1. Multimedia DBs

2. Multimedia dbs A multimedia database stores text, strings and images Similarity queries (content based retrieval) Given an image find the images in the database that are similar (or you can “describe” the query image) Extract features, index in feature space, answer similarity queries using GEMINI Again, average values help! (Used QBIC –IBM Almaden)

3. Image Features Features extracted from an image are based on: Color distribution Shapes and structure …..

4. Images - color what is an image? A: 2-d RGB array

5. Images - color Color histograms, and distance function

6. Images - color Mathematically, the distance function between a vector x and a query q is: D(x, q) = (x-q) T A (x-q) =  a ij (x i -q i ) (x j -q j ) A=I ?

7. Images - color Problem: ‘cross-talk’: Features are not orthogonal -> SAMs will not work properly Q: what to do? A: feature-extraction question

8. Images - color possible answers: avg red, avg green, avg blue it turns out that this lower-bounds the histogram distance -> no cross-talk SAMs are applicable

9. Images - color performance: time selectivity w/ avg RGB seq scan

10. Images - shapes distance function: Euclidean, on the area, perimeter, and 20 ‘moments’ (Q: how to normalize them?

11. Images - shapes distance function: Euclidean, on the area, perimeter, and 20 ‘moments’ (Q: how to normalize them? A: divide by standard deviation)

12. Images - shapes distance function: Euclidean, on the area, perimeter, and 20 ‘moments’ (Q: other ‘features’ / distance functions?

13. Images - shapes distance function: Euclidean, on the area, perimeter, and 20 ‘moments’ (Q: other ‘features’ / distance functions? A1: turning angle A2: dilations/erosions A3:... )

14. Images - shapes distance function: Euclidean, on the area, perimeter, and 20 ‘moments’ Q: how to do dim. reduction?

15. Images - shapes distance function: Euclidean, on the area, perimeter, and 20 ‘moments’ Q: how to do dim. reduction? A: Karhunen-Loeve (= centered PCA/SVD)

16. Images - shapes Performance: ~10x faster # of features kept log(# of I/Os) all kept

17. Dimensionality Reduction Many problems (like time-series and image similarity) can be expressed as proximity problems in a high dimensional space Given a query point we try to find the points that are close… But in high-dimensional spaces things are different!

18. Effects of High-dimensionality Assume a uniformly distributed set of points in high dimensions [0,1] d Let’s have a query with length 0.1 in each dimension  query selectivity in 100-d 10 -100 If we want constant selectivity (0.1) the length of the side must be ~1!

19. Effects of High-dimensionality Surface is everything! Probability that a point is closer than 0.1 to a (d-1) dimensional surface D=2 0.36 D = 10 ~1 D=100 ~1

20. Effects of High-dimensionality Number of grid cells and surfaces Number of k-dimensional surfaces in a d- dimensional hypercube Binary partitioning  2 d cells Indexing in high-dimensions is extremely difficult “curse of dimensionality”

21. X-tree Performance impacted by the amount of overlap between index nodes Need to follow different paths Overlap, multi-overlap, weighted overlap R*-tree when overlap is small Sequential access when overlap is large When an overflow occurs Split into two nodes if overlap is small Otherwise create a super-node with twice the capacity Tradeoffs made locally over different regions of data space No performance comparisons with linear scan!

22. Pyramid Tree Designed for Range queries Map each d-dimensional point to 1-d value Build B+-tree on 1-d values A range query is transformed into a set of 1-d ranges More efficient than X-tree, Hilbert order, and sequential scan

23. Pyramid transformation pyramids 2d pyramids with top at center of data-space points in different pyramids ordered based on pyramid id points within a pyramid ordered based on height value(v) = pyramid(v) + height(v)

24. Vector Approximation (VA) file Tile d-dimensional data-space uniformly A fixed number of bits in each dimensions (8) 256 partitions along each dimension 256 d tiles Approximate each point by corresponding tile size of approximation = 8d bits = d bytes size of each point = 4d bytes (assuming a word per dimension) 2-step approach, the first using VA file

25. Simple NN searching δ = distance to kth NN so far For each approximation ai If lb(q,ai) < δ then Compute r = distance(q,vi) If r < δ then Add point i to the set of NNs Update δ Performance based on ordering of vectors and their approximations

26. Near-optimal NN searching δ = kth distant ub(q,a) so far For each approximation ai Compute lb(q,ai) and ub(q,ai) If lb(q,ai) <= δ then If ub(q,ai) < δ then Add point i to the set of NNs Update δ InsertHeap(Heap,lb(q,ai),i)

27. Near-optimal NN searching (2) δ = distance to kth NN so far Repeat Examine the next entry (li,i) from the heap If δ < li then break Else Compute r = distance(q,vi) If r < δ then Add point i to the set of NNs Update δ Forever Sub-linear (log n) vectors after first phase

28. SS-tree and SR-tree Use Spheres for index nodes (SS-tree) Higher fanout since storage cost is reduced Use rectangles and spheres for index nodes Index node defined by the intersection of two volumes More accurate representation of data Higher storage cost

29. Metric Tree (M-tree) Definition of a metric d(x,y) >= 0 d(x,y) = d(y,x) d(x,y) + d(y,z) >= d(x,z) d(x,x) = 0 Non-vector spaces Edit distance d(u,v) = sqrt ((u-v) T A(u-v) ) used in QBIC

30. Basic idea Index entry = (routing object, distance to parent,covering radius) x,d(x,p),r(x)y,d(y,p),r(y) Parent p x y All objects in subtree are within a distance of “covering radius” from routing object. z d(y,z) <= r(y)

31. Range queries x,d(x,p),r(x)y,d(y,p),r(y) Parent p x y z Query q with range t d(q,z) >= d(q,y) - d(y,z) d(y,z) <= r(y) So, d(q,z) >= d(q,y) -r(y) if d(q,y) - r(y) > t then d(q,z) > t Prune subtree y if d(q,y) - r(y) > t (C1) q t

32. Range queries x,d(x,p),r(x)y,d(y,p),r(y) Parent p x y z Query q with range t d(q,y) >= d(q,p) - d(p,y) d(q,y) >= d(p,y) - d(q,p) So, d(q,y) >= |d(q,p) - d(p,y)| if |d(q,p) - d(p,y)| - r(y) > t then d(q,y) - r(y) > t Prune subtree y if |d(q,p) - d(p,y)| - r(y) > t (C2) q t Prune subtree y if d(q,y) - r(y) > t (C1)

33. Range query algorithm RQ(q, t, Root, Subtrees S1, S2, …) For each subtree Si prune if condition C2 holds otherwise compute distance to root of Si and prune if condition C1 holds otherwise search the children of Si

34. Nearest neighbor query Maintain a priority list of k NN distances Minimum distance to a subtree with root x d min (q,x) = max(d(q,x) - r(x), 0) |d(q,p) - d(p,x)| - r(x) <= d(q,x) - r(x) may not need to compute d(q,x) Maximum distance to a subtree with root xd max (q,x) = d(q,x) + r(x) x q z r(x) d(q,z) + r(x) >= d(q,x) d(q,z) >= d(q,x) - r(x) d(q,z) <= d(q,x) + r(x)

35. Nearest neighbor query Maintain an estimate d p of the kth smallest maximum distance Prune a subtree x if d min (q,x) >= d p

36. References Christos Faloutsos, Ron Barber, Myron Flickner, Jim Hafner, Wayne Niblack, Dragutin Petkovic, William Equitz: Efficient and Effective Querying by Image Content. JIIS 3(3/4): 231-262 (1994)Ron BarberMyron FlicknerJim HafnerWayne NiblackDragutin PetkovicWilliam EquitzJIIS 3 Stefan Berchtold, Daniel A. Keim, Hans-Peter Kriegel: The X-tree : An Index Structure for High-Dimensional Data. VLDB 1996: 28-39Daniel A. KeimHans-Peter KriegelVLDB 1996 Stefan Berchtold, Christian Böhm, Hans-Peter Kriegel: The Pyramid- Technique: Towards Breaking the Curse of Dimensionality. SIGMOD Conference 1998: 142-153Christian BöhmHans-Peter KriegelSIGMOD Conference 1998 Roger Weber, Hans-Jörg Schek, Stephen Blott: A Quantitative Analysis and Performance Study for Similarity-Search Methods in High- Dimensional Spaces. VLDB 1998: 194-205Hans-Jörg SchekStephen BlottVLDB 1998 Paolo Ciaccia, Marco Patella, Pavel Zezula: M-tree: An Efficient Access Method for Similarity Search in Metric Spaces. VLDB 1997: 426-435Marco PatellaPavel ZezulaVLDB 1997