Editor: Richard DoyleJet Propulsion Labrdoyle@jpl.nasa.gov

A I i n S p a c e

Express. These orbiters are surveying the entire Martiansurface to understand the planet’s past and the geological,climatic, and other processes responsible for its presentstate. They gather ever-increasing amounts of spatiallyextended data. Science data archived from all planetarymissions prior to the 2001 Mars Odyssey mission totalsapproximately 5 terabytes. NASA expects that number todouble over the Odyssey’s duration and to increase by afactor of 10 with the newest Mars Reconnaissance mission.

This data deluge presents difficult transmission, storage,and distribution challenges. Less publicized is the scien-tific community’s challenge to process, analyze, and ulti-mately turn a significant portion of the collected data intoknowledge. Only a small fraction of the data is analyzedat this time because analysis still involves traditionalmethods that rely on visual inspection and descriptivecharacterization.

Automated or semiautomated tools for Martian dataanalysis can substantially broaden the scope of scientificinquiry. Recognizing this opportunity, we’ve undertakenresearch to apply pattern-recognition and machine-learningtools to automatic analysis and characterization of theMars surface. This research includes machine surveys ofspecific landforms, such as impact craters and valley net-works, and automatic generation of geomorphic maps.

Geomorphic mappingA geomorphic map is a thematic map of topographical

expressions or landforms. Machine learning can play avital role in automating this mapping process. A learningsystem can employ clustering techniques to fully auto-mate the discovery of meaningful landform classes. Alter-natively, it can use classification techniques to predictunlabeled landform classes after an expert has manually

labeled a representative landform sample. These tech-niques are often referred to as unsupervised and super-vised learning, respectively (see the “Unsupervised versusSupervised Machine Learning” sidebar on p. 102). Giventhe size of the Martian surface that remains unmapped,they can be immensely valuable to topographical analysis.

We faced many design choices in developing appropri-ate tools. These included selecting an appropriate data setand machine-learning technique as well as topographicobjects and their features. We based our tools on topo-graphic data (see the “Measuring Martian Topography”sidebar on p. 104), which offers a more fundamental sur-face description than image data and is well suited forautomated mapping. Topographic data is available as agrid-based digital elevation model. A DEM stores eachpixel’s elevation in a grid node. We developed both clus-tering and classification mapping techniques, with eachapproach calling for a different choice of objects andtopographic features.

Clustering-based mappingA clustering tool based on unsupervised learning of-

fers maximum automation for geomorphic mapping.This approach can find clusters corresponding to noveltopographical expressions that haven’t been previouslyrecognized. Our tool is somewhat analogous to multispec-tral image mapping of terrestrial land covers,1 but it ap-plies to topographic rather than image data. The basictopographic object is a DEM pixel that carries a vector oftopographic features. The tool derives all the featuresfrom an elevation field, including variables such as slopeand topographic curvature. It maps a given site by apply-ing a clustering algorithm over all the site’s feature vec-tors. The clustering algorithm outputs a set of mutuallyexclusive and exhaustive clusters. Each cluster comprisespixels carrying similar feature vectors, which are thoughtto be instances of a single landform.

We’ve applied our clustering-based mapping tool toseveral Martian sites.2–5 The generated maps are qualita-tively different from traditional geomorphic maps. Figure

Mars is at the center of current solar system explo-

ration. Three spacecraft are presently orbiting the

planet: NASA’s Mars Odyssey and Mars Reconnaissance

orbiters as well as the European Space Agency’s Mars

Machine Learning Tools for Automatic Mapping of Martian Landforms

Tomasz Stepinski, Lunar and Planetary InstituteRicardo Vilalta, University of HoustonSoumya Ghosh, University of Colorado

100 1541-1672/07/$25.00 © 2007 IEEE IEEE INTELLIGENT SYSTEMSPublished by the IEEE Computer Society

1a shows a standard, manually constructedMartian geomorphic map,6 and figure 1bshows a map of the same region gener-ated by our mapping tool. The manualmap emphasizes specific landforms pur-posefully selected by an expert in geologicmapping. Each landform has a clearly de-fined semantic meaning. In contrast, theautomatically generated map is more ge-neric. Although it clearly partitions thesite, some landforms lack a semanticmeaning that a geologist could readilyidentify. This is because clusters derivedunder a proximity measure might not con-stitute a landform that an expert perceivesas interesting.

For example, figure 1b divides the inter-crater plateau into several landforms be-cause they have different elevations. How-ever, from the perspective of the particulardomain expert who mapped this site, suchdifferences were uninteresting and the inter-crater plateau wasn’t mapped at all. Thisdoesn’t mean that the generated map iswrong—merely that its content differs fromtraditional maps. In fact, such maps mightbe very useful for studying various statisti-cal aspects of the Martian surface, but thecontext of such investigation would need tobe developed outside the framework of tra-ditional geomorphology.

Classification-based mappingClustering-based mapping shows that

manual geomorphic mapping relies onobservation, comparison, and interpre-tation—processes that unsupervised learn-ing has difficulty emulating. A mappingtool that can approximate the intangiblequalities of manually constructed mapsmust rely on supervised learning. There-fore, we developed a classification-basedmapping tool designed to map landformsas chosen and defined beforehand by anexpert. Supervised learning requires atraining set of terrain objects to which anexpert has already assigned landform la-bels. The mapping tool constructs a label-ing function that it then applies to label allother objects. The labeling function is anextensive, computer-derived rule set thatreflects a connection between an object’snumerical features and the landform labelsassigned by an expert.

In supervised learning, we must carefullychoose the objects to be classified. Classify-ing individual pixels has questionable valuebecause pixels are too small for a human

interpreter to assign them labels with ahigh degree of confidence. Researchersrecognize a pixel’s limitation as a classifi-able object, and current research is focusingon a segmentation-based technique that firstsubdivides a site into meaningful segmentsfor subsequent classification.7

We designed our classification-basedmapping tool on a segmentation-basedprinciple. It has two major components: thesegmentation module and the classificationmodule.

Segmentation module. This module di-vides the site into small segments that haveapproximately uniform pixel-based featurevectors. Computer vision researchers havestudied raster segmentation intensely, butsegmentation requirements in the computer-vision domain differ from those in the clas-sification context. In computer vision, largesegments are desirable as long as they con-tain uniform feature vectors. In our classifi-cation context, we prefer relatively small,approximately equal-sized segments, evenif they cut through larger uniform fields offeature vectors. The smaller segments elim-inate the danger of misclassifying a large

segment and thus generating a grossly in-correct map.

On the other hand, a misclassification ofa small segment results in a map that, al-though slightly less accurate, maintains itsinterpretability. In addition to terrain fea-tures, our segmentation module uses pixelspatial coordinates as additional features.This controls the segment sizes and pro-duces segments with shapes that an algor-ithm can use as additional cues during clas-sification. For example, in areas whereterrain features change over a length scalelarger than a segment size, the segmentsexhibit round shapes because the unifor-mity of spatial coordinates controls theirextents. On the other hand, in areas whereterrain features change over a length scalesmaller than a segment size, the segmentsare elongated in a direction perpendicularto the change gradient.

Classification module. The classificationmodule assigns a label (landform desig-nation) to unlabeled segments (landscapeelements) on the basis of patterns learnedfrom examples. The classification subjectsare segments that the segmentation module

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(b)

(a)

Figure 1. Geomorphic maps of Terra Cimmeria on Mars. (a) A manually constructedmap reflects an expert’s mapping of nine different landforms: fresh impact craters,fresh ejecta, wrinkle ridges, major valleys, dichotomy escarpment, drainage divides,basin interior mountains, intravalley basin floors, and terminal basin floors. The large gray portion of the site, consisting mostly of intercrater plateau, was assignedno landform designation. (b) The clustering-based mapping algorithm shows 19 “landforms” that represent clusters of feature vectors. An expert must interpret their meanings.

establishes, and a value of a segment-based feature vector determines the land-form designation. A segment-based featurevector consists of physical and spatial fea-tures. The physical features are averagevalues of pixel-based physical attributescalculated over an ensemble of pixels con-stituting a segment. The spatial featuresdescribe the segment itself—that is, itsgeometrical and neighboring properties.

To demonstrate how the classification-based mapping algorithm works, we ap-plied it to a site on Mars located around

Tisia Valles. This site represents a typicalold Martian surface dominated by craterswith various sizes, depths, and degrees ofpreservation. Figure 2a shows its topogra-phy. Planetary scientists are interested inthe spatial variability of crater parameters,so the landforms of interest are craterfloors, convex crater walls, concave craterwalls, and intercrater plateaus. In addition,this site contains escarpments that aren’tparts of craters, so we selected convex andconcave ridges as additional landformclasses. The algorithm segmented the site

into 6,593 segments, as shown in figure 2b.An expert labeled 500 segments represen-tative of all six landform classes to form atraining set. We used this set to construct aclassifier using a Support Vector Machines(SVMs) algorithm. Figure 2c shows thefinal map, resulting from applying the clas-sifier to all 6,593 segments. Using the clas-sification-based mapping tool with smalllabeling overhead, we obtained a map thatgeologists can readily interpret. By com-parison, figure 2d shows the clustering-based mapping of the site. This map con-

102 www.computer.org/intelligent IEEE INTELLIGENT SYSTEMS

Unsupervised learning is instrumental in grouping similardata types without assuming any external classifications priorto analysis. It relies on clustering techniques to automaticallydiscover natural similarities in data. This kind of learning ismost useful in exploratory data analysis, such as pattern dis-covery. Post-processing of resultant clusters characterizes themby their number, size, and feature profiles. In addition, it cancalculate a hierarchical tree structure of similarity betweendifferent clusters.

In our geomorphic mapping application, an unsupervised-learning algorithm groups similar pixels from a geomorphicfeature space. Figure A illustrates how this process works. Weemployed a probabilistic algorithm working under a Bayesianframework to obtain the clusters. For sites too large to be clus-tered by a probabilistic algorithm, we switched to an algor-ithm implementing the self-organizing map and Ward hierar-chical clustering method.1

Supervised learning is used to predict the class value of newobjects. A teacher or domain expert determines the class ofknown objects prior to the data analysis. Classification is onetype of supervised learning. The target classes correspond tonominal values, and the classification algorithm labels objectson the basis of their feature vectors.

In our application, supervised-learning algorithms assignlandform labels to terrain segments. Figure B shows how itworks. Terrain segments are more natural classification objects

than pixels. To calculate segments, we employ a K-means clus-tering algorithm that groups pixels according to their similar-ity between their geomorphic features as well as their spatialproximity. A larger K value obtains smaller segments. To clas-sify the cluster segments, we use three algorithms that repre-sent conceptually different classification approaches and eval-uate their performance using cross validation.

Reference

1. B.D. Bue and T.F. Stepinski, “Automated Classification of Land-forms on Mars,” Computers & Geoscience, vol. 32, no. 5, 2006,pp. 604–614.

Unsupervised versus Supervised Machine Learning

Pixel-based featurevector {u1, u2, ..., un}

Input data Clustered data

Each pixel is assigned toa unique cluster

Figure A. Unsupervised learning. The learning algorithm groups64 input-data pixels into nine clusters according to the similaritybetween pixel-based geomorphic feature vectors.

Pixel-based featurevector {u1, u2, ..., un}

Segment-based featurevector {U1, U2, ..., Um}

Input data Segmented data

Classified data

Landform class

Figure B. Supervised learning. The initial 64 pixels are first segmented into 23 segments on the basis of similarity betweenpixel-based feature vectors. These segments are then classifiedinto four landform classes on the basis of similarity betweensegment-based feature vectors.

sists of 12 landforms, corresponding to theoptimal number of clusters in the featurespace, and it’s not readily interpretable.Expert examination of these clusters re-grouped them into four superclusters thatgeologists can more readily interpret.

Different classification algorithmsThe map quality generated by the classi-

fication-based tool depends on many fac-tors. These include available features, seg-mentation quality, training-set quality, andthe classifier type used to assign segmentlabels. We used all available features, gen-erated segmentation with desirable proper-ties, and carefully established a representa-tive training set. We tested three differentlearning algorithms to classify segmentsand generate geomorphic maps: naïveBayes, bagging (using decision trees asbase learners), and SVMs.

Naïve Bayes uses Bayes’ theorem to esti-mate the landform label’s posterior probabil-ity given a feature vector representing thesegment. The computation of the likelihoodis simplified by assuming feature indepen-dence given the landform label. Because wederive all features from the same DEM, ourfeatures don’t meet the independence as-sumption, and we don’t expect the naïveBayes classifier to produce good maps.Rather, we expect them to serve as a baselinefor comparison with the maps generated byother classifiers.

Bagging is an ensemble-learning algo-rithm. It generates multiple models byrunning a single learning algorithm multi-ple times over a bootstrapped sample ofthe training set. The final landform label isthe result of voting over the contributingmodels—one from each bootstrap sample.Bagging has proved effective for complexdata sets. It’s particularly attractive whenthe training set is noisy, as is the case inour application. We use a C4.5 decisiontree as the base learner.

Finally, SVMs use a statistical learningalgorithm that works by finding an optimalhyperplane in a transformed feature space.The optimal hyperplane maximizes the sep-aration between landform classes. SVMsexploit local data patterns and have provedeffective in spatial data mining applications.

Figure 3 shows another set of Tisia Vallesmaps. Figure 3a shows the site topographyfrom the southeast perspective. Figure 3bshows a geomorphic map of the six land-forms obtained from an expert’s manual

labeling of the segments; this map servesas ground truth for maps generated on thesame segmentation but with the naïve Bayes,bagging, and SVMs classifier algorithmsin figures 3c, 3d, and 3e, respectively.Comparing the generated maps to theground-truth map in figure 3b shows thenaïve Bayes map to be overall inaccurateand inferior to the bagging and SVMsmaps. The bagging and SVMs maps dif-fer in character: the SVMs-generated mapshows more detail, whereas the bagging-generated map shows better discriminationbetween crater walls and ridges.

Generalizing from training setsThe classification-based algorithm can

achieve fast, accurate generation of multi-ple geomorphic maps if the training set isrepresentative for all sites to be mapped. Ifone or more sites contain landforms notrepresented in the training set, the risk ofmapping them incorrectly is high. To checkthe potential of our mapping algorithm togeneralize from a single site to multiplesites, we applied it to five different sitesusing the training set established for TisiaValles. The five sites—labeled Vichada, Al-Qahira, Dawes, Evros, and Margaritifer—

NOVEMBER/DECEMBER 2007 www.computer.org/intelligent 103

(b)(a)

(d)(c)

Intercrater plateau

Crater floor

Convex crater wall

Concave crater wall

Convex ridge

Concave ridge

Intercrater plateau

Inside craters

Ridges

Channels

Figure 2. The Martian Tisia Valles site: (a) topographical site map approximately 215 km west to east and 192 km south to north (red-to-blue gradient indicates high-to-low elevation); (b) site segmentation into 6,593 segments; (c) geomorphic sitemap generated by the classification-based mapping algorithm using a Support VectorMachines classifier; and (d) site map generated by the clustering-based tool using a probabilistic algorithm working under the Bayesian framework.

A precise map of Martian topography, accurate around theplanet to within 13 meters of elevation, is available to the sci-entific community as a result of measurements taken by theMars Orbiter Laser Altimeter. The MOLA instrument went intospace onboard the Mars Global Surveyor, which launched inNovember 1996 and arrived at Mars in September 1997.

The Laser Remote Sensing Branch of NASA Goddard SpaceFlight Center designed MOLA. It’s a laser operating at a wave-length of 1,064 nm and emitting 8-ns pulses with energy of 40mJ. MOLA measured the round-trip time that individual laserpulses took to travel between the spacecraft and the Martiansurface. Interpolating the spacecraft orbital trajectory to thelaser measurement’s time and correcting for the atmosphere’srefraction index gave the one-way light time between thespacecraft and the surface. Finally, subtracting the measured

range from the spacecraft orbit yielded the Martian radius in acenter-of-mass reference frame.

The instrument was operational for 1,696 days and madeabout 640 million measurements of the Mars surface. Themeasurements’ spatial resolution is 300 to 400 m along thetrack and about 1,000 m between tracks. The Martian topog-raphy is defined as the MOLA-measured planetary radius mi-nus the radius of the geoid, which is a gravitational equipo-tential surface. Figure C shows an example of the MOLAmeasurements over a portion of a single track.

Figure D shows a global topographic map of Mars createdby binning altimetry measurements from the mission’s entireduration into grid-based, digital-elevation-model data struc-tures called the MOLA Mission Experiment Gridded Data Rec-ord.1 The MOLA team released the final MEGDR on 7 May 2003.The data is available from the Planetary Data Service geosci-ence node (http://pds-geosciences.wustl.edu) at resolutions of4, 16, 32, 64, and 128 pixels per degree. Polar maps are avail-able in resolutions of 128, 256, and 512 pixels per degree.

The algorithms for automatic geomorphic mapping de-scribed in this article use the MEGDR with resolution of 128pixels per degree.

Reference

1. D. Smith et al., Mars Global Surveyor Laser Altimeter Mission Exper-iment Gridded Data Record, NASA Planetary Data System, MGS-M-MOLA-5-MEGDR-L3-V1.0, 2003; www.gps.caltech.edu/~marsdata/mars_MOLA_mgsl_300x_aareadme.txt.

104 www.computer.org/intelligent IEEE INTELLIGENT SYSTEMS

Measuring Martian Topography

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Figure C. Mars Orbiter Laser Altimeter elevation data over 180-km-diameter Dawes crater. (a) The red line shows the spacecraft’s ground track against a background image on orbit10922. (b) The MOLA measurements are combined to produce a topographic profile showing a flat-floored crater that’s almost2500 m deep.

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Figure D. Global topography maps of Mars. (Top left) South poleregion in stereographic projection. (Top right) North pole regionin stereographic projection. (Bottom) Regions between latitudesof 70S and 70N in Mercator projection showing the elevationdifference between the northern and southern hemispheres.

NOVEMBER/DECEMBER 2007 www.computer.org/intelligent 105

have the same geologic character as theTisia Valles site but differ in their dominantlandforms, such as a big crater or a largevalley. Figure 4 shows the generated mapsfor these sites. They depict the six pre-defined landforms quite well, except forMargaritifer, where significant confusionshows up between the “concave crater wall”landform and the “concave ridge” land-form. These two landform classes are themost difficult to distinguish because theyhave similar physical features and differonly in a large-scale spatial context. TheMargaritifer site contains segments thathave feature values not well represented inthe Tisia Valles site-based training set.

Future workThe tools we’ve developed can map large

regions on Mars quickly and consistently.We’re planning now to develop a methodfor automating the comparison and classifi-cation of geomorphic maps—an activitymotivated by the large number of maps theautomated mapping process could makeavailable. Given a collection of maps, wewould establish a similarity structure bycalculating a “distance” between every pairof maps in the collection. The major intel-lectual challenge is to develop an appropri-ate measure of such a distance.

One approach is to use the concept ofmutual information.8 In information theory,mutual information of two variables quan-tifies the reduction in the degree of uncer-tainty about one variable when the othervariable is known. We can measure the dis-

tance between two maps by calculating thedegree of normalized mutual information(NMI) between the distribution of land-form classes and the distribution of maps(a choice between the maps). A small NMIvalue indicates that knowing a distributionof landform classes doesn’t significantlydecrease the uncertainty in distinguishingbetween two maps—the two landscapesare similar. On the other hand, a large NMIvalue indicates that knowing a distributionof landform classes helps to distinguish be-

tween the two landscapes because they’redissimilar.

Another approach to measuring the dis-tance between maps uses normalized com-pression distance. NCD is a practical im-plementation of information distance thatuses file compressors or zippers. It calcu-lates the proximity between objects that arerepresented as strings of characters from afinite alphabet. This “clustering by com-pression” approach has successfully classi-fied objects such as text, music, and DNA

(a)

Intercrater plateau

Crater floor

Convex crater wall

Concave crater wall

Convex ridge

Concave ridge

(b) (c)

(e)(d)

Figure 3. Geomorphic maps of the Tisia Valles site: (a) southeast perspective view of the site’s topography; (b) analyst-drawn maps of landforms; and maps generatedby a classification-based tool using (c) naïve Bayes classifier, (d) bagging classifier, and(e) SVMs classifier.

(a) (b) (c) (e)(d)(a) (b) (c) (e)(d)

Figure 4. Geomorphic maps of (a) Vichada, (b) Al-Qahira, (c) Dawes, (d), Evros, and (e) Margaritifer Martian sites generated by theclassification-based tool using SVMs. The top row shows the sites’ topography; the bottom row shows the actual maps.

106 www.computer.org/intelligent IEEE INTELLIGENT SYSTEMS

sequences into meaningful categories.9 Thechallenge to using it for classifying rasterdata sets, such as geomorphic maps, isfinding a raster-string conversion methodthat’s independent (or weakly dependent)on raster orientation.

Both these methods yield a similaritymatrix, a data structure that must be visual-ized in terms of a dendrogram (binary tree)that agrees with the matrix but presents thesimilarity structure in a cognitively accept-able format.

A utomatic map analysis will enable thestudy of spatial variability of surface ex-pressions on a scale larger than individuallandforms. The automated mapping we’vedescribed in this article identifies landformsfrom feature patterns associated with pixels.The map analysis we’re planning will iden-tify types of landscapes from the landformpatterns, supporting rapid extraction ofhigh-level information from topographicdata—something only domain experts cando at this time.

Acknowledgments

The Lunar and Planetary Institute fundedportions of this work under LPI contribution no.1372. The Universities Space Research Associa-tion operates LPI under NASA contract CAN-NCC5-679. Other funding came from the USNational Science Foundation under grants IIS-0431130, IIS-448542, and IIS-0430208 andfrom NASA under grant NNG06GE57G.

References

1. D. Landgrebe, “Information Extraction Prin-ciples and Methods for Multispectral andHyperspectral Image Data,” Information Pro-cessing for Remote Sensing, C.H. Chen, ed.,World Scientific Publishing, 1999.

2. T.F. Stepinski and R. Vilalta, “Digital Topog-raphy Models for Martian Surfaces,” IEEEGeoscience and Remote Sensing Letters, vol.2, no. 3, 2005, pp. 260–264.

3. B.D. Bue and T.F. Stepinski, “AutomatedClassification of Landforms on Mars,” Com-puters & Geoscience, vol. 32, no. 5, 2006, pp.604–614.

4. T.F. Stepinski, S. Ghosh, and R.Vilalta, “Auto-matic Recognition of Landforms on MarsUsing Terrain Segmentation and Classifica-tion,” Proc. Int’l Conf. Discovery Science,LNAI 4265, Springer, 2006, pp. 255–266.

5. T.F. Stepinski, S. Ghosh, and R. Vilalta,

“Machine Learning for Automatic Mappingof Planetary Surfaces,” Proc. 19th InnovativeApplications of Artificial Intelligence Conf.,AAAI Press, 2007, pp. 7–18.

6. R.P. Irwin and A.D. Howard, “Drainage BasinEvolution in Noachian Terra Cimmeria,Mars,” J. Geophysical Research, vol. 107 E7,2002, pp. 10-1–10-23.

7. M. Baatz and A. Schäpe, “Multiresolution Seg-mentation: An Optimization Approach forHigh Quality Multi-Scale Image Segmenta-tion,” Angewandte Geographische Informa-tionsverarbeitung XII [Applied GeographicalData Processing],Wichmann, 2000, pp. 12–23.

8. T.K. Remmel and F. Csillag, “Mutual Infor-mation Spectra for Comparing CategoricalMaps,” Int’l J. Remote Sensing, vol. 27, no.7, 2006, pp. 1425–1452.

9. R. Cilibrasi and M.P. Vitanyi, “Clustering byCompression,” IEEE Trans. Information The-ory, vol. 51, no. 4, 2005, pp. 1523–1545.

Tomasz Stepinskiis a staff scientist atthe Lunar and Plan-etary Institute inHouston, Texas. Hisresearch interest iscomputational geo-morphology withapplication to Mars

and Earth. He received his PhD in appliedmathematics from the University of Ari-zona. Contact him at tom@lpi.usra.edu.

Ricardo Vilalta isan assistant profes-sor in the Depart-ment of ComputerScience at the Uni-versity of Houston.His research inter-ests are in machinelearning, statistical

learning theory, data mining, and AI. Hereceived his PhD in computer sciencefrom the University of Illinois at Urbana-Champaign. Contact him at vilalta@cs.uh.edu.

Soumya Ghosh isa graduate studentin the Departmentof Computer Sci-ence at the Univer-sity of Colorado,Boulder. His re-search interests lieat the intersection

of machine learning and computer visionand in the applicability of this research todomains such as robotics. He received hisMS in computer science from the Univer-sity of Houston. Contact him at soumya.ghosh@colorado.edu.

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