Multimedia DBs

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Multimedia DBs
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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)

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Image Features

• Features extracted from an image are based on
• Color distribution
• Shapes and structure
• ..

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Images - color
what is an image? A 2-d RGB array
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Images - color
Color histograms, and distance function
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Images - color
Mathematically, the distance function between a
vector x and a query q is
D(x, q) (x-q)T A (x-q) S aij (xi-qi) (xj-qj)
AI ?
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Images - color

• Problem cross-talk
• Features are not orthogonal -gt
• SAMs will not work properly
• Q what to do?
• A feature-extraction question

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Images - color

• possible answers
• avg red, avg green, avg blue
• it turns out that this lower-bounds the histogram
  distance -gt
• no cross-talk
• SAMs are applicable

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Images - color
time
performance
seq scan
w/ avg RGB
selectivity
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Images - shapes

• distance function Euclidean, on the area,
  perimeter, and 20 moments
• (Q how to normalize them?

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Images - shapes

• distance function Euclidean, on the area,
  perimeter, and 20 moments
• (Q how to normalize them?
• A divide by standard deviation)

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Images - shapes

• distance function Euclidean, on the area,
  perimeter, and 20 moments
• (Q other features / distance functions?

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Images - shapes

• distance function Euclidean, on the area,
  perimeter, and 20 moments
• (Q other features / distance functions?
• A1 turning angle
• A2 dilations/erosions
• A3 ... )

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Images - shapes

• distance function Euclidean, on the area,
  perimeter, and 20 moments
• Q how to do dim. reduction?

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Images - shapes

• distance function Euclidean, on the area,
  perimeter, and 20 moments
• Q how to do dim. reduction?
• A Karhunen-Loeve ( centered PCA/SVD)

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Images - shapes

• Performance 10x faster

log( of I/Os)
all kept
of features kept
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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!

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Effects of High-dimensionality

• Assume a uniformly distributed set of points in
  high dimensions 0,1d
• Lets 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!

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Effects of High-dimensionality

• Surface is everything!
• Probability that a point is closer than 0.1 to a
  (d-1) dimensional surface
• D2 0.36
• D 10 1
• D100 1

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Effects of High-dimensionality

• Number of grid cells and surfaces
• Number of k-dimensional surfaces in a
  d-dimensional hypercube
• Binary partitioning ? 2d cells
• Indexing in high-dimensions is extremely
  difficult curse of dimensionality

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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!

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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

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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)

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Vector Approximation (VA) file

• Tile d-dimensional data-space uniformly
• A fixed number of bits in each dimensions (8)
• 256 partitions along each dimension
• 256d 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

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Simple NN searching

• d distance to kth NN so far
• For each approximation ai
• If lb(q,ai) lt d then
• Compute r distance(q,vi)
• If r lt d then
• Add point i to the set of NNs
• Update d
• Performance based on ordering of vectors and
  their approximations

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Near-optimal NN searching

• d kth distant ub(q,a) so far
• For each approximation ai
• Compute lb(q,ai) and ub(q,ai)
• If lb(q,ai) lt d then
• If ub(q,ai) lt d then
• Add point i to the set of NNs
• Update d
• InsertHeap(Heap,lb(q,ai),i)

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Near-optimal NN searching (2)

• d distance to kth NN so far
• Repeat
• Examine the next entry (li,i) from the heap
• If d lt li then break
• Else
• Compute r distance(q,vi)
• If r lt d then
• Add point i to the set of NNs
• Update d
• Forever
• Sub-linear (log n) vectors after first phase

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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

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Metric Tree (M-tree)

• Definition of a metric
• d(x,y) gt 0
• d(x,y) d(y,x)
• d(x,y) d(y,z) gt d(x,z)
• d(x,x) 0
• Non-vector spaces
• Edit distance
• d(u,v) sqrt ((u-v)TA(u-v) ) used in QBIC

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Basic idea
x,d(x,p),r(x)
y,d(y,p),r(y)
Parent p
y
x
d(y,z) lt r(y)
z
Index entry (routing object, distance to
parent,covering radius)
All objects in subtree are within a distance of
covering radius from routing object.
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Range queries
x,d(x,p),r(x)
y,d(y,p),r(y)
Parent p
y
Query q with range t
x
t
q
z
d(q,z) gt d(q,y) - d(y,z) d(y,z) lt r(y) So,
d(q,z) gt d(q,y) -r(y) if d(q,y) - r(y) gt t then
d(q,z) gt t Prune subtree y if d(q,y) - r(y) gt t
(C1)
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Range queries
x,d(x,p),r(x)
y,d(y,p),r(y)
Parent p
y
Query q with range t
x
t
q
z
Prune subtree y if d(q,y) - r(y) gt t (C1)
d(q,y) gt d(q,p) - d(p,y) d(q,y) gt d(p,y) -
d(q,p) So, d(q,y) gt d(q,p) - d(p,y) if d(q,p)
- d(p,y) - r(y) gt t then d(q,y) - r(y) gt
t Prune subtree y if d(q,p) - d(p,y) - r(y) gt t
(C2)
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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

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Nearest neighbor query

• Maintain a priority list of k NN distances
• Minimum distance to a subtree with root
  x dmin(q,x) max(d(q,x) - r(x), 0)
• d(q,p) - d(p,x) - r(x) lt d(q,x) - r(x)
• may not need to compute d(q,x)
• Maximum distance to a subtree with root
  x dmax(q,x) d(q,x) r(x)

x
q
d(q,z) r(x) gt d(q,x) d(q,z) gt d(q,x) - r(x)
r(x)
d(q,z) lt d(q,x) r(x)
z
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Nearest neighbor query

• Maintain an estimate dp of the kth smallest
  maximum distance
• Prune a subtree x if dmin(q,x) gt dp

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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)
• Stefan Berchtold, Daniel A. Keim, Hans-Peter
  Kriegel The X-tree An Index Structure for
  High-Dimensional Data. VLDB 1996 28-39
• Stefan Berchtold, Christian Böhm, Hans-Peter
  Kriegel The Pyramid-Technique Towards Breaking
  the Curse of Dimensionality. SIGMOD Conference
  1998 142-153
• Roger Weber, Hans-Jörg Schek, Stephen Blott A
  Quantitative Analysis and Performance Study for
  Similarity-Search Methods in High-Dimensional
  Spaces. VLDB 1998 194-205
• Paolo Ciaccia, Marco Patella, Pavel Zezula
  M-tree An Efficient Access Method for Similarity
  Search in Metric Spaces. VLDB 1997 426-435