David Fleet We need many clusters Increasing number of clusters Problem Search time storage cost subspace 1 subspace 2 subspace 1 subspace 2 subspace 1 subspace 2 subspace 1 ID: 722686
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Slide1
Cartesian k-means
Mohammad Norouzi
David FleetSlide2Slide3Slide4Slide5
We need many clusters
Increasing
number of
clusters
Problem:
Search time, storage
cost Slide6Slide7Slide8
(subspace 1)
(subspace 2)Slide9
(subspace 1)
(subspace 2)Slide10
(subspace 1)
(subspace 2)Slide11
(subspace 1)
(subspace 2)Slide12
(subspace 1)
(subspace 2)Slide13
(subspace 1)
(subspace 2)Slide14
Compositional representation
subspaces
regions per subspace
Slide15
Compositional representation
subspaces
regions per subspace
centers
Slide16
Compositional representation
subspaces
regions per subspace
centers
parameters
Slide17
Which subspaces?Slide18
Which subspaces?
LearningSlide19
k-means
cluster centers:
Slide20
k-means
cluster centers:
is a
one-of-
encoding
Slide21
k-means
cluster centers:
is a
one-of-
encoding
Slide22
Orthogonal k-means
center basis vecotrs:
is an arbitrary
-bit encoding
Slide23
Orthogonal k-means
center basis vecotrs:
is an arbitrary
-bit
encoding
#
centers:
Slide24
Orthogonal k-means
center basis vecotrs:
Additional constraints:
LS estimate of
given
is
Slide25
identity
Learned
Iterative Quantization
[
Gong & Lazebnik, CVPR’11
]Slide26Slide27Slide28
Product Quantization
[
Jegou
,
Douze
,
Schmid
, PAMI’11
]Slide29
Cartesian k-means
Slide30
one-of-
encoding
one-of-
encoding
Cartesian k-means
#centers:
Slide31
one-of-
encoding
one-of-
encoding
Cartesian k-means
#centers:
Storage cost:
Search time:
Slide32
Learning Cartesian k-means
Slide33
Learning
Cartesian k-means
Slide34
Learning Cartesian k-means
Slide35
Learning Cartesian k-means
Slide36
Learning Cartesian k-means
Slide37
Learning Cartesian k-means
Update
and
by one step of k-means in
Slide38
Learning Cartesian k-means
Update
and
by one step of k-means in
Slide39
Learning Cartesian k-means
Update
by
SVD
to
solve Orthogonal
procrustes
Slide40
Cartesian k-means
#centers:
Storage cost:
Search time:
(
)
one-of-
one-of-
Slide41
Cartesian k-means
ok-means
k-means
subspaces,
regions per subspace
compositionalitySlide42Slide43Slide44Slide45
Slide46Slide47
Slide48
Codebook learning (CIFAR-10)
Codebook
Accuracy
k-means
(
)
k-means (
)
Codebook
AccuracySlide49
Codebook learning (CIFAR-10)
Codebook
Accuracy
k-means
(
)
ck
-means (
)
k-means (
)
ck
-means (
)
Codebook
AccuracySlide50
Codebook learning (CIFAR-10)
Codebook
Accuracy
k-means
(
)
ck
-means (
)
PQ (
)
k-means (
)
ck
-means (
)
PQ (
)
Codebook
AccuracySlide51Slide52
Quantized
images (
bits)
Slide53
images
Slide54
Run-time complexity
Inference to quantize a point
A big rotation of size
can be expensive
PCA to reduce
dimensionality to
as pre-processing and optimize
a
projection
within the model
Learning
The most expensive part in
each
training iteration
is to solve SVD to estimate
which is of
Can be done faster if we have a
rotation
Slide55
Summary
o
k-means
ITQ
ck
-means
PQSlide56
Thank you for your attention!
Slide57
Slide58Slide59Slide60Slide61Slide62Slide63Slide64
bit
Slide65
bit
bit
Slide66
Query-specific table (
)
bit
bit
bit
Query-specific table (
)
Slide67