Iterative Contraction and Merging Bayesian Sequential Partitioning JNDBSP 1 Manifold Learning Bosh Shih 2 O utline Introduction Principal Component Analysis PCA Linear Discriminant Analysis LDA ID: 796719
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Slide1
Outline
Manifold LearningIterative Contraction and MergingBayesian Sequential PartitioningJND-BSP
1
Slide2Manifold Learning
Bosh Shih2
Slide3Outline
IntroductionPrincipal Component Analysis (PCA)Linear Discriminant Analysis (LDA)Multi-Dimensional Scaling (MDS)Isometric Feature Mapping (
Isomap
)
Demo
3
Slide4Introduction
Question:Complicated Feature → High Dimension → Data (exponential growth)The curse of dimensionalityDifferent Appearance
Answer:
Dimensionality Reduction
Manifold Learning (one of them)
Visualize
Ref :
The Manifold Ways of Perception.
4
Slide5Introduction
Low dimensional manifold embedded in the high dimensional space
Ref :
中央
研究院週報
(
第
1058
期
)
流行學習與人臉辨識
5
Slide6Principal Component Analysis (PCA)
Ref :
Principal Component Analysis (PCA) ,
NTHU , Open Course Ware
6
Slide7Linear Discriminant Analysis (LDA)
↑
↓
PCA
LDA
Supervised Learning
U
nsupervised Learning
7
Slide8Multi-Dimensional Scaling (MDS)
Ref :
Modern Multidimensional Scaling:
Theory
and
Applications
古典
多維標度法
(MDS
) ,
線
代
啟示錄
Advanced
Introduction to Machine
Learning ,
CMU-10715
8
Slide9Isometric Feature Mapping (Isomap
) Ref : A Global Geometric Framework for Nonlinear Dimensionality Reduction.
Step1
:
Neighborhood Graph (
)
Step2
: S
hortest Paths (
)
Step3
:
9
Slide10Demo
Ref : http://www.math.ucla.edu/~wittman/mani Advanced Introduction to Machine Learning,
CMU-10715
10
Slide11Swiss Roll
11
Slide12Twin Peaks
12
Slide13Curvature
13
Slide14Corners
14
Slide1515
Slide16Toroidal Helix
16
Slide17Iterative Contraction and Merging
IEEEJia-Hao Syu , Sheng-Jyh Wang & Li-Chun Wang2017
Ref :
Hierarchical Image Segmentation based on
Iterative
Contraction and Merging
17
Slide18Introduction
Segmentation (ICM)a sequel of optimizationpixel-based
+
grid-based
region-based
hierarchical
multi-resolution
18
Slide19Outline
Pixel-basedAffinityEnergy FunctionOptimal SolutionJust-Noticeable Difference (JND)
Cells
Remnant Removal
19
Region-based
Color
Texture
Region Size
Spatial Intertwining
Slide20Pixel-based
Affinity
Energy Function
Ref :
Learning-based hierarchical graph for
unsupervised
matting and foreground estimation
color
mean
window
covariance
number
identity
regularization
20
Slide21Pixel-based
Optimal SolutionJust-Noticeable Difference (JND)
Smooth areas
identity
L
aplacian
21
Slide22Pixel-based
CellsRemnant Removal
22
Slide23Region-based
Color
23
Slide24Region-based
TextureGray-LevelWeber Local Descriptor (WLD)24
Ref :
WLD: A Robust Local Image Descriptor
Slide25Region-based
Region SizeSpatial Intertwining25
100 100 5
100
4 1.3
4 4 1
64
4 1.6
Slide26Region-based
ColorTextureRegion SizeSpatial Intertwining
26
Slide27ICM
27
Slide28Bayesian Sequential Partitioning
Journal of the American Statistical AssociationLuo Lu , Hui Jiang & Wing H. Wong2013
Ref : Multivariate Density Estimation by Bayesian Sequential Partitioning
28
Slide29Outline
Density EstimationKernel & HistogramBayesian Sequential Partitioning (BSP)
29
Slide30Density Estimation
Given : Data
Goal :
Estimate common density function
30
Slide31Kernel
Histogram
Kernel & Histogram
31
Ref :
What are the limitations of Kernel methods and when to use
kernel
?
http
://
en.wikipedia.org/wiki/Kernel_density_estimation
Slide32Importance Sampling
Monte Carlo SamplingImportance Sampling32
Ref
:
Sampling Methods
Importance
Sampling
Slide33Bayesian Sequential Partitioning (BSP)
CharacteristicNonparametricPiecewise Constant FunctionsBinary PartitionFast
33
Slide34Bayesian Sequential Partitioning (BSP)
Partition Score34
Ref :
Dirichlet
distribution
Slide35Bayesian Sequential Partitioning (BSP)
Sequential Importance Sampling
35
Slide36Bayesian Sequential Partitioning (BSP)
Sequential Importance SamplingImportance weightRandom Weights
36
2
1
1
Slide37Bayesian Sequential Partitioning (BSP)
Resampling37
Ref :
TLD (Tracking-Learning-Detection
)
Slide38Bayesian Sequential Partitioning (BSP)
Example : 38
Ref :
K.C. Lo ’s group-meeting PPT
Slide39Unsupervised Hierarchical Image Segmentation
based on Bayesian Sequential Partitioning IEEEHao-Wei Yeh, Chen-Yu Tseng, Tung-Yu Wu, Sheng-Jyh
Wang
2015
Ref :
Unsupervised Hierarchical Image Segmentation
based
on
Bayesian
Sequential Partitioning
39
Slide40Method
Split PhaseJust-Noticeable-Difference Bayesian Sequential Partitioning (JND-BSP
)
[1] color
differences among
pixels
[2]
just-noticeable
difference
prior
Merge PhaseHierarchical
40
Slide41Random Walk Model
41
Slide42JND-BSP
42
Slide43JND-BSP
43
Slide44Reference
The Manifold Ways of Perception.中央研究院週報 (第1058期) 流行學習與人臉辨識
Principal Component Analysis (PCA) , NTHU , Open Course
Ware
Modern Multidimensional Scaling: Theory and Applications
古典
多維標度法
(MDS) ,
線代啟示錄
Advanced
Introduction to Machine Learning ,
CMU-10715A Global Geometric Framework for Nonlinear Dimensionality Reduction.
http://www.math.ucla.edu/~wittman/maniAdvanced Introduction to Machine Learning, CMU-10715 Hierarchical Image Segmentation based on Iterative Contraction and
Merging
Learning-based hierarchical graph for unsupervised matting and foreground
estimation
Multivariate Density Estimation by Bayesian Sequential
Partitioning
What are the limitations of Kernel methods and when to use kernel
?
http://en.wikipedia.org/wiki/Kernel_density_estimationSampling Methods
Importance Sampling Dirichlet
distributionTLD (Tracking-Learning-Detection)K.C. Lo ’s group-meeting PPT
Unsupervised Hierarchical Image Segmentation based on Bayesian Sequential Partitioning
44
Slide4545