Feature Mining Paradigms for Scientific Data∗

Ming Jiang† Tat-Sang Choy‡ Sameep Mehta† Matt Coatney† Steve Barr‡

Kaden Hazzard‡ David Richie§ Srinivasan Parthasarathy† Raghu Machiraju†

David Thompson¶ John Wilkins‡ Boyd Gatlin¶

Abstract

Numerical simulation is replacing experimentation as ameans to gain insight into complex physical phenom-ena. Analyzing the data produced by such simulationsis extremely challenging, given the enormous sizesof the datasets involved. In order to make efficientprogress, analyzing such data must advance fromcurrent techniques that only visualize static images ofthe data, to novel techniques that can mine, track, andvisualize the important features in the data. In thispaper, we present our research on a unified frameworkthat addresses this critical challenge in two sciencedomains: computational fluid dynamics and moleculardynamics. We offer a systematic approach to detectthe significant features in both domains, characterizeand track them, and formulate hypotheses with regardto their complex evolution. Our framework includestwo paradigms for feature mining, and the choiceof one over the other, for a given application, canbe determined based on local or global influence ofrelevant features in the data.

Keywords: feature mining, computational fluid

dynamics, molecular dynamics, shock detection, vortex

verification, defect evolution

1 Introduction

The physical and engineering sciences are increasinglyconcerned with the study of complex, large-scale evo-lutionary phenomena. Such studies are often based onanalyzing data generated from either traditional exper-iments or numerical simulations. Given recent con-current advances in computer hardware and numeri-

∗Supported by the National Science Foundation (ACI-9982344,

ACS-0085969, EEC-0121807, 764AT-51028A), the Department

of Energy (DE-FG02-99ER45795), and the U.S. Army Research

Office (DAA-D19-00-1-0155).†Dept. of Computer and Information Science, The Ohio State

University, {jiang,srini,raghu}@cis.ohio-state.edu‡Dept. of Physics, The Ohio State University§High Performance Technologies, Inc.¶Dept. of Aerospace Engineering, Mississippi State University

cal methods, it is now possible to simulate physicalphenomena at very fine spatial and temporal resolu-tions. As a result, the amount of data generated isoverwhelming and unprecedented. Examples of suchlarge-scale simulations can be found in numerous sciencedomains, including fluid dynamics and molecular dy-namics. Computational fluid dynamics (CFD) seeks tounderstand flow patterns to enhance, for instance, drugdelivery schemes for pulmonary treatments of asthma.Molecular dynamics (MD), on the other hand, seeks tounderstand the evolution of defect structures that canaffect the properties or performance of industrial mate-rials.

The size of many simulation datasets significantlychallenges our ability to explore and comprehend thegenerated data. Currently, a well-trained individualmay need several days, or even weeks, to analyze thedata generated by an MD simulation and create a listof viable defect structures. Similarly, in the extremelylarge datasets generated by simulations of complexfluid flows, locating and tracking relevant features aredaunting tasks, given their large number and vastmultitude of interactions.

Therefore, we believe it is crucial that some degreeof automation be incorporated into the data explorationprocess for large-scale datasets. One such successful ap-proach is described in [24] and is based on a representa-tional scheme that facilitates ranked access to macro-scopic features in the dataset. However, other thanidentifying, denoising, and ranking the features, no at-tempt is made to extract useful information about thefeatures, such as geometrical and dynamical attributes,that can be used for tracking features.

A seemingly obvious approach would be to applytraditional data mining techniques to these scientificdata. However, it is our contention that existing datamining techniques, applied in isolation, are simply toogeneral to be of any use for our applications. One wayto remedy this problem is to embed domain expertisein the data mining process. While some data miningtechniques do allow domain expertise to be incorporatedin specific ways, in general, they are not flexible enough

to meet all the subtle requirements of domain experts.Furthermore, the application of traditional data miningtechniques may not be the most efficient of solutions,particularly for analyzing time-varying simulation data,which can easily surpass the terabyte range. Whatis needed, in this case, are linear- or quasilinear-timealgorithms, as opposed to high-order polynomial-timealgorithms.

To address these perceived shortcomings, we are de-veloping a feature-centric unified framework for miningscientific data that we term generalized feature min-

ing and are applying it to CFD and MD simulationdata. Our intent is to exploit the underlying physicsof the problems in order to develop highly discriminat-ing, application-dependent detection, characterization,and tracking algorithms for features of interest. Thenusing available data mining algorithms where appropri-ate, to classify, cluster, and categorize the identified fea-tures. We further claim that the large-data explorationmethodology we describe is sufficiently general so thatother application domains can be incorporated into ourapproach. This claim is demonstrated by the applica-tion of our framework to two disparate application do-mains.

It should be noted that Yip and Zhao [43] pro-posed a similar, albeit more general, framework. Theyrelied on spatial aggregation to cluster both physicaland abstract entities and constructed imagistic solversto gain insights about physical phenomena. The mainoutcome is a spatial aggregation language (SAL) whichis offered as the basis for further data mining or explo-ration. Their claim, as is ours, is that feature mining,including aggregation and tracking, is the first step to-wards a comprehensive analysis of scientific data. Ourwork differs from theirs in that we focus more on three-dimensional computational datasets, demonstrate ourframework on time-varying datasets, and exploit moreof the underlying physics.

A version of our physics-based feature mining ap-proach appeared recently in [40]. However, we did notdescribe it as part of our unified framework for min-ing scientific data; moreover, we only demonstrated itseffectiveness in the CFD application domain. In this pa-per, we demonstrate the generality of our feature miningparadigms by including results from both CFD and MDsimulations. The remainder of this paper is organized asfollows. In Section 2, we describe related research con-ducted elsewhere. Section 3 presents the two featuremining paradigms in detail. Section 4 shows prelimi-nary results we have obtained so far for the two sciencedomains. Finally, we summarize our results and providea road map for future work in Section 5.

2 Related Work

Knowledge discovery and data mining (KDD) refersto the overall process of discovering new patterns orbuilding models from a given dataset. FundamentalKDD research in the last decade has primarily focusedon: i) new techniques to preprocess, mine, and evaluatethe data, ii) efficient algorithms that implement thesetechniques, and iii) the applications of above techniquesin business and marketing domains.

More recently, researchers have started tacklingthe problem of mining scientific data. In particularapproaches for mining astronomical [5, 16], biological [8,21, 41], chemical [7], and fluid dynamical [10] datasetshave been recently proposed by various researchers.Few of the above methods actually account for thekinematically and dynamically driven characteristics ofthe data. Abstract representations in the form of graphsare often extracted and variants of the traditionalfrequent itemset discovery technique are employed toglean insights into the physical phenomena.

Frequent substructure discovery is a pertinent ex-ample of traditional data mining techniques for scien-tific data, with applications ranging from computationalfluid dynamics to chemical compounds. By modelingthe features in a dataset with graphs, the problem offinding frequent patterns in the dataset becomes that ofdiscovering subgraphs that occur frequently throughoutthe entire set of graphs. Kuramochi and Karypis [17, 18]developed an efficient algorithm for discovering frequentsubgraphs in graph databases and applied it to chemicalcompound datasets. A similar technique can also be ap-plied to two-dimensional turbulent flow fields. Graphscan be constructed with the nodes representing the spa-tial location of coherent structures (e.g., vortices) withinthe turbulent flow field and the edges connecting nodesbased on spatial proximity. Subgraphs thus discoveredcan suggest various forms of spatial interactions amongthe coherent structures across time. However, such anabstract approach cannot exploit many of the inherentphysical and dynamical properties of flow fields.

For MD simulation data, we initially experimentedwith variants of the molecular substructure discoveryalgorithms [7, 8, 41]. We adapted the technique byParthasarathy and Coatney [26], for mining biologicalmacromolecules in protein data, in order to locate de-fects in silicon bulk lattices. The technique relies onrange pruning and candidate pruning for reducing thesearch space of possible frequent structures. Since alarge part of the lattice that we are considering is bulk,atoms associated with any instantiation of a highly fre-quent substructure can be safely pruned; the remain-ing atoms would constitute the defect [30]. The algo-rithm uses fuzzy recursive hashing for rapid matching

of structures to determine frequency of occurrence. Thehashing technique is used in lieu of the geometric hash-ing method [19, 42] given its lower costs and flexibility.The fuzziness is introduced to handle noise effects in thedata [35], especially for lattices at finite temperatures.The approach in general worked reasonably well but re-quired a lot of manual tuning of various parameters [6].The disadvantage of this approach is its computationalcomplexity and hence the need to search for more effi-cient alternatives.

Visualization literature is also replete with workson feature extraction and data analysis. Numer-ous schemes have been devised to automatically lo-cate shocks and other flow field discontinuities. Theseschemes are typically defined in terms of the numeri-cal gradients of solution variables [22, 23, 25, 38] andare generally effective for locating features that can beadequately described by magnitude changes in scalarfields. Critical points of vector fields define the struc-tural topology of the field and provide a convenientmethod of analysis [9, 20, 36]. However, fluid dy-namists are typically interested in macroscopic features,such as vortices, rather than the location of discretecritical points. Significant progress has been made inthe area of identifying vortices, or regions of swirlingflow [2, 4, 12, 27, 33, 39].

The consideration of time-varying data introducesan additional complexity through the need for trackingfeatures across multiple time steps of the dataset [29,37]. According to [34], five distinct evolutionary eventscan occur to features in scientific simulations: amalga-mation, bifurcation, continuation, creation, and dissi-pation. Each of these events must be accounted for indesigning a comprehensive feature tracking algorithm.

3 Feature Mining

Essentially, there is a need to detect features and de-rive their structures and characteristics from large-scaledatasets to better understand the evolutionary phenom-ena. In addition to feature detection algorithms, aggre-gation, characterization, and spatio-temporal trackingalgorithms must be utilized, in conjunction with tradi-tional data mining techniques, to gain scientific insights.We propose a general framework utilizing the followingtechniques to address the problems associated with ana-lyzing large-scale datasets generated from CFD and MDsimulations:

1. Event Detection:A “trigger-based” multiscale approach to temporalevent detection. Physically derived attributes,or triggers, are monitored for temporal events atmultiple time scales. For instance, this attribute

can be swirl in a CFD simulation or energy in aMD simulation.

2. Feature Mining:A systematic approach to locating, characterizing,and tracking features in unsteady phenomena. Themost salient aspects of feature mining include: fea-ture detection and aggregation, shape and attributecharacterization, and spatio-temporal tracking.

3. Interaction Discovery:Mining for important kinematical and dynamicalinteractions among the features of interest. Ourintention is to apply traditional data mining tech-niques, such as frequent substructure discovery, onthe processed features rather than the unprocessedraw data.

We term this integrated approach generalized feature

mining. In the following subsections, we describe indetail the two feature mining paradigms that comprisethe second step of the proposed framework.

3.1 What Is a Feature?

Perhaps the most appropriate response to this questionis, “It depends on what you’re looking for.” In general,a feature is a pattern occurring in a dataset that is themanifestation of correlations among various componentsof the data. For instance, a shock in a supersonic fluidflow would be considered a significant feature. Whensuch a shock occurs, the pressure increases abruptly inthe direction of the flow, and the fluid velocity decreasesin a prescribed manner. A significant feature also hasspatial and temporal scale coherence. In most cases,an adequately resolved feature spans several discretespatial or temporal increments. One can find similarexamples in the MD domain.

For many applications, generic data mining tech-niques such as clustering, association, and sequencingcan reveal statistical correlations among various com-ponents of the data. Returning to the shock example,we could use statistical mining to ferret out associations,but it might be difficult to attach precise spatial associa-tions for the rules discovered. A fluid dynamicist, how-ever, would like to locate features with a rather highdegree of certainty. Such qualitative assertions alonewill not suffice.

This is where our approach to feature mining comesin: we take advantage of the fact that, for simulationsof physical phenomena, the field variables satisfy cer-tain physical laws. We can exploit these kinematicand dynamic considerations to locate regions of interest(ROIs). The resulting feature detection algorithms, bytheir very nature, are highly application-specific. How-ever, the fidelity improvements garnered by tailoring

Local Binary Classification

Aggregation Aggregate Verification

Aggregation

Tracking

Local OperatorLocal Operator

Denoising

Ranking

Shape Characterization

ROIs

ROIs

Data

Figure 1: The figure shows the two feature min-ing paradigms being discussed here. The point-classification paradigm is depicted on the left branch,and the aggregate classification paradigm is depictedon the right branch.

these highly discriminating feature detection algorithmsto the particular application far outweigh any loss ofgenerality.

Since physically-based feature detection algorithmstend to be application specific, we defer discussion ofthese techniques until a later section. We now describetwo distinct feature mining paradigms. The commonthread is that both are bottom-up feature constructionswith underlying physically based criteria. The twoperform essentially the same steps, but in differentorder. These two paradigms are used depending on thelocal and global nature of the features. As will becomemore evident from the examples, it is unlikely thatnon-physics-based techniques can provide the fidelityneeded to locate complex flow field structures. Below weprovide general methodologies that can locate featuresacross a vareity of domains. Figure 1 shows the variousstages of the two paradigms.

3.2 Point Classification Paradigm

Many features can be identified using only the localcharacteristics of the data. These types of features lendthemselves to the feature mining paradigm which weterm point classification. More specifically, for the pointclassification paradigm to be appropriate for a givenfeature, that feature must be amenable to a detectionoperator and a classification criterion that are bothbased only on local characteristics of the data. Ashock in fluid mechanics simulation is an example ofa feature of this type. Similarly, a quenched defectwhich has attained local equilibria will also qualify formining with the point classification paradigm. Thepoint classification paradigm requires several operationsin the following sequence:

• Local feature detection at every point

• Point-based binary classification (verification)

• Aggregation of similarly classified points

• Denoising to eliminate weak features

• Ranking based on saliency of derived attributes

• Shape and dynamical attributes characterization

• Spatial and temporal feature tracking

This approach first identifies individual points as be-longing to a feature and then aggregates them to formcontiguous regions. Although the points are the entitiesthat are classified, it is the aggregated point sets thatare identified as features. The points are obtained froma tour of the discrete domain and may be the vertices ofthe mesh or sites of atoms used for the simulation. TheROIs can be represented as a list of volumetric elements(for CFD) or a point cloud (for MD).

3.3 Aggregate Classification Paradigm

Identification of other types of features may require in-formation that is less localized than the neighborhood ofa point. Further, we may need to classify a set of pointsbased on their collective behavior. We term this sec-ond feature mining paradigm aggregate classification.A vortex is an example of a feature in fluid dynamicsfor which this approach is appropriate. Point classifi-cation techniques can also be used to locate vorticesl;however, without the verification step, false positivescan pervade the analysis [40] and invariably cause er-roneous conclusions to be drawn or meaningless modelsto be built.

Aggregate classification follows a somewhat differ-ent sequence of operations than point classification:

• Local feature detection at every point

• Aggregation of contiguous candidate points

• Binary classification (verification) of aggregates

• Denoising to eliminate weak features

• Ranking based on saliency of derived attributes

• Shape and dynamical attributes characterization

• Spatial and temporal feature tracking

This approach first identifies individual points as be-ing candidate points in a feature using a local opera-tor. Then these points are aggregated to identify regionsthat potentially contain a feature. The classification al-gorithm, a physically-based regional criteria, is appliedto the aggregate to determine whether the candidateregion constitutes a feature. More detail is provided inthe next section. Note that it is a set of points that isclassified; however, the local operator applied here canbe very efficient and simultaneously liberal with its cri-teria, since aggregate verification will eliminate the falsepositives.

3.4 Denoising, Ranking, and Tracking

The set of detected features, or ROIs, may containanomalous entries. These entries may have inadequatespatial or temporal resolution. Denoising is oftenconducted to remove these features that may not besignificant. This operation can be as simple as usinga threshold for sizes of ROIs or can use a scale-spacedenoising technique [3, 40]. The ROIs can then beranked based on their size and an appropriate measureof feature strength (e.g. the density change for ashock or the total energy for a defect). By accordingranks, the most significant features can be accessed first.Geometrical shapes attributes are then extracted fromthe features. Note that we can also extend the conceptof shape attributes to include other kinematical anddynamical attributes. Tracking ROIs can be conductedon the extracted attributes. This approach providesan efficient solution to the problem of correspondencebetween features at different time steps.

4 Feature Mining Paradigms at Work

Feature mining enables us to gain insights about data indisparate application domains in an abstract way. In thesubsections that follow, we demonstrate the applicationof feature mining to CFD and MD simulation data. Wealso describe our efforts to characterize features, such asvortices and defects, with a sequence of elliptical frustaand tagged point clouds, respectively.

4.1 Paradigm 1: Point Classification

We describe below examples of features which can bemined using the point classification paradigm. The firstexample is mining shock waves in a CFD dataset. Wethen describe how a defect can be mined in a siliconbulk lattice, which is quenched and at equilibrium.

4.1.1 CFD Example: Shocks

As the first example of the point classification paradigm,we consider shock wave detection in flow fields. Ashock is a compression wave that may occur in fluidflows when the velocity of the fluid exceeds the localspeed of sound. A shock is characterized by abruptchanges in flow quantities such as pressure, velocity,and density. A physical shock is nearly a singularity– the changes occur over a distance equal to a fewmean free paths of the fluid molecules. In the case ofnumerical data, however, the discontinuity is typicallysmeared over several cells due to the errors inherent inthe discrete approximation. The properties of shocksare explained in more detail in [1]. These propertieshave to be exploited to develop highly discriminatingshock detection algorithms [15, 22, 25].

The key quantity in a shock detection algorithm isthe Mach number (ratio of the velocity magnitude to thelocal sound speed) normal to the shock wave. For a sta-tionary shock, the normal Mach number changes fromgreater than unity to less than unity in the directionof the flow. Further, near a shock, the pressure gradi-ent is aligned along the local shock normal. Therefore,the scalar product of the normalized pressure gradient∇P/|∇P | and velocity vector ~V can be used to identifycompression as well as the normal Mach number Mn

(after division by the local acoustics speed a) as givenby

Mn =~V

a·∇P

|∇P |.(4.1)

In regions where Mn changes from greater thanunity to less than unity in the direction of the flow,a shock exists. Notice that our operator, the changeof Mn in the direction of the flow, is a local definitiontherefore making this approach amenable to the point-classification paradigm. The detected point may thenbe aggregated to identify the region containing theshock. Of course, care must be taken not to divideby zero in regions where the pressure gradient is zero.Further, a correction term must be computed to accountfor the temporal variation of the flow field [22].

As an example of our shock detection technique, weshow two images for the standard blunt fin/flat plateflow field solution in Figure 2. Figure 2(a) shows adetached oblique shock that wraps around the blunt fin.

(a) Oblique shock on blunt fin/flat plate (b) Close up of λ-shock

Figure 2: Point classification paradigm shock waves in flow fields.

Figure 2(b) shows the symmetry plane which intersectsa λ-shock. It should be noted that the grid usedhere is relatively coarse which contributes to the rapiddissipation of the shock.

4.1.2 MD Example: Defect Evolution in Silicon

We address the challenge of mining structural defectsduring an ongoing MD simulation with the applicationof real-time multiresolution analysis (RTMRA) tech-niques and the point classification paradigm. Waveletanalysis is exploited in the time domain to analyze thedynamics. For each atom, its sequence of positions areprojected on a wavelet basis, with the expansion coeffi-cients generated incrementally, in real-time, using com-ponents supplied by the StormRT Scientific WaveletPackage [31]. These components treat streaming datamore efficiently than more conventional “fast” wavelettransform (fwt) techniques.

In any persistent structure, “defect” atoms mustbe distinguished from “bulk” atoms. While this taskis more challenging at finite temperature due to thethermal noise, a single local operator works perfectlyfor all quenched (clean) structures and surprisingly wellfor thermal (noisy) structures. A bulk silicon atom hasprecisely four neighbors within the distance of 2.6 Aand the angles between any two bonds lie within 90◦-130◦. Any other atom is a defect. Similar definitionscan be formulated for other systems. In a solid, theperiodic boundary condition has to be treated with careto obtain the correct bond lengths and distances nearthe boundary.

Here, we illustrate how the point classificationparadigm can be employed toward the defects in thequenched and finite temperatures structures. Each

Figure 3: Defect atoms are marked black. Structure(left) is identified at 1000K, which is quenched, us-ing first principles quantum machines, into structure(right). Even though the atoms in the top structureare displaced due to thermal noise, the same atoms aremarked as defect in both structures.

atom site is visited and the atom is tested for member-ship in a defect ensemble. The classification criterionfor this application is as follows. We define two condi-tions C1 (number of neighbors as above) and C2 (bondangle as above) to accurately classify bulk atoms. Theconjunction of the above two conditions as well as thedisjunction are evaluated for all atom sites. The atomsites which satisfy the conjunction are the ones whichdefinitely belong to the bulk. Those that satisfy thedisjunction would, with some likelihood, belong to thebulk. The remaining atom sites are definitely part of thedefect. Such atoms are referred to as defect atoms. Thedefect atoms are then spatially clustered, or aggregated,into possible defect structures. One can generalize this

method to include other local conditions, as may be thecase for alloy lattices.

Figure 4: Two spatially separated defect clusters (blackand grey) marked by local binary classification, followedby aggregation code.

Aggregation is crucial to large-scale simulation dueto the presence of multiple, spatially disconnected,defect clusters. A line is drawn connecting all defectatoms that lie within 4 A of each other. Each clusteris then a connected graph, which is computationallyinexpensive to obtain given the relatively small numberof atoms in a defect. Figure 4 shows two defectsembedded in a 512 atom lattice. The different shadesrepresent distinct and seperated spatial clusters.

We have empirically validated that this methodworks well even on noisy data. Figure 3(left) showsa persistent structure at 1000 K. The atoms markedblack are those identified as defect atoms. Fig-ure 3(right) shows the same structure quenched witha first-principles approach. Quenching removes thermalnoise at a heavy computational cost. The same atomsare marked in both structures which demonstrates thismethod works on noisy structures.

4.2 Paradigm 2: Aggregate Classification

We describe below examples of features which can bemined using the aggregate classification paradigm. Thefirst example is from CFD. We examine how vorticescan be automatically detected and verfied by resortingto the underlying physics of the flow field. Similarly, weallude to how the aggregate classification paradigm canbe used to mine defects in a silicon bulk lattice at finite

temperature.

4.2.1 CFD Example: Vortices

We now consider the application of the aggregate clas-sification paradigm to mining vortices in flow fields. Bymost accounts [27, 32], a vortex is characterized by theswirling motion of fluid around a central region. Thischaracterization stems from our visual perception of theswirling phenomena that are pervasive throughout thenatural world. However, translating that perceptual un-derstanding of a vortex into a formal definition has beenquite a challenge. Robinson [32] proposed the followingdefinition for the presence of a vortex:

A vortex exists when instantaneous streamlines

mapped onto a plane normal to the vortex core

exhibit a roughly circular or spiral pattern,

when viewed from a reference frame moving

with the center of the vortex core.

We recently developed vortex detection and verifi-cation algorithms based on the aggregate classificationparadigm [13, 14]. For the local detection operator, acombinatorial labeling scheme is employed to identifyall the grid points that belong to vortex cores. Whatmakes this approach so effective at detecting vortex coreregions is its close resemblence to Sperner’s lemma fromCritical Point Theory in combinatorial topology.

Swirl Plane

i i+1i−1j−1

j+1

k−1

k+1

k

j

A

CB

E

Figure 5: 3D vortex core region detection algorithm.

The connection between vortices and critical pointsare well known [39]. Whereas Sperner’s lemma labelsthe vertices of a simplex and identifies the fixed pointsof a labeled subdivision [11], our detection algorithm la-bels the velocity vectors of the grid points and identifies

(a) Detected core regions for blunt fin/flat plate (b) Illustration of verification algorithm

Figure 6: Aggregate classification paradigm for mining vortices in flow fields. Note the highly elliptic cross sectionof the vortex core region.

grid cells that are most likely to contain critical points.Each velocity vector is labeled according to the directionin which it points. Since velocity vectors around coreregions exhibit certain flow patterns that are unique tovortices, it is sufficient to examine the immediate neigh-borhood of a grid point for the existence of those flowpatterns. Figure 5 illustrates the detection algorithm inthree dimensions, where it is necessary to approximatethe vortex core tangent vector first, and then projectthe neighboring velocity vectors onto the swirl planenormal to it, before applying the above procedure tothe projected velocity vectors.

Our technique segments candidate vortex core re-gions by aggregating points identified from the detec-tion step. We then classify (or verify) these candidatecore regions based on the existence of swirling stream-lines surrounding them. For features that lack a for-mal definition, such as the vortex, we must choose theverification criterion so that it concurs with the intu-itive understanding of the feature. In this case, verify-ing whether a candidate core region is an actual vortexcore requires checking for swirling streamlines surround-ing it. Checking for swirling flow in three dimensions isa non-trivial problem since vortices can bend and twistin various ways. Given a candidate core region, our ver-ification algorithm automatically searches for swirlingstreamlines surrounding it, where the measure for swirlis defined in terms of the differential geometry proper-ties of the streamline. The technique we developed es-sentially checks to see if the local tangent to the stream-line, when projected onto the swirl plane normal to the

candidate core tangent vector, spans a measure of 2π.The aggregate nature of this classification step is ap-parent. Checking for swirling streamlines is a global (oraggregate) approach to feature classification (or verifi-cation) because swirling is measured with respect to theentire core region, not just individual points within thecore region.

As a demonstration of our algorithm, we ap-plied the aggregate classification paradigm to theblunt fin/flat plate flow field as shown in Figure 6. InFigure 6(a) we show the detected vortex core regionsand the the verifying streamlines near the fin/plate in-tersection. In Figure 6(b) (top left) we show a close-up of the primary vortex located adjacent to the flatplate. Notice that even though the vortex cross sec-tion is highly elliptical, the tangent vectors projectedinto the local swirling plane, gray vectors in Figure 6(b)(bottom), still satisfy the 2π swirling criterion.

4.2.2 MD Example: Defect Evolution

The large number of identified structures must besorted into a smaller set of distinct types. Quenchingsolves this problem but is computationally expensive.In addition, some structures are stable only at hightemperatures. By quenching, these structures are lost.Identifying time averaged structures is a great challenge.Occasionally with noisy data, too many or too fewatoms are marked. Figure 7 demonstrates this process.These two structures have different numbers of defectatoms marked, yet when quenched are the same. Theapplication of the aggregate classification paradigm for

mining MD data is still under development.

Figure 7: These two structures have a different numberof defect atoms marked. When quenched however theyare the same structure.

4.3 Shape Characterization

Having extracted features either as vortices (CFD) ordefects (MD), we describe the next step: characteriz-ing them using shapes attributes. Our objective is toprovide a characterization mechanism to facilitate thecorrespondence of features at different time steps to im-prove tracking efficiency. Therefore, it is critical thatthe geometrical and dynamical attributes selected rep-resent salient characteristics of the feature. Althoughnot discussed here, we anticipate that geometrical shapeattributes will be an invaluable tool when we endeavorto categorize evolutionary phenomena.

2

1

a

b 2

1

ab

h

Figure 8: Elliptical frustum

4.3.1 Vortices as Shapes

The swirling region of vortices can be characterizedusing a sequence of elliptical frusta. An ellipticalfrustum resembles a conical frustum, except that its twoends are ellipses rather than circles. This is illustratedin Figure 8, where h is the height of the frustum and

ai and bi are the length of the minor and major axes ofthe two ellipses. The restriction here is that the axesmust be aligned and their length must be proportional,(i.e. a1

a2

= b1b2

). The volume can be computed by thefollowing analytical formula:

V =1

3h(A1 + A2 +

√

A1A2)(4.2)

where Ai = πaibi are the areas of the two ellipses.The shape of an ellipse is usually expressed by

its eccentricity, conventionally denoted by e, which isrelated to ai and bi by the formula: b2

i = a2

i (1 − e2

i ).Eccentricity is a positive number less than 1, or 0 inthe case of a circle. A higher value corresponds to amore elongated ellipse. This is an important geometricalaspect of swirling regions that can be captured by usingelliptical frusta. In Reinders et al. [28], they used conicalfrusta to “flesh out” the skeleton graph. For modelingthe shape of vortical regions, this approach is not ideal.

The shape characterization process starts at thefinest level of approximation to the swirling region ofthe vortex. Starting from the upstream extent of thevortex core, the modeling process seeds a set of swirlingstreamlines surrounding the core region. The advantageof this paradigm is that the swirling streamlines arealready known from the previous verification step. Eachelliptical frustum is oriented along the longest segmentof the vortex core that does not curve by more than auser-specified amount εC . The ellipses at each end of thefrustum is fitted to the set of streamlines intersecting theswirling plane at each end of the frustum. This adaptiveapproach to shape modeling allows the minimal numberof elliptical frusta to characterize the swirling region.

Once the modeling process is finished at the finestlevel of approximation, the next level of elliptical frustaare produced by merging every contiguous pair of ellip-tical frusta at the current level. Given two contiguouselliptical frusta at the same level, the merging processpreserves their volumes in the new frustum, while av-eraging the rest of their shape attributes. By averag-ing the shape attributes of the merged elliptical frusta,the merging process also serves the purpose of a low-pass filter, smoothing the combined shape attributes athigher levels of approximation. In this fashion, a com-plete and concise hierarchical shape characterization ofthe swirling region is produced.

We illustrate the adaptive and hierarchical shapecharacterization process using the blunt fin/flat plateflow field. Figure 9 shows the sequence of ellipticalfrusta obtained at the finest level in (a) and after oneand three levels of merging in (b) and (c), respectively.

(a) (b) (c)

Figure 9: Adaptive and hierarchical shape characterization of the vortices in the blunt fin data set: (a) level 1,(b) level 2, and (c) level 4.

4.3.2 Defects as Shapes

We next illustrate how to represent defect structuresand distinguish among them. Molecules and their sub-structures are often described as three-dimensional co-ordinate graphs, where atoms are nodes and chemicalbonds are edges. Two substructures are consideredequal if, after an arbitrary number of spatial transla-tions (and/or rotations) on one substructure, both sub-structures are described by the same graph.

Defects are represented simply by atom locations,(i.e., their (x, y, z) coordinates). In order to match de-fect structures, one approach is to store complete three-dimensional information between all pairs of atoms(mining bonds) belonging to a defect. The mining bondM(AiAj) is a 3-tuple of the form

M(AiAj) = {Aitype,Ajtype, distance(AiAj)}

A k-atoms et X, which is a substructure containing kconnected atoms, is then defined as a tuple of the form

X = {SX, A1, A2, . . . , Ak},

where Ai is the ith atom and SX is the set of miningbonds describing the atomset. By defining atom paircombinations with mining bonds, the 3D graph iscompletely represented in a form, such that two atomsets X and Y are considered to be the same chemicalsubstructure if SX = SY. To compare two defects wesimply need to compare the corresponding X tuplesof the corresponding atomsets represented by the twodefects. The problem with this naive approach is that itis not very robust to noise (missing or perturbed defectatoms) and the memory requirements are O(k2) where krepresents the number of atoms in the defect structure.

As an alternative to the above approach, we decom-pose each defect structure into k spherical regions, each

one centered around every atom belonging to the defect.The substructures formed by all those atoms within theROI are represented as using mining bonds. The keytwist is that substructures of interest are matched us-ing recursive fuzzy hashing, a technique that allows usto handle noise-effects in the data [26]. The memoryutilization is O(km) where m < k.

This set of “interesting” substructures is used togenerate a substructural fingerprint for a given de-fect. A substructure fingerprint for a particular de-fect is a vector representation of the set of “interest-ing” substructures; elements representing substructurescontained in that defect are marked, either with a 1(present) or a 0 (absent) [26]. Defect disambiguationcan then be conducted by comparing the correspondingfingerprint vectors. It turns out that this simple ap-proach is robust to noise as well as efficient to compute.Moreover, as we can see from Table 10, the disambigua-tion is near perfect (non-diagonal elements are 0, diag-onal elements are 1) for a set of 14 defect types acrossmultiple simulation runs (0 indicating perfect dissimi-larity and 1 representing high similarity).

This approach clearly lends itself to identifying dis-criminating motifs, (i.e., substructures that can disam-biguate between different defects). Moreover these mo-tifs are likely to be much smaller than the defect struc-tures enabling one to develop more efficient defect classi-fiers, based on the presence or absence of these discrim-inatory motifs d-motifs. Essentially, instead of generat-ing all the motifs for a given defect and then construct-ing a fingerprint, we would only need to check for thepresence or absence of these d-motifs. The robustnessof this strategy, is currently being evaluated.

Defect 1 2 3 4 5 6 7 8 9 10 11 12 13 14

1 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

2 0.0 1.0 0.08 0.04 0.04 0.04 0.08 0.0 0.0 0.0 0.0 0.0 0.07 0.09

3 0.0 0.08 1.0 0.04 0.04 0.04 0.04 .0.0 0.0 0.0 0.08 0.04 0.0 0.094 0.0 0.04 0.04 1.0 0.1 0.11 0.0 0.0 0.0 0.04 0.0 0.0 0.04 0.05

5 0.0 0.04 0.04 0.1 1.0 0.15 0.04 0.05 0.04 0.03 0.04 0.04 0.07 0.04

6 0.0 0.04 0.04 0.11 0.15 1.0 0.0 0.05 0.05 0.14 0.09 0.0 0.04 0.05

7 0.0 0.08 0.04 0.0 0.04 0.0 1.0 0.0 0.0 0.0 0.0 0.04 0.03 0.048 0.0 0.0 0.0 0.0 0.05 0.05 0.0 1.0 0.13 0.0 0.05 0.0 0.04 0.0

9 0.0 0.0 0.0 0.0 0.04 0.05 0.0 0.13 1.0 0.0 0.04 0.0 0.04 0.0

10 0.0 0.0 0.0 0.04 0.03 0.14 0.0 0.0 0.0 1.0 0.12 0.0 0.0 0.011 0.0 0.0 0.08 0.0 0.04 0.09 0.0 0.05 0.04 0.12 1.0 0.0 0.03 0.0

12 0.0 0.0 0.04 0.0 0.04 0.0 0.04 0.0 0.0 0.0 0.0 1.0 0.03 0.0

13 0.0 0.07 0.0 0.04 0.07 0.04 0.03 0.04 0.04 0.0 0.03 0.03 1.0 0.0

14 0.0 0.09 0.09 0.05 0.04 0.05 0.04 0.0 0.0 0.0 0.0 0.0 0.0 1.0

Figure 10: Familiarity based on Sub structural Fingerprinting

5 Summary

The steady increase in computing power perenniallychallenges our ability to learn new science from themassive amount of data that are being generated. Ourscience applications, computational fluid dynamics andmolecular dynamics, raise central problems that we planto address using a common framework which we havechristened generalized feature mining. Components ofthis approach include temporal event detection, localand global feature mining paradigms, and kinematicaland dynamical interactions discovery.

Our science applications are very distinct and at-tempt to characterize very diverse phenomena. How-ever, they both have commonalities that are exploitedby the above set of techniques. We reported some ongo-ing research in designing feature mining paradigms forlarge-scale simulation datasets. The results obtainedhave been very encouraging. A systematic approachto feature mining was conceived to locate both localand global features. However, much more remains tobe done to realize the complete unified framework men-tioned above. Our next main task will be tracking thecharacterized features by exploiting the similarities inthe extracted geometrical and dynamical attributes toaddress the correspondence problem between features atdifferent time steps. Finally, we plan to find associationsbetween features and events to gain further scientific in-sights.

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