Visualizing Distributed Memory Computationswith Hive Plots

Sophie EngleUniversity of San Francisco

Harney Science Center, Room 5322130 Fulton Street

San Francisco, CA 94117-1080sjengle@cs.usfca.edu

Sean WhalenColumbia University

450 Computer Science Building1214 Amsterdam Avenue, Mailcode: 0401

New York, NY 10027-7003swhalen@cs.columbia.edu

ABSTRACTA hive plot is a network layout algorithm that uses a parallelcoordinate plot in which axes are radially arranged and nodeposition is based on structural properties of that node [8]. Weapply hive plots to message-passing communication networksformed by different high performance computing applica-tions at Lawrence Berkeley National Laboratory. Hive plotshave advantages over common network visualization methods,abandoning the popular “hairballs” of force-directed networklayouts and opting instead for a tunable, repeatable, andinterpretable view of network-theoretic properties. Smallmultiples of these hive plots, called hive panels, are analyzedto suggest which properties contribute to accurate classifica-tion of application behavior for anomaly detection in highperformance computing environments.

Categories and Subject DescriptorsC.2.0 [Computer-Communication Networks]: General—Security and protection; C.2.4 [Computer-CommunicationNetworks]: Distributed Systems—Distributed applications;E.1 [Data]: Data Structures—Graphs and networks; I.3.0[Computer Graphics]: General

General TermsDesign, Experimentation, Security

KeywordsHive plots, network visualization, high performance comput-ing, anomaly detection

1. INTRODUCTIONDistributed computing systems, including clouds and high

performance computing clusters, are attractive targets formisuse by both external attackers and insiders. An oft-neglected class of such systems are the supercomputers oper-ated by government labs which consistently rank among the

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fastest in the world, yet are not known to have safeguardsagainst cracking encryption keys or performing nuclear simu-lations for hostile entities, for example.

The de-facto standard for distributed memory parallel pro-gramming in high performance computing environments isMessage Passing Interface (MPI). Programs written usingMPI can scale to thousands of nodes, where each node per-forms local computation and requests non-local data fromremote nodes using MPI calls. The pattern of MPI calls ishighly structured and tied to the underlying algorithm; simi-lar algorithms express similar patterns, and computationalequivalence classes have been found [5].

Communication between nodes is modeled as a directedgraph where ranks are nodes and MPI calls are edges. Sucha graph may have edges scaling exponentially with the num-ber of nodes, which themselves may number in the dozens,hundreds, thousands, or even tens of thousands for typical sci-entific computations. The analysis of such non-trivial graphsis the domain of network theory where they are termedcomplex networks.

Dozens of statistics exist for quantifying the structureof complex networks, but information overload is a perva-sive problem with their visualization—drawing thousandsof nodes with millions of edges in two or three dimensionsis a challenging problem with no universal solution. Visual-izations using popular force-directed layouts are helpful forsmall networks, but quickly lose their interpretability andoften lack discussion of what insight (if any) was gained bytheir use. The problem is compounded when multiple prop-erties are overlaid onto the same visualization. This poses acatch-22 for machine learning and its application to computersecurity in the form of anomaly detection: visualization canidentify predictive features and reduce the dimensionality ofboth data and model, yet identifying relevant patterns canbe difficult in the presence of visual complexity.

This paper explores a recent visualization technique calledhive plots [8] that aim to resolve problems with currentforce-directed layouts and present a tunable, repeatable, andinterpretable view of complex networks. We apply hive plotsas an exploratory step to identify which network propertiesmay lead to better classification results and more accurateanomaly detection, and demonstrate the advantages of hiveplots over traditional network layouts for revealing commu-nication patterns while remaining easily comparable acrossdatasets. We first discuss details of our network data in-cluding relevant background on high performance computingand communication logging. We then review hive plots, dis-

cuss our implementation, and demonstrate how hive plotscontribute to our understanding of predictive network char-acteristics.

2. DATASETOur dataset consists of MPI calls made between the com-

putational nodes of several high performance computing ap-plications at Lawrence Berkeley National Laboratory. Fromthese logs we generate directed multiple-edge graphs andcompute per-node network measures using the igraph li-brary [7] in the R statistical computing package. In thissection we provide additional detail on this dataset and howit was collected, as well as describe the data processing stepstaken prior to visualization.

2.1 BackgroundParallel programming models can be broadly divided into

shared memory models where computations share a commonaddress space, and distributed memory models where com-putations are restricted to a local subset of global memory.Message Passing Interface (MPI) is the de-facto standard fordistributed memory parallel programming in both industryand academia, with many cross-platform implementationsoptimized for different combinations of computational andnetworking hardware and software. The basic model involvescomputational nodes (referred to as ranks due to the uniqueidentifier assigned to each node) performing computationon local data and requesting data from remote nodes whenrequiring access to non-local data. Communication betweennodes is thus an essential characteristic of MPI, and imple-menting efficient communication for a given algorithm isoften the subject of dedicated research areas.

Due to the link between data access and communication,the patterns of messages exchanged between compute nodesis closely tied to the underlying algorithm. Thus, differentalgorithms will result in different patterns of MPI calls, whilealgorithms with similar memory access patterns may exhibitsimilar communications. This is a subtle but importantdistinction from a security perspective: While we can obtainground truth about communication patterns by capturingnetwork traffic or logging calls using shared libraries, wecannot know what code is executing on a system by examiningjob submission logs or looking at binary names since suchinformation is trivial to manipulate. An attacker could runan executable with the same name as a molecular dynamicssimulator while the underlying computation brute forces anencryption key. However, if they wish to perform a certainkind of computation they must either make the necessarycalls which will be patterned, or try to fool an observer byemulating other patterns at the cost of efficiency for theirtrue goal.

2.2 Data CollectionIn order to visualize communication patterns and identify

useful attributes for anomaly detection, we first need a mech-anism of observing MPI calls. To collect communicationsfrom running MPI programs we use a shared library calledIntegrated Performance Monitoring (IPM) [4]. The IPMlibrary provides low-overhead logging of MPI call featuressuch as the call name, the source and destination rank, thenumber of bytes sent, and aggregate performance counterssuch as the number of integer and floating point operations.

Our original dataset includes 1681 logs of 29 MPI-enabled

scientific computations collected for Lawrence Berkeley Na-tional Laboratory by the National Energy Research ScientificComputing Center. Multiple logs exist for each program withvarying ranks, parameters, architectures, and datasets whenpossible. Several simpler codes were logged by us; codesrequiring significant domain knowledge or private datasetswere logged from willing specialists on production systems.As a result, the inputs and parameters for some codes werenot under our control. However, this dataset is several or-ders of magnitude larger than related efforts and we believecontains a representative sample of the application classesfound in scientific computing.

Our analysis focuses on 8 of the 29 scientific computa-tions collected in the original dataset: cactus (astrophysics),ij (algebraic multi-grid), milc (lattice gauge theory), namd(molecular dynamics), paratec (materials science), superlu(sparse linear algebra), tgyro (magnetic fusion), and vasp

(materials science). These codes mostly span the basic classesof scientific computation outlined by Asanovic et al. [2] withsome overlap to demonstrate how hive plots distinguish simi-lar networks. To equalize visual comparison we use a singlelog from each code running on 64 computational nodes.

2.3 PreprocessingWe first construct directed graphs from each log with MPI

call names as edge labels. For greater interpretability, wefocus on point-to-point MPI calls and filter out broadcastmessages. We load these directed, multiple-edge graphsin the R statistical computing package and use the igraph

library to calculate per-node network properties [7]. Sincethese graphs contain one directed edge per type of MPI callmade, edge counts range from 1000 to over 10000. Theigraph library was unable to calculate certain properties forextremely dense graphs such as paratec and vasp, so thesecodes were dropped from our final analysis.

We calculate the degree, betweenness, closeness, eccentric-ity, page rank, and transitivity for each node and distinguishbetween incoming and outgoing edges where appropriate. Forexample, we calculate closeness for all edges, only incomingedges, and only outgoing edges. Our final analysis focuses ondegree, betweenness (undirected), page rank, and transitivitysince these measures produced the most informative hiveplots. The degree of a node is the number of edges connectedto that node. The betweenness of a node indicates how manyshortest paths travel through that node. Transitivity, alsoknown as the clustering coefficient, measures the connectivityof a node’s neighbors. Finally, page rank is an eigenvectorcentrality measure.

3. HIVE PLOTSA hive plot is a network layout algorithm that uses a

parallel coordinate plot in which axes are radially arrangedand node position is based on structural properties of thatnode, introduced by Krzywinski et al. [8]. Each hive plot iscreated using several rules: axes assignment and node posi-tioning rules, axes layout rules, and edge drawing rules. Weachieve repeatable, comparable layouts by using consistentrules across datasets.

For example, to create a hive plot using the degree of eachnode, we must first create simple Boolean tests to assign eachnode to a single axis. The following is an example of sucha test: “Is the node degree less than or equal to 32?” Wethen use the degree value to determine the node’s position

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Figure 1: Panels (a) and (b) provide hive plots for degree of the cactus and tgyro datasets respectively.

on the assigned axis. For example, a node of degree 32 willbe placed at the outer-most position on the axis since themaximum degree allowed by our example axis assignmenttest is 32. Edges are drawn as curves between nodes, withspecial rules governing how edges are drawn between nodeson the same axis. Example hive plots based on degree aregiven in Figure 1.

Several implementations of hive plots are available fromthe project’s website at hiveplot.net. However, we foundthat these implementations did not meet our needs. Wecreated a custom implementation of hive plots in the R usingthe ggplot2 library [15]. We chose the ggplot2 library forits adherence to well-established visual design principles [11,16]. We followed many of the recommended axes assignment,layout, and edge drawing rules from the original paper [8],but did make several design modifications to maximize ourspecific goals. We discuss these decisions next.

3.1 Axes AssignmentAxes assignment rules determine the number of axes to

use in each hive plot and how to assign nodes to those axes.We use three axes positioned every 2π/3 radians to avoidedge crossings over axis lines. However, there may still beedges between nodes on the same axis. We discuss how theseedges are drawn in Section 3.3.

Each hive plot visualizes a single attribute such as degree,betweenness, or other per-node network properties. Wecalculate the minimum and maximum value of each attributeacross all datasets and divide that range between the threeaxes using 3-quantiles at probabilities 0.25 and 0.75. Eachdataset uses the same range of values for each axis to allowfor comparison across datasets.

For example, see panel (a) of Figure 1. This hive plot usesdegree to assign nodes from the cactus dataset to differentaxes. The north axis contains nodes with degree less thanor equal to 32, while the south-west axis contains all nodes

with degrees greater than 32 but less than or equal to 259.The south-east axis contains all nodes with degree greaterthan 259 and less than or equal to the maximum value of 837,but no such nodes exist for the cactus dataset. Contrastthis to the hive plot in panel (b) for the tgyro dataset, whichuses the same cutoff values for each axis and contains onehigh-degree node on the south-east axis.

3.2 Axes LayoutEach node has an angle (theta) and distance (radial value)

for plotting in polar coordinates. The axes assignment rulesdetermine the theta value for the node position. The axeslayout rules determine the radial value of a node along an axis.We normalized the axis length to 1 and explored differentapproaches for calculating node positions.

In order to address the case where many nodes sharethe same attribute value, we select from three different ap-proaches to calculate node positions. For example, the su-

perlu dataset has 25 nodes with degree 79. Figure 2 showseach approach.

The first method, illustrated by panel (a), orders nodesby attribute value and evenly spaces nodes along the axis.While this approach maximizes the space used along theaxis, the actual range of attribute values are obscured. Forexample, it appears that the degree values for superlu on thesouth-west axis range from 32 to 259 in panel (a), whereasin reality the values range from 79 to 175.

Our second method uses linear interpolation from theminimum to maximum possible value for an axis. Thisapproach provides a better estimation of the actual range ofvalues on a given axis, but nodes with the same value areplotted at the same location. As a result, only one node oredge appears where several occur. For example, there are 25nodes with degree 79, but only one node appears with thatvalue in panel (b) of Figure 2.

To address this issue, we combine linear interpolation with

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Figure 2: Hive plots of degree for the superlu dataset using different node layout and edge drawing rules.Panel (a) uses evenly-spaced node positions and fixed edge alpha values. Panel (b) uses linear interpolationfor node positions and fixed edge alpha values. Panels (c) and (d) uses linear interpolation plus a repellingscheme for node positions and fixed versus variable edge alpha values, respectively.

a repelling scheme so nodes with the same value appearclustered next to each other. We can still visually estimatethe range of values on an axis, but are also able to estimatethe number of nodes on an axis and how many of those nodesshare the same value. This approach is illustrated in panel(c) of Figure 2.

3.3 Edge DrawingAll edges are drawn as curves between the polar coordinates

associated with each node. If there are any edges betweennodes on the same axis, the axis line and associated nodesare duplicated π/6 radians next to the original axis. Edgesbetween nodes on the same axis are drawn between theoriginal and duplicate axis lines. For example, the edgebetween the node on the south-east axis and its duplicate inFigure 2 indicates that node has a self loop.

We also address the visual density of edges between axesin high-degree datasets such as ij and namd. In some cases,aggregate edge density obscured individual edge lines and theresulting communication patterns. For example, the densityof edges between the original and duplicate axis in panel (b)of Figure 2 results in a nearly solid block of color.

The visual density of these edges is not an accurate reflec-tion of actual edge density in the original graphs, especiallysince the hive plots do not convey multiple edges or direc-tionality. However, lowering the overall alpha (opacity) valuefor the entire graph forces edges such as the one between thesouth-east axis and its duplicate axis to disappear. Instead,we calculate a per-edge alpha value that approximates nearbyedge density. The result of this variable per-edge alpha isshown in panel (d) of Figure 2, which better visualizes indi-vidual edges between the axis lines and the banding structurecaused by the communication between these nodes.

3.4 ImprovementsThere are several directions for improving our hive plot

implementation. First, we use linear scaling to positionnodes along axes. Future implementations would allow foradditional scales. Second, we use a normalized axis lengththat creates the appearance of each axis covering an equalrange of values. We address this by including labels indicatingthe range of each axis, but believe non-normalized axis lengthis also informative. Lastly, we did not experiment withapproaches for conveying the directionality and multipleedges present in our communication networks with hive plots.This is a limitation of hive plots in general and is not specificto our implementation, though it may be possible through acombination of color, alpha values, and edge decoration.

4. RESULTSOur primary goal is not to use visualization directly for

anomaly detection, but instead to use exploratory data visu-alization to help identify which network properties are likelyto improve our classification results for anomaly detection.Towards this goal, visualization must reveal communicationpatterns between nodes while remaining easily comparableacross datasets. This section discusses how our approachmeets this goal.

4.1 Communication PatternsPlotting the complementary cumulative distribution func-

tion (CCDF) of network properties is a standard visualizationtechnique. For example, CAIDA provides CCDF plots to

compare Internet topologies for network properties includingdegree, betweenness, eccentricity, and transitivity [10]. Weshow the CCDF of degree for our datasets in Figure 3. Fromthis plot we are able to compare the degree distributionsof different datasets. However, the communication patternsexhibited by these networks are lost in the CCDF plot.

Notice in Figure 3 that the CCDF plots for cactus andtgyro are similar despite the codes having very differentfunctionality (astrophysics vs. magnetic fusion). Comparedto their hive plots in Figure 1 we can still see that bothdatasets have similar degree ranges, but the communicationpatterns between these nodes exhibit different shapes andslightly different banding patterns between axes. Hive plotsallow us to visually differentiate between these datasets.

Instead of CCDF and hive plots, one may use other net-work layout algorithms to visualize communication patternspresent within these networks. Many of these algorithms areunsuitable for comparison of networks, as we discuss next.

4.2 ComparabilityThe result of force-based network layout algorithms for

medium and large networks are sometimes referred to as“hairballs” as the number of nodes and edges obscure anydiscernible structure. The unpredictability inherent in suchalgorithms makes it difficult to compare different networks, oreven compare the the same network with minimal structuralchanges such as adding or removing a single node.

Hive plots address the underlying issues that make force-based network layout algorithms unsuitable for network com-parison [8]. This is especially true of hive panels, which aresmall multiple visualizations of hive plots across attributesand datasets using consistent assignment, layout, and edgedrawing rules. Using hive panels we are able to directly com-pare the “quantitative visual signature” of each plot acrossdatasets.

A hive panel for degree, undirected betweenness, transi-tivity, and page rank is shown in Figure 4. From the panelwe see ij and namd share similar patterns for degree andpage rank. We expect similarities in these datasets sinceboth have nearly fully-connected topologies. However, wecan visually distinguish between them by looking at theirbetweenness and transitivity properties instead. The codescactus and milc have similar topologies as well, and as aresult the betweenness plots are quite similar except for twohigh-valued nodes in cactus. However, they exhibit verydifferent degree plots due to the diversity of MPI calls madebetween nodes.

The properties shown in Figure 4 were selected for theirability to visually distinguish codes. Other properties re-sulted in informative but less distinct hive plots, and weexpect will be less informative for building models of nor-mal behavior for anomaly detection. The evaluation of thishypothesis is left for future work.

5. RELATED WORKThere are many applications of visualization to intrusion

detection and specifically anomaly detection, often focusingon post-hoc analysis independent from system design. Closestin spirit to our approach are papers by Xin et al. [17] andLaskov et al. [9] which use visualization to guide featureselection during the initial design and refinement of intrusiondetection systems as opposed to the more common post-hocanalyses of log data, for example.

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Figure 3: A complementary cumulative distribution function (CCDF) plot for degree. The shape of theCCDF plots for cactus and tgyro are similar despite the codes having different functionality.

Parallel coordinates [12] are a well-established method forvisualizing multivariate data and have been previously ap-plied in a security context [3, 6]. A hive plot is essentially aparallel coordinate plot with a radial axis layout where nodesare placed using the projection of structural properties of agraph. However, as discussed by Krzywinski et al. [8], thesedifferences lead to more compact and interpretable represen-tations over related techniques such as parallel coordinates orsemantic substrates [1]. Previous applications of hive plotsfocus on biological networks such as gene regulation and geneinteraction networks.

Previous work using this dataset found that MPI commu-nication patterns reveal the underlying computation withhigh accuracy [13, 14]. This result was motivated by earlierwork on computational equivalence classes called dwarves [5]defined as “a pattern of communication and computationcommon across a set of applications” [2]. We aim to useexploratory visualization with hive plots to select featuresfor a purely complex networks-based approach to anomalydetection in high performance computing.

6. FUTURE WORKThis work represents an initial step towards improving

classification for anomaly detection. Specifically, we use hivepanels to reveal communication patterns and identify whichnetwork properties lead to distinct hive plots for distinctdata sets. The next step is to examine whether hive plots formultiple runs of the same code with different run-time param-eters are similar. For example, the hive plots of the cactus

code when run on 64 compute nodes should be visually sim-ilar to the hive plots of cactus when run on 128 computenodes. Finally, we must explore whether the network proper-ties identified during this exploratory data visualization stepactually improve classification results and the accuracy ofanomaly detection.

Our visualization approach may also be improved. Whileinteractivity was not necessary for our immediate classifi-

cation goal, adding interactivity may improve our under-standing of the communication patterns for each type ofcomputational dwarf. We may also explore including moreinformation from the original data set, such as the number ofbytes communicated between nodes and the different typesof MPI calls made between nodes.

7. CONCLUSIONSHigh performance computing environments are overlooked

by existing anomaly detection systems, but regularities inthe patterns of messages exchanged between compute nodesmake them a suitable target for such systems. These patternsare captured by multiple-edge directed graphs, and ensemblesof statistical properties from the field of complex networktheory can distinguish graphs that otherwise appear similarusing traditional approaches.

Selecting the properties most relevant for machine learningmodels results in faster, more general anomaly detectors.Exploratory visualization can be a powerful tool for suchfeature selection. However, traditional force-directed networklayout algorithms suffer from lack of reproducibility andan inability to compare across networks or their statisticalproperties. We use a recent network visualization techniquecalled hive plots which address these weaknesses by modifyingparallel coordinate plots to use radial axes with special rulesfor assigning nodes to axes and the position of nodes alongeach axis. Hive panels are formed using small multiples ofmany hive plots for visualizing different network propertiesand datasets.

Our initial results are promising. Using a hive panel weare able to determine which network properties generatedistinct visual signatures in a repeatable and comparableway. We also gain more intuition for the communicationpatterns exhibited by different scientific computing applica-tions than provided by traditional CCDF plots. We find thatdifferent codes with certain topological similarities, whilehaving visually similar hive plots for certain properties, are

consistently distinguished by multiple other properties. Wealso find that, in agreement with our hypothesis, certainproperties fail to visually distinguish different codes and areunlikely to contribute significantly to an accurate classifier.

We plan to extend this work by examining hive plots forthe same code across different numbers of compute nodesand observing if the resulting visualizations remain similar.While this work focused primarily on the implementation andevaluation of hive plots for visualizing the communicationpatterns resulting from distributed memory computations, weplan to design and evaluate a new anomaly detection systemmodified from previous work [13, 14] and will determine ifthe features suggested by the hive plots do indeed lead tomore accurate anomaly detection.

8. ACKNOWLEDGMENTSThanks to Scott Campbell and David Skinner for capturing

IPM data at NERSC. This research was supported in partby the Director, Office of Computational and TechnologyResearch, Division of Mathematical, Information, and Com-putational Sciences of the U.S. Department of Energy, undercontract number DE-AC02-05CH11231. This research usedresources of the National Energy Research Scientific Com-puting Center, which is supported by the Office of Scienceof the U.S. Department of Energy under contract numberDE-AC02-05CH11231. The views and conclusions containedin this document are those of the authors and not necessarilythose of its sponsors.

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Figure 4: A hive panel showing total degree, undirected betweenness, transitivity, and page rank for eachdataset using linear interpolation plus a repelling scheme for node positions and variable edge alpha values.