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!

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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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Dimensionality Reduction

• The main idea reduce the dimensionality of the
  space.
• Project the d-dimensional points in a
  k-dimensional space so that
• k ltlt d
• distances are preserved as well as possible
• Solve the problem in low dimensions
• (the GEMINI idea of course)

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DR requirements

• The ideal mapping should
• Be fast to compute O(N) or O(N logN) but not
  O(N2)
• Preserve distances leading to small discrepancies
• Provide a fast algorithm to map a new query (why?)

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MDS (multidimensional scaling)

• Input a set of N items, the pair-wise (dis)
  similarities and the dimensionality k
• Optimization criterion
• stress (?ij(D(Si,Sj) - D(Ski, Skj) )2 /
  ?ijD(Si,Sj) 2) 1/2
• where D(Si,Sj) be the distance between time
  series Si, Sj, and D(Ski, Skj) be the Euclidean
  distance of the k-dim representations
• Steepest descent algorithm
• start with an assignment (time series to k-dim
  point)
• minimize stress by moving points

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MDS

• Disadvantages
• Running time is O(N2), because of slow
  convergence
• Also it requires O(N) time to insert a new point,
  not practical for queries

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FastMap Faloutsos and Lin, 1995

• Maps objects to k-dimensional points so that
  distances are preserved well
• It is an approximation of Multidimensional
  Scaling
• Works even when only distances are known
• Is efficient, and allows efficient query
  transformation

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FastMap

• Find two objects that are far away
• Project all points on the line the two objects
  define, to get the first coordinate

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FastMap - next iteration
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Results
Documents /cosine similarity -gt Euclidean
distance (how?)
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