Neuroimaging Databases: A Data Engineering Perspective

1. Neuroimaging Databases:A Data Engineering Perspective Amarnath Gupta University of California San Diego

2. Find a pair of employees who always work on the same project in the same location? Three Queries • select E.eID, M.eID • from emp E, emp M, dept D • where E.salary > ( • select avg(salary) • from emp E2, dept D2 • where E2.eID = D2.mgrID • ) and M.eID = D.mgrID and • E.salary > M.salary • group by E.eID Emp(eID, name, degree, salary). Project(pID, start_date, end_date, status). Dept(dID, name, mgrID). Works_For(pID, eID, location). • Which employees have a Ph.D. degree and work in the San Francisco office? • select E.eID • from emp E, works_for W • where E.degree = ‘Ph.D’ and • E.eID = W.eID and • W.location = ‘San Francisco’ • select E1.eID, E2.eID • from emp E1, emp E2, works_for W1, works_for W2 • where E1.eID = W1.eID and E2.eID = W2.eID and • W1.pID = W2.pID and • W1.location = W2.location and • E1.eID != E2.eID • In La Jolla SEARS, find all employees E who earn more than the average manager’s salary (over all departments), and the list the managers M who earn less than E.

3. Now Try These Queries • In mice, which ‘calcium binding’ proteins are found in the brain region ‘hippocampus’? • Find protein pairs that act as voltage-gated channels and are always co-localized in the region “cerebellum”. • In mouse-strain X, find all brain regions R which express more a-synuclein than the average a-synuclein expression level over all other brain regions, and list the brain regions S that express less a-synuclein than R. • Why are these queries inherently harder? • Why is it a very hard task to build systems that would answer queries like these and produce scientifically valid results?

4. The Data Modeling Problem Lack of disciplined abstraction in modeling the data

5. Large Scale Brain Maps • Custom high precision montaging stage • 40 X 30 image panels • 40X 1.3 oil objective • 800 Mb full resolution TIFF

6. The Molecular Distribution Case • Protein localization queries • Which proteins are found more in the granule cell layer of than the Purkinje cell layer? • Are proteins P1 and P2 always co-localized, sometimes co-localized or never co-localized in the cerebellum? • Which proteins follow the distribution pattern CA1 > (basal ganglia ~ deep cerebellar nuclei) > CA3 ? • The abstract model • Array Data Model (Libkin, Machlin, Wong 1996) • Histogram Data Model (Santini, Gupta 1999) • A molecular distribution can be modeled as a “block histogram” where the “base dimensions” are in R2 (or R3) • A cell in the histogram can contain a tuple (or a vector) of aggregate values

7. Block Histogram as an ADT Abstract Data Types Block Histogram type image { id: identifier, picture: blob regions: set(region), color block histogram: 2Darray(histogram), }; type region { label: string, shape: polygon }; type histogram { variable name: string, value:1Darray(bucket), }; type bucket { start bucket: integer, end bucket: integer, count: integer };

8. Querying Block Histograms • Which proteins follow the distribution pattern CA1 > (basal ganglia ~ deep cerebellar nuclei) > CA3 ? • cut: histogram  polygon  histogram • agg: agg_func  histogram  attribute_name  number • sim_dist: number  number  number select protein from brain_level_protein_distributions D, mouse_atlas M where a1 is agg(avg, D.pd_hist.cut(M.ca1_poly), protein_amt) and a2 is agg(avg, D.pd_hist.cut(M.bg_poly), protein_amt) and a3 is agg(avg, D.pd_hist.cut(M.dcn_poly), protein_amt) and a4 is agg(avg, D.pd_hist.cut(M.ca3_poly), protein_amt) and sim_dist(a1, a2) > 0.2 and sim_dist(a2, a3) < 0.1 and sim_dist(a3, a4) > 0.2 Similar models on Volumes and Surfaces are being developed

9. The Representation Selection Problem Often multiple representations of the data are created for different purposes, but the queries are over the “generic” data

10. Surface Representations Neuroscientists use different representations of the cortex surfaces for different purposes Fiducial representation: as-exact-as-possible representation of the cortex, with all the folds and the creases of the actual surface. Allows the measurement of all geometric quantities of interest, including differen- tial properties (Gaussian curvature..) but most quantities are difficult to compute, as they require the integration of the local properties of the surface. Spherical map: the cortex can be projected on the surface of a sphere in a way that preserves (approximately) the distances between points. This represnta- tion affords the efficient computation of distances,areas, and topological relations, but not of properties related to the curvature of the surface. All these representations are stored in the database, but scientists ask questions on a conceptual model based on the fiducial representation. How can we rewrite the query to make optimal use of the available representations? flat map: preserves the area of the regions, but introduces cuts so that distances and topological properties can’t be computed

11. Configuration Conversion of attributes between representations <RewriteConfiguration> <ReplaceTypes> <Type name="Cortex"/> <Type name="Spherical"/> </ReplaceTypes> <FunctionParameterTable> <Function name="Area"> <Type name="Cortex" feasibility="2"/> <Type name="Spherical" feasibility="5"/> <Type name="Flat" feasibility="8"/> </Function> <Function name="Connectivity"> <Type name="Cortex" feasibility="5"/> <Type name="Spherical" feasibility="5"/> <Type name="Flat" feasibility="0"/> </Function> </FunctionParameterTable> <AttributeConversionTable> <ConversionSpec type="Cortex"> <Attribute name="A"> <Translation type="Spherical"> $.Q </Translation> <Translation type="Flat"> $.A </Translation> </Attribute> </ConversionSpec> <ConversionSpec type="Spherical"> <Attribute name="AREA"> <Translation type="Flat"> $.A*2 </Translation> </Attribute> </ConversionSpec> </AttributeConversionTable> <Strategy> <Step type="replacement" threshold="2"/> <Step type="consolidation" /> </Strategy> </RewriteConfiguration> declaration of the types that can be replaced Function-type table: for each function of the geometric data cartridge, lists the various representations, and the feasibility of computing that function with the given data type. Feasibility=0 means that the function can’t be computed with data of that type. Query rewriting strategy

12. Variable replacement-step 1 VLDB 2002 query query select from where select from where AND a a b c a b c b=a F(b) Insertion of the new variable a F(b)

13. Variable replacement-step 2 query query select from where select from where AND AND a a a b c a b c b=a b=a F(b) F(replace(a)) During consolidation, every other function that can be efficiently computed using the variable a (which has already been inserted) will be computed using it.

14. Scenario Replace if: The current representation has efficiency less than aANDthere is a representation with efficiency at least b Query: select * from Cortex c where (Connectivity(c.TOPO) = 2 AND Gauss(c.PEAKS) < 2) AND Area(c.PTS) < 100 Fiducial Spherical Flat 6 8 1 Gauss Area 2 5 8 Strategy 1: 1. R(3,3): Area -> Flat Connectivity 5 6 0 Strategy 2: 1. R(8,8): Gauss -> Spherical, Area->Flat Strategy 3: 1. R(8,8): Gauss -> Spherical, Area->Flat 2. C: 3. R(6,6): Connectivity -> Spherical

15. A Thought Multimedia Databases advocated the need to query by features and k-NN queries The mainstream DBs hasn’t quite “bought” the idea of features Is this the time to think how attribute-value based querying and feature-based querying would work together?

16. The Semantic Rewriting Problem The user prefers to query on a high-level schema (remember “conceptual query languages”?) So the system should rewrite the query on the logical schema but the rewriting should be semantically sound

17. A Deception • The scientific question • Are proteins P1 and P2 always co-localized, sometimes co-localized or never co-localized in the cerebellum? • The database queries • Find all images I such that • anatomic structure A is observed in I • A is cerebellum ORpart-of(A, cerebellum) • R_P1 is a region where P1 is found in I • R_P2 is a region where P2 is found in I • boundary(A) overlaps boundary(R_P1) • boundary(A) overlaps boundary(R_P2) • Count the number of images I • Similarly find other images where • P1 is present but P2 is not in the same regions • Report the ratios • Find all images I1, I2 such that • anatomic structure A1is observed in I1 • anatomic structure A2 is observed in I2 • A1 is cerebellum OR part-of(A1, cerebellum) • part-of(A2, A1) • R_P1 is a region where P1 is found in I1 • R_P2 is a region where P2 is found in I2 • boundary(A1) overlaps boundary(R_P1) • boundary(A2) overlaps boundary(R_P2) part-of(A, cerebellum)

18. An External “Knowledge Source”ANATOM Domain Map SSDBM 2000

19. Using the Ontology • SMOP – a simple matter of (query) planning? • Rewrite the query with the ontology source O, and write a rule to execute the O.part_of predicate first • Semantic Correctness • Purkinje cells are part of the cerebellum • dendrite is a compartment of the (generic) neuron • Should the images be selected if • Image I has P1, P2 in a region marked ‘dendrite’ ? • Image I has P1 in a region labeled ‘dendrite’ and P2 in a different region also marked ‘dendrite’? • Image I1 has P1 in a region marked ‘Purkinje Cell’ and I2 has P2 in a region marked ‘Purkinje cell dendrite’? • Image I1 has P1 in a region marked ‘SER’ and P2 in a region marked ‘Spine’, both covered by a larger region marked ‘dendrite’? • How can these cases be automatically taken care of in the query rewriting process?

20. The Ontology Search Problem(aside from the subsumption problem) The Ontology can be viewed a large graph where the edges denote relations. These edges may have many labels with widely different semantics. We need to perform meaningful graph-search over them.

21. Graph-Structured Knowledge Sources • Taxonomies are often directed and acyclic • Querying labeled graphs • A large fragment of the ontologies we encounter are DAGs where edges are often transitive • We represent DAGs in a relational structure • Each node carries its DFS traversal numbers • Ancestor and Descendant operations become range queries • Left biased Numbering scheme • Merge nodes: have pointers to all parents • Other nodes: have pointers to leftmost parents • Parent pointers carry edge labels • Path Expressions are evaluated using an extension of the PathStack algorithm (Srivastava et al, 2001) • Adds linear (in the number of variables of the path expression) complexity over PathStack What about more general graphs? What about graphs where the edge labels have specific semantics? Current 2003

22. binds to activates regulates inhibits binds to regulates A A C A’ A A D B B B B’ B regulates(up) A B F(A,B,e) inhibits(proc, proc) Modeling Interactions(Towards a “Disease Map”) • An interaction in a graph is • A labeled edge • regulates(A,B) • A parameterized edge • regulates(up)(A,B) • The specialization of an edge • activates(A,B,phosphorylation)::regulates(A,B) • A conditional edge • inhibits(A,B,deacetylation)  binds_to (C,A)  exists((low(nitrogen)):condition) • A complex edge • inhibits(binding(A,B), binding(C,D)) • A state transition • releases(Byck1p,Tpk1p) • … POSTCOND bound(Byck1p,cAMP) AND free(Tpk1p) PRECOND bound(Byck1p,Tpk1p) THEN binds_to (cAMP, Byck1p)

23. The Feasible Rewriting Problem If sources admit limited access patterns, can feasible plans be constructed?

24. A Touch of Theory (Nash and Ludäscher, 2003) • Web sources, functions and web services can be modeled as relations with limited access patterns • Planning an arbitrary Union of Conjunctive Queries (UCQ) with negation • Checking feasibility is equivalent to checking containment for UCQ and is hence P2P-complete • Plan computation for UCQ queries can be approximated by producing an underestimate and an overestimate of the query and deferring the feasibility check • Complete answers can be obtained even if the parts of the plan are not answerable • partial results are produced when some of the conjuncts are feasible

25. The Execution Planning Problem Remote, Distributed Functions, and Data Movement (where Data Engineering meets the Grid Environments)

26. Planning Queries with Functions where a1 is agg(avg, D.pd_hist.cut(M.ca1_poly), protein_amt) and … sim_dist(a1, a2) > 0.2 and … • X0  select ca1_poly from M @AtlasSource • X1  D.pd_hist.cut(X0) @Datacutter • a1  avg(X0, protein_amt) @Mediator • temp_store(a1) @MediatorStore Standard Mediator Distributed System over the Grid • Create transaction T1( • X0  select ca1_poly from M @AtlasSource • Store X0 into $V1 @ AtlasWrapper) • Create transaction T2( • X1  D.pd_hist.cut(fetch(X0, $T0)) @Datacutter • Store X1 into $V2 @TempStore) • a1  avg(X0, protein_amt) • temp_store(a1) @MediatorStore

27. Planning Queries with Functions Distributed System over the Grid with GridService Catalog • Create transaction T1( X0  select ca1_poly from M @AtlasSource Store X0 into $V1 @ AtlasWrapper) • Create transaction T2( ServiceCatalog.lookup(histogram_cutting_service, $resource, $paramList) R1  constructRequest ((X1  D.pd_hist.cut(fetch(X0, $T0))), $resource, $paramList) X1  ExecuteRequest(R1)) • Create transaction T3( S1  getSize(X1) ServiceCatalog.lookup(dataStorageService, S1, $resource, $params2) R2  constructRequest ((Store X1 into $V2), $resource, $params2)) How do you plan (and cost estimate) the operations ?

28. The “Goodness of Result” Problem The query retrieves information from the information sources. The Result Processor may need to estimate the “quality” of the results with respect to a reference

29. Two Viewpoints • The application person • Send the result retrieved • Case 1 • To a statistical package and compute standard statistics S1…Sk • Case 2 • To a program that generates a specialized random set of data and matches the statistical significance of the retrieved results • The database person • For these applications • Can we perform the queries on a sample rather than the entire data? Any guidelines on the sampling method? • Can we use approximations instead of producing exact answers? • Should we find only “interesting” or “most frequent” data by using data mining algorithms? • Can we package the descriptive statistics that a DBMS can compute to make the overall work more efficient? • Can the use of user-defined aggregates (cf. ATLAS project at UCLA) help eliminate the statistical package?

30. In Essence • A tour of a few “database-y” problems we have encountered so far in our work with Neuroimaging and associated information • Still scratching the surface of most problems • The help of forward-thinking domain scientists has been the most crucial asset in figuring out the problems at a deeper-than-usual level • The database scientists, need to be “cross-thinkers” to venture beyond our own domain of specific expertise to develop a holistic approach to these problems • There are many more exciting problems – let’s go get them!!

31. Acknowledging • Maryann Martone • who always asks hard questions I don’t know how to answer • Bertram Ludäscher • who has finally convinced me that “theory” is more practical than I thought • Simone Santini • the feature-man who (almost) always wins the argument on any technical matter • Animesh Ray • the geneticist, who is forcing me to learn and think about process interactions and models of complex phenomena • Mark Ellisman • the godfather who excels at making offers we can’t refuse • The staff and students who make it happen