP. While less patterns have to be explored on average with MiTemP more frequent patterns are found at an earlier refinement level

Temporalized logics and automata for time granularity

Suitable extensions of the monadic second-order theory of k successors have been proposed in the literature to capture the notion of time granularity. In this paper, we provide the monadic second-order theories of downward unbounded layered structures, which are infinitely refinable structures consisting of a coarsest domain and an infinite number of finer and finer domains, and of upward unbounded layered structures, which consist of a finest domain and an infinite number of coarser and coarser domains, with expressively complete and elementarily decidable temporal logic counterparts. We obtain such a result in two steps. First, we define a new class of combined automata, called temporalized automata, which can be proved to be the automata-theoretic counterpart of temporalized logics, and show that relevant properties, such as closure under Boolean operations, decidability, and expressive equivalence with respect to temporal logics, transfer from component automata to temporalized ones. Then, we exploit the correspondence between temporalized logics and automata to reduce the task of finding the temporal logic counterparts of the given theories of time granularity to the easier one of finding temporalized automata counterparts of them.Comment: Journal: Theory and Practice of Logic Programming Journal Acronym: TPLP Category: Paper for Special Issue (Verification and Computational Logic) Submitted: 18 March 2002, revised: 14 Januari 2003, accepted: 5 September 200

Conformance Checking Based on Multi-Perspective Declarative Process Models

Process mining is a family of techniques that aim at analyzing business process execution data recorded in event logs. Conformance checking is a branch of this discipline embracing approaches for verifying whether the behavior of a process, as recorded in a log, is in line with some expected behaviors provided in the form of a process model. The majority of these approaches require the input process model to be procedural (e.g., a Petri net). However, in turbulent environments, characterized by high variability, the process behavior is less stable and predictable. In these environments, procedural process models are less suitable to describe a business process. Declarative specifications, working in an open world assumption, allow the modeler to express several possible execution paths as a compact set of constraints. Any process execution that does not contradict these constraints is allowed. One of the open challenges in the context of conformance checking with declarative models is the capability of supporting multi-perspective specifications. In this paper, we close this gap by providing a framework for conformance checking based on MP-Declare, a multi-perspective version of the declarative process modeling language Declare. The approach has been implemented in the process mining tool ProM and has been experimented in three real life case studies

Discovering temporal patterns for interval-based events.

Kam, Po-shan.Thesis (M.Phil.)--Chinese University of Hong Kong, 2000.Includes bibliographical references (leaves 89-97).Abstracts in English and Chinese.Abstract --- p.iAcknowledgements --- p.iiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Data Mining --- p.1Chapter 1.2 --- Temporal Data Management --- p.2Chapter 1.3 --- Temporal reasoning and temporal semantics --- p.3Chapter 1.4 --- Temporal Data Mining --- p.5Chapter 1.5 --- Motivation --- p.6Chapter 1.6 --- Approach --- p.7Chapter 1.6.1 --- Focus and Objectives --- p.8Chapter 1.6.2 --- Experimental Setup --- p.8Chapter 1.7 --- Outline and contributions --- p.9Chapter 2 --- Relevant Work --- p.10Chapter 2.1 --- Data Mining --- p.10Chapter 2.1.1 --- Association Rules --- p.13Chapter 2.1.2 --- Classification --- p.15Chapter 2.1.3 --- Clustering --- p.16Chapter 2.2 --- Sequential Pattern --- p.17Chapter 2.2.1 --- Frequent Patterns --- p.18Chapter 2.2.2 --- Interesting Patterns --- p.20Chapter 2.2.3 --- Granularity --- p.21Chapter 2.3 --- Temporal Database --- p.21Chapter 2.4 --- Temporal Reasoning --- p.23Chapter 2.4.1 --- Natural Language Expression --- p.24Chapter 2.4.2 --- Temporal Logic Approach --- p.25Chapter 2.5 --- Temporal Data Mining --- p.25Chapter 2.5.1 --- Framework --- p.25Chapter 2.5.2 --- Temporal Association Rules --- p.26Chapter 2.5.3 --- Attribute-Oriented Induction --- p.27Chapter 2.5.4 --- Time Series Analysis --- p.27Chapter 3 --- Discovering Temporal Patterns for interval-based events --- p.29Chapter 3.1 --- Temporal Database --- p.29Chapter 3.2 --- Allen's Taxonomy of Temporal Relationships --- p.31Chapter 3.3 --- "Mining Temporal Pattern, AppSeq and LinkSeq" --- p.33Chapter 3.3.1 --- A1 and A2 temporal pattern --- p.33Chapter 3.3.2 --- "Second Temporal Pattern, LinkSeq" --- p.34Chapter 3.4 --- Overview of the Framework --- p.35Chapter 3.4.1 --- "Mining Temporal Pattern I, AppSeq" --- p.36Chapter 3.4.2 --- "Mining Temporal Pattern II, LinkSeq" --- p.36Chapter 3.5 --- Summary --- p.37Chapter 4 --- "Mining Temporal Pattern I, AppSeq" --- p.38Chapter 4.1 --- Problem Statement --- p.38Chapter 4.2 --- Mining A1 Temporal Patterns --- p.40Chapter 4.2.1 --- Candidate Generation --- p.43Chapter 4.2.2 --- Large k-Items Generation --- p.46Chapter 4.3 --- Mining A2 Temporal Patterns --- p.48Chapter 4.3.1 --- Candidate Generation: --- p.49Chapter 4.3.2 --- Generating Large 2k-Items: --- p.51Chapter 4.4 --- Modified AppOne and AppTwo --- p.51Chapter 4.5 --- Performance Study --- p.53Chapter 4.5.1 --- Experimental Setup --- p.53Chapter 4.5.2 --- Experimental Results --- p.54Chapter 4.5.3 --- Medical Data --- p.58Chapter 4.6 --- Summary --- p.60Chapter 5 --- "Mining Temporal Pattern II, LinkSeq" --- p.62Chapter 5.1 --- Problem Statement --- p.62Chapter 5.2 --- "First Method for Mining LinkSeq, LinkApp" --- p.63Chapter 5.3 --- "Second Method for Mining LinkSeq, LinkTwo" --- p.64Chapter 5.4 --- "Alternative Method for Mining LinkSeq, LinkTree" --- p.65Chapter 5.4.1 --- Sequence Tree: Design --- p.65Chapter 5.4.2 --- Construction of seq-tree --- p.69Chapter 5.4.3 --- Mining LinkSeq using seq-tree --- p.76Chapter 5.5 --- Performance Study --- p.82Chapter 5.6 --- Discussions --- p.85Chapter 5.7 --- Summary --- p.85Chapter 6 --- Conclusion and Future Work --- p.87Chapter 6.1 --- Conclusion --- p.87Chapter 6.2 --- Future Work --- p.88Bibliography --- p.9

Multivariate time series classification with temporal abstractions

The increase in the number of complex temporal datasets collected today has prompted the development of methods that extend classical machine learning and data mining methods to time-series data. This work focuses on methods for multivariate time-series classification. Time series classification is a challenging problem mostly because the number of temporal features that describe the data and are potentially useful for classification is enormous. We study and develop a temporal abstraction framework for generating multivariate time series features suitable for classification tasks. We propose the STF-Mine algorithm that automatically mines discriminative temporal abstraction patterns from the time series data and uses them to learn a classification model. Our experimental evaluations, carried out on both synthetic and real world medical data, demonstrate the benefit of our approach in learning accurate classifiers for time-series datasets. Copyright © 2009, Assocation for the Advancement of ArtdicaI Intelligence (www.aaai.org). All rights reserved