Discovering unexpected patterns in temporal data using temporal logic

Personalized medicine recommendation is a key job in contemporary healthcare, tasked with making precise and safe prescriptions based on an individual patient's profile. Most traditional recommendation models fail to accurately represent the complicated relationships between patients, diseases, and drugs and the temporal patterns of patient health records. In this work, we introduce GR-Med, a new hybrid system combining Graph Neural Networks (GNNs) and Recurrent Neural Networks (RNNs) for improving the performance of medicine recommendations. The GNN module best captures structural relationships between medical entities through utilization of heterogeneous graph data, while the RNN module captures temporal patterns in data to incorporate temporal patterns in diagnoses and treatments. We test GR-Med on actual real-world electronic health record (EHR) datasets, showing its better performance compared to current baseline models regarding recommendation accuracy, reliability, and clinical sensitivity. Our findings point to the promise of leveraging graph and sequential learning to improve smart healthcare systems and enable more intelligent clinical decision-making. This system recommends the best medicine for breast cancer chemotherapy with minimal side effects or no side effects.

Subsequence clustering of multivariate time series is a useful tool for discovering repeated patterns in temporal data. Once these patterns have been discovered, seemingly complicated datasets can be interpreted as a temporal sequence of only a small number of states, or clusters. However, discovering these patterns is challenging because it requires simultaneous segmentation and clustering of the time series. Here we propose a new method of model-based clustering, which we call Toeplitz Inverse Covariance-based Clustering (TICC). Each cluster in the TICC method is defined by a correlation network, or Markov random field (MRF), characterizing the interdependencies between different observations in a typical subsequence of that cluster. Based on this graphical representation, TICC simultaneously segments and clusters the time series data. We solve the TICC problem through a scalable algorithm that is able to efficiently solve for tens of millions of observations. We validate our approach by comparing TICC to several state-of-the-art baselines in a series of synthetic experiments, and we then demonstrate on an automobile dataset how TICC can be used to learn interpretable clusters in real-world scenarios.

Finding patterns in temporal data is an important data analysis task in many domains. Static visualizations can help users easily see certain instances of patterns, but are not specially designed to support systematic analysis tasks, such as finding all instances of a pattern automatically. VizPattern is an interactive visual query environment that uses a comic strip metaphor to enable users to easily and quickly define and locate complex temporal patterns. Evaluations provide evidence that VizPattern is applicable in many domains, and that it enables a wide variety of users to answer questions about temporal data faster and with fewer errors than existing state-of-the-art visual analysis systems.

Abstract. As one spatio-temporal data mining task, clustering helps the exploration of patterns in the data by grouping similar elements together. However, previous studies on spatial or temporal clustering are incapable of analysing complex patterns in spatio-temporal data. For instance, concurrent spatio-temporal patterns in 2D or 3D datasets. In this study we present two clustering algorithms for complex pattern analysis: (1) the Bregman block average co-clustering algorithm with I-divergence (BBAC_I) which enables the concurrent analysis of spatio-temporal patterns in 2D data matrix, and (2) the Bregman cube average tri-clustering algorithm with I-divergence (BCAT_I) which enables the complete partitional analysis in 3D data cube. Here the use of the two clustering algorithms is illustrated by Dutch daily average temperature dataset from 28 weather stations from 1992 to 2011. For BBAC_I, it is applied to the averaged yearly dataset to identify station-year co-clusters which contain similar temperatures along stations and years, thus revealing patterns along both spatial and temporal dimensions. For BCAT_I, it is applied to the temperature dataset organized in a data cube with one spatial (stations) and two nested temporal dimensions (years and days). By partitioning the whole dataset into clusters of stations and years with similar within-year temperature similarity, BCAT_I explores the spatio-temporal patterns of intra-annual variability in the daily temperature dataset. As such, both BBAC_I and BCAT_I algorithms, combined with suitable geovisualization techniques, allow the exploration of complex spatial and temporal patterns, which contributes to a better understanding of complex patterns in spatio-temporal data.

ABSTRACTOverviews of spatiotemporal data are acknowledged to play an important role in visualization in initiating and supporting geovisualization and exploratory data analysis (EDA). However, relatively little research has focused on the visual overviews themselves, and their potential impacts on EDA outcomes. In a user study, we evaluated the influence of different levels of domain knowledge on the usefulness of four distinct types of static visual overview of spatiotemporal data. Beyond simply orienting users, our results indicate that visual overviews can be important in gaining insights into a data set, for example, in learning about metadata. Although subjects without domain knowledge struggled to judge the quality of their findings, they were as successful at identifying interesting patterns in the data as those with domain expertise. Our results suggest that detailed background knowledge of a data set can actively hinder EDA. Being already familiar with their own data sets, our results highlight the tendency of data experts to disregard findings that do not match their pre-existing domain knowledge. Based on these findings, our conclusions identify a range of potential avenues for future work, including the use of visual overviews that deliberately do not, from first view, reveal the context of the data they show. This later approach could help in cases where domain experts need to see their data with ‘fresh eyes’, and detect interesting patterns in spatiotemporal data before relating the findings to specific knowledge about the data sets and the domain.

In general, databases store current data. However,the capability to maintain temporal data is a crucial requirement for many organizations and provides the base for organizational intelligence. A temporal database maintains time-varying data, that is, past, present, and future data. In this chapter, we focus on the relational data model and address the subtle issues in modeling and designing temporal databases. A common approach to handle temporal data within the traditional relational databases is the addition of time columns to a relation. Though this appears to be a simple and intuitive solution, it does not address many subtle issues peculiar to temporal data, that is, comparing database states at two different time points, capturing the periods for concurrent events and accessing times beyond these periods, handling multi-valued attributes, coalescing and restructuring temporal data, and so forth, [Gadia 1988, Tansel and Tin 1997]. There is a growing interest in temporal databases. A first book dedicated to temporal databases [Tansel at al 1993] followed by others addressing issues in handling time-varying data [Betini, Jajodia and Wang 1988, Date, Darwen and Lorentzos 2002, Snodgrass 1999].

BackgroundFetal movement counting has long been suggested as a screening tool to identify impaired placental function. However, quantitative limits for decreased fetal movement perform poorly for screening purposes, indicating the need for methodological refinement. We aimed to identify the main individual temporal patterns in fetal movement counting charts, and explore their associations with pregnancy characteristics.MethodsIn a population-based prospective cohort in Norway, 2009–2011, women with singleton pregnancies counted fetal movements daily from pregnancy week 24 until delivery using a modified "count-to-ten” procedure. To account for intra-woman correlation of observations, we used functional data analysis and corresponding functional principal component analysis to identify the main individual temporal patterns in fetal movement count data. The temporal patterns are described by continuous functional principal component (FPC) curves, with an individual score on each FPC for each woman. These scores were later used as outcome variables in multivariable linear regression analyses, with pregnancy characteristics as explanatory variables.ResultsFetal movement charts from 1086 pregnancies were included. Three FPC curves explained almost 99% of the variation in the temporal data, with the first FPC, representing the individual overall counting time, accounting for 91% alone. There were several statistically significant associations between the FPCs and various pregnancy characteristics. However, the effects were small and of limited clinical value.ConclusionsThis statistical approach for analyzing fetal movement counting data successfully captured clinically meaningful individual temporal patterns and how these patterns vary between women. Maternal body mass index, gestational age and placental site explained little of the variation in the temporal fetal movement counting patterns. Thus, a perceived decrease in fetal movement should not be attributed to a woman’s basic pregnancy characteristics, but assessed as a potential marker of risk.

By finding broader temporal and spatial patterns of brain activity, dictionary learning and sparse coding techniques circumvent the constraints of typical voxel-level studies of task-based functional magnetic resonance imaging (fMRI) data. Prior applications of these algorithms to task-related fMRI data, on the other hand, have not been tuned to simultaneously uncover temporal patterns of activity that change in tandem with changes in task circumstances and spatial patterns that exploit existing neuroscience knowledge. This work, presents a sparse dictionary learning method that decomposes fMRI data into temporal patterns of signals that loosely differ between task conditions and sparse spatial patterns that are at least partially similar to known functional network hubs, based on prior knowledge of the temporal pattern of task conditions and the locations of brain regions hypothesized to be involved in the task. To over come the a major drawback of the prior work in terms being constrained to provide an equal number of spatial and temporal patterns, even when the data was more accurately represented by a larger number spatial than temporal patterns (or vice versa), this work also propose a constrained decoupled dictionary learning method that uses prior knowledge related to task paradigms and the spatial locations of task-related brain regions to estimate decoupled spatial and temporal patterns that represent the fMRI data. The utility of sparse dictionary learning methods applied to task fMRI data is increased by simultaneously exploiting the task's known temporal structure and biasing solutions towards putative network hubs. The method identifies a high percentage of the spatial and temporal patterns programmed into simulated fMRI data. The temporal and spatial patterns are identified using an effective on-line optimization methodology. The technique detects geographical and temporal patterns in synthetic task fMRI data. When applied to two real-world fMRI data sets, the method: 1. automatically identifies temporal and spatial patterns that were known by neuroscientists to be task-related a priori but were not provided as inputs to the method; 2. provides measurements that differ significantly between differing tasks. When applied to real fMRI data from 100 participants two different studies, the suggested method also identifies geographic regions known a priori to be engaged by the Attention Network Task (ANT), AX-Continuous Performance Task (AX-CPT) and Stroop Task more thoroughly than competing methods. Using task information to partially constrain dictionary learning allowed this method to identify task related networks in real and synthetic fMRI data.

Linear time temporal logic (LTL) has become a well established tool for specifying the dynamic behaviour of reactive systems with an interleaving semantics, and the automata-theoretic approach has proven to be a very useful mechanism for performing automatic verification in this setting. Especially alternating automata turned out to be a powerful tool in constructing efficient yet simple to understand decision procedures and directly yield further on-the-fly model checking procedures. In this paper we exhibit a decision procedure for LTL over Mazurkiewicz traces which generalises the classical automata-theoretic approach to a linear time temporal logic interpreted no longer over sequences but certain partial orders. Specifically, we construct a (linear) alternating Buchi automaton accepting the set of linearisations of traces satisfying the formula at hand. The salient point of our technique is to apply a notion of independence-rewriting to formulas of the logic. Furthermore, we show that the class of linear and trace-consistent alternating Buchi automata corresponds exactly to LTL formulas over Mazurkiewicz traces, lifting a similar result from Loding and Thomas formulated in the framework of LTL over words.

Developmental biology often yields data in a temporal context. Temporal data in phylogenetic systematics has important uses in the field of evolutionary developmental biology and, in general, comparative biology. The evolution of temporal sequences, specifically developmental sequences, has proven difficult to examine due to the highly variable temporal progression of development. Issues concerning the analysis of temporal sequences and problems with current methods of analysis are discussed. We present here an algorithm to infer ancestral temporal sequences, quantify sequence heterochronies, and estimate pseudoreplicate consensus support for sequence changes using Parsimov-based genetic inference [PGi]. Real temporal developmental sequence data sets are used to compare PGi with currently used approaches, and PGi is shown to be the most efficient, accurate, and practical method to examine biological data and infer ancestral states on a phylogeny. The method is also expandable to address further issues in developmental evolution, namely modularity.

Mining Temporal Patterns from temporal databases is challenging as it requires handling efficient database scan. A pattern is temporally similar when it satisfies subset constraints. The naive and apriori algorithm designed for non-temporal databases cannot be extended to find similar temporal patterns from temporal databases. The brute force approach requires computing \(2^n\) true support combinations for ‘n’ items from finite item set and falls in NP-class. The apriori or fp-tree based approaches are not directly extendable to temporal databases to obtain similar temporal patterns. In this present research, we come up with novel approach to discover temporal association patterns which are similar for pre-specified subset constraints, and substantially reduce support computations by defining expressions to estimate support bounds. The proposed approach eliminates computational overhead in finding similar temporal patterns. The results prove that the proposed method outperforms brute force approach.

Mining local periodic patterns in a discrete sequence

We investigate logical consequence in temporal logics in terms of logical consecutions, i.e., inference rules. First, we discuss the question: what does it mean for a logical consecution to be ‘correct’ in a propositional logic. We consider both valid and admissible consecutions in linear temporal logics and discuss the distinction between these two notions. The linear temporal logicLDTL, consisting of all formulas valid in the frame 〈L≤, ≥〉 of all integer numbers, is the prime object of our investigation. We describe consecutions admissible inLDTLin a semantic way—via consecutions valid in special temporal Kripke/Hintikka models. Then we state that any temporal inference rule has a reduced normal form which is given in terms of uniform formulas of temporal degree 1. Using these facts and enhanced semantic techniques we construct an algorithm, which recognizes consecutions admissible inLDTL. Also, we note that using the same technique it follows that the linear temporal logicL(N) of all natural numbers is also decidable w.r.t. inference rules. So, we prove that both logicsLDTLandL(N) are decidable w.r.t. admissible consecutions. In particular, as a consequence, they both are decidable (known fact), and the given deciding algorithms are explicit.

Databases in general store current data. However, the capability to maintain temporal data is a crucial requirement for many organizations and provides the base for organizational intelligence. A temporal database has a time dimension and maintains time-varying data (i.e., past, present, and future data). In this article, we focus on the relational data model and address the subtle issues in modeling temporal data, such as comparing database states at two different time points, capturing the periods for concurrent events, and accessing to times beyond these periods, handling multivalued attributes, coalescing, and restructuring temporal data (Gadia 1988, Tansel & Tin, 1997). Many extensions to the relational data model have been proposed for handling temporal data.

We introduce Parametric Linear Dynamic Logic (PLDL), which extends Linear Dynamic Logic (LDL) by temporal operators equipped with parameters that bound their scope. LDL was proposed as an extension of Linear Temporal Logic (LTL) that is able to express all $\omega$-regular specifications while still maintaining many of LTL's desirable properties like an intuitive syntax and a translation into non-deterministic B\"uchi automata of exponential size. But LDL lacks capabilities to express timing constraints. By adding parameterized operators to LDL, we obtain a logic that is able to express all $\omega$-regular properties and that subsumes parameterized extensions of LTL like Parametric LTL and PROMPT-LTL. Our main technical contribution is a translation of PLDL formulas into non-deterministic B\"uchi word automata of exponential size via alternating automata. This yields a PSPACE model checking algorithm and a realizability algorithm with doubly-exponential running time. Furthermore, we give tight upper and lower bounds on optimal parameter values for both problems. These results show that PLDL model checking and realizability are not harder than LTL model checking and realizability.