Upload
others
View
4
Download
0
Embed Size (px)
Citation preview
Network Methods for Big Data: Applications toAstroinformatics
Ognyan Kounchev
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-Universityof Bonn
Supported by the Humboldt Foundation and Project between Serbianand Bulgarian Academy of Sciences
X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 1
/ 32
Main purpose of the talk
Show recent approach of Signal Processing on Graphs/Networks
Using Spectral Graph theory
Spectral Graph Wavelets = Multiscale Concepts
Importance of Multiscale approach in analysis of AstronomicalImages
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 2
/ 32
Main purpose of the talk
Show recent approach of Signal Processing on Graphs/Networks
Using Spectral Graph theory
Spectral Graph Wavelets = Multiscale Concepts
Importance of Multiscale approach in analysis of AstronomicalImages
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 2
/ 32
Main purpose of the talk
Show recent approach of Signal Processing on Graphs/Networks
Using Spectral Graph theory
Spectral Graph Wavelets = Multiscale Concepts
Importance of Multiscale approach in analysis of AstronomicalImages
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 2
/ 32
Main purpose of the talk
Show recent approach of Signal Processing on Graphs/Networks
Using Spectral Graph theory
Spectral Graph Wavelets = Multiscale Concepts
Importance of Multiscale approach in analysis of AstronomicalImages
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 2
/ 32
Methods of Signal Processing for Analysis of Big Data
The main points:
Representation and processing of massive data sets with irregularstructure in the areas
Same methods in: Engineering, Astronomy, Social Networks,Biomolecular research (biochemical and genetics), Commerce(consumer behaviour studies), Security
Our approach: Discrete Signal Processing (DSP) onNetworks/Graphs using Spectral theory and Wavelets
Challenges: Large-scale filtering and frequency analysis
The new notions which generalize those of the classical DSP: Graphsignals, Graph filters, Graph Fourier transform, Graph frequency,Spectrum ordering
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 3
/ 32
Methods of Signal Processing for Analysis of Big Data
The main points:
Representation and processing of massive data sets with irregularstructure in the areas
Same methods in: Engineering, Astronomy, Social Networks,Biomolecular research (biochemical and genetics), Commerce(consumer behaviour studies), Security
Our approach: Discrete Signal Processing (DSP) onNetworks/Graphs using Spectral theory and Wavelets
Challenges: Large-scale filtering and frequency analysis
The new notions which generalize those of the classical DSP: Graphsignals, Graph filters, Graph Fourier transform, Graph frequency,Spectrum ordering
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 3
/ 32
Methods of Signal Processing for Analysis of Big Data
The main points:
Representation and processing of massive data sets with irregularstructure in the areas
Same methods in: Engineering, Astronomy, Social Networks,Biomolecular research (biochemical and genetics), Commerce(consumer behaviour studies), Security
Our approach: Discrete Signal Processing (DSP) onNetworks/Graphs using Spectral theory and Wavelets
Challenges: Large-scale filtering and frequency analysis
The new notions which generalize those of the classical DSP: Graphsignals, Graph filters, Graph Fourier transform, Graph frequency,Spectrum ordering
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 3
/ 32
Methods of Signal Processing for Analysis of Big Data
The main points:
Representation and processing of massive data sets with irregularstructure in the areas
Same methods in: Engineering, Astronomy, Social Networks,Biomolecular research (biochemical and genetics), Commerce(consumer behaviour studies), Security
Our approach: Discrete Signal Processing (DSP) onNetworks/Graphs using Spectral theory and Wavelets
Challenges: Large-scale filtering and frequency analysis
The new notions which generalize those of the classical DSP: Graphsignals, Graph filters, Graph Fourier transform, Graph frequency,Spectrum ordering
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 3
/ 32
Methods of Signal Processing for Analysis of Big Data
The main points:
Representation and processing of massive data sets with irregularstructure in the areas
Same methods in: Engineering, Astronomy, Social Networks,Biomolecular research (biochemical and genetics), Commerce(consumer behaviour studies), Security
Our approach: Discrete Signal Processing (DSP) onNetworks/Graphs using Spectral theory and Wavelets
Challenges: Large-scale filtering and frequency analysis
The new notions which generalize those of the classical DSP: Graphsignals, Graph filters, Graph Fourier transform, Graph frequency,Spectrum ordering
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 3
/ 32
3 examples of Signals on graphs
Top: Samples of the signal cos (2πn/6): edges show causality of time;
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 4
/ 32
Examples above:
Sensor network – edges show closeness of locations of the sensors;WWW: nodes = websites with website features, edges = hyperlinksSocial Network: nodes = individuals, edges = connection andstrengthAstronomical Images and their Network approximationsNetwork Approximations have nodes which are galaxies, stars,clusters; nodes are intersection of lines along edges; closer Nodesrepresent similar features within the dataAn Examplary OBJECTIVE of OUR WORK: Find a method forhigh speed automatic classification of galaxiespreviously done by thousands of volunteersApplication to: images of distant clusters of galaxies thatcontain several different types of galaxiesGeneral approach of Machine Learning: This is the art of ”teaching”the algorithms the experience of people accumulated for a long time.Applications of the same methods e.g. in medicine, for helping tospot tumours, or in security, to find suspicious items in airport scans.
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 5
/ 32
Example of Network - LinkedIn
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 6
/ 32
Example - LinkedIn
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 7
/ 32
Biostatistics - example graph
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 8
/ 32
Influencer Network-graph
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 9
/ 32
General principles of SP on graphs
DSP is applied to data sets in which the elements are related bydependency, similarity, physical porximity, etc.
data elements vj ∈ G = nodes of the graph/network, forj = 1, 2, ...,N
A = (aij ) is the weighted adjacency matrix where aij shows thesimilarity/closeness between nodes vi and vj
Signal S = (sj )Nj=1 is a sequence of numbers which are valued on the
nodes vj
The ”neighbouring” nodes for the node νj is the set
Nj
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 10
/ 32
General principles of SP on graphs
DSP is applied to data sets in which the elements are related bydependency, similarity, physical porximity, etc.
data elements vj ∈ G = nodes of the graph/network, forj = 1, 2, ...,N
A = (aij ) is the weighted adjacency matrix where aij shows thesimilarity/closeness between nodes vi and vj
Signal S = (sj )Nj=1 is a sequence of numbers which are valued on the
nodes vj
The ”neighbouring” nodes for the node νj is the set
Nj
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 10
/ 32
General principles of SP on graphs
DSP is applied to data sets in which the elements are related bydependency, similarity, physical porximity, etc.
data elements vj ∈ G = nodes of the graph/network, forj = 1, 2, ...,N
A = (aij ) is the weighted adjacency matrix where aij shows thesimilarity/closeness between nodes vi and vj
Signal S = (sj )Nj=1 is a sequence of numbers which are valued on the
nodes vj
The ”neighbouring” nodes for the node νj is the set
Nj
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 10
/ 32
General principles of SP on graphs
DSP is applied to data sets in which the elements are related bydependency, similarity, physical porximity, etc.
data elements vj ∈ G = nodes of the graph/network, forj = 1, 2, ...,N
A = (aij ) is the weighted adjacency matrix where aij shows thesimilarity/closeness between nodes vi and vj
Signal S = (sj )Nj=1 is a sequence of numbers which are valued on the
nodes vj
The ”neighbouring” nodes for the node νj is the set
Nj
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 10
/ 32
General principles of SP on graphs
DSP is applied to data sets in which the elements are related bydependency, similarity, physical porximity, etc.
data elements vj ∈ G = nodes of the graph/network, forj = 1, 2, ...,N
A = (aij ) is the weighted adjacency matrix where aij shows thesimilarity/closeness between nodes vi and vj
Signal S = (sj )Nj=1 is a sequence of numbers which are valued on the
nodes vj
The ”neighbouring” nodes for the node νj is the set
Nj
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 10
/ 32
Multiscale structure Analysis of Network Signals
1 Graph shift - generalizes the usual DSP time delay; taking averageover the Neighbours
sn = ∑m∈Nn
An,msm
2 Graph Fourier transform needs the Graph Laplace operator (weassume undirected graph): for a signal f on the graph we define
Lfm := ∑n∈Nm
am,n (fm − fn)
3 L is a real symmetric matrix: we denote the N (orthonormal)eigenvectors and eigenvalues of L by
χ(n) =(
χ(n)1 , ..., χ
(n)N
)∈ RN ,
λ0 ≤ λ1 ≤ · · · ≤ λN−1.
They are the analogue to e ikt , since − d2
dt2e ikt = k2e ikt
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 11
/ 32
Example of eigenvectors
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 12
/ 32
Fourier and Wavelet Analysis on Graphs
Hence, we have Fourier Analysis
fm = ∑ f̂nχ(n)m
One may define Wavelet Analysis by using appropriate filter functiong , as follows:
Wf (p) =N−1∑n=0
g (λn) f̂nχ(n)p
We may define the scale t by putting
Wf (p; t) =N−1∑n=0
g (tλn) f̂nχ(n)p
The role of t - the scale of the localized at node a wavelet ψt,a
where (a ∈ G ).
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 13
/ 32
Fourier and Wavelet Analysis on Graphs
Hence, we have Fourier Analysis
fm = ∑ f̂nχ(n)m
One may define Wavelet Analysis by using appropriate filter functiong , as follows:
Wf (p) =N−1∑n=0
g (λn) f̂nχ(n)p
We may define the scale t by putting
Wf (p; t) =N−1∑n=0
g (tλn) f̂nχ(n)p
The role of t - the scale of the localized at node a wavelet ψt,a
where (a ∈ G ).
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 13
/ 32
Fourier and Wavelet Analysis on Graphs
Hence, we have Fourier Analysis
fm = ∑ f̂nχ(n)m
One may define Wavelet Analysis by using appropriate filter functiong , as follows:
Wf (p) =N−1∑n=0
g (λn) f̂nχ(n)p
We may define the scale t by putting
Wf (p; t) =N−1∑n=0
g (tλn) f̂nχ(n)p
The role of t - the scale of the localized at node a wavelet ψt,a
where (a ∈ G ).
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 13
/ 32
Fourier and Wavelet Analysis on Graphs
Hence, we have Fourier Analysis
fm = ∑ f̂nχ(n)m
One may define Wavelet Analysis by using appropriate filter functiong , as follows:
Wf (p) =N−1∑n=0
g (λn) f̂nχ(n)p
We may define the scale t by putting
Wf (p; t) =N−1∑n=0
g (tλn) f̂nχ(n)p
The role of t - the scale of the localized at node a wavelet ψt,a
where (a ∈ G ).
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 13
/ 32
Examples of localizations – Swiss roll
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 14
/ 32
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 15
/ 32
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 16
/ 32
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 17
/ 32
Main Objective: Clusterization (Community Detection ongraphs)
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 18
/ 32
Continued
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 19
/ 32
Comparison with other methods for Community Detection
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 20
/ 32
Possible Applications outside and in Astronomy
Remote Sensing Network for Time-Sensitive Detection of Fine ScaleDamage to Transportation Infrastructure
Expoiting existing ground-based remote sensing Networks to improveHigh-resolution weather forecasts.
Neural Network Applications in High-Resolution Atmospheric RemoteSensing
Development of a Real Time Remote Sensing Network to MonitorSmall Fluctuations in Urban Air Quality
Network clustering by graph coloring: An application to astronomicalimages
Astronomical image segmentation by Networks and wavelets
Machine learning method to analyse galaxy images
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 21
/ 32
Possible Applications outside and in Astronomy
Remote Sensing Network for Time-Sensitive Detection of Fine ScaleDamage to Transportation Infrastructure
Expoiting existing ground-based remote sensing Networks to improveHigh-resolution weather forecasts.
Neural Network Applications in High-Resolution Atmospheric RemoteSensing
Development of a Real Time Remote Sensing Network to MonitorSmall Fluctuations in Urban Air Quality
Network clustering by graph coloring: An application to astronomicalimages
Astronomical image segmentation by Networks and wavelets
Machine learning method to analyse galaxy images
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 21
/ 32
Possible Applications outside and in Astronomy
Remote Sensing Network for Time-Sensitive Detection of Fine ScaleDamage to Transportation Infrastructure
Expoiting existing ground-based remote sensing Networks to improveHigh-resolution weather forecasts.
Neural Network Applications in High-Resolution Atmospheric RemoteSensing
Development of a Real Time Remote Sensing Network to MonitorSmall Fluctuations in Urban Air Quality
Network clustering by graph coloring: An application to astronomicalimages
Astronomical image segmentation by Networks and wavelets
Machine learning method to analyse galaxy images
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 21
/ 32
Possible Applications outside and in Astronomy
Remote Sensing Network for Time-Sensitive Detection of Fine ScaleDamage to Transportation Infrastructure
Expoiting existing ground-based remote sensing Networks to improveHigh-resolution weather forecasts.
Neural Network Applications in High-Resolution Atmospheric RemoteSensing
Development of a Real Time Remote Sensing Network to MonitorSmall Fluctuations in Urban Air Quality
Network clustering by graph coloring: An application to astronomicalimages
Astronomical image segmentation by Networks and wavelets
Machine learning method to analyse galaxy images
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 21
/ 32
Possible Applications outside and in Astronomy
Remote Sensing Network for Time-Sensitive Detection of Fine ScaleDamage to Transportation Infrastructure
Expoiting existing ground-based remote sensing Networks to improveHigh-resolution weather forecasts.
Neural Network Applications in High-Resolution Atmospheric RemoteSensing
Development of a Real Time Remote Sensing Network to MonitorSmall Fluctuations in Urban Air Quality
Network clustering by graph coloring: An application to astronomicalimages
Astronomical image segmentation by Networks and wavelets
Machine learning method to analyse galaxy images
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 21
/ 32
Possible Applications outside and in Astronomy
Remote Sensing Network for Time-Sensitive Detection of Fine ScaleDamage to Transportation Infrastructure
Expoiting existing ground-based remote sensing Networks to improveHigh-resolution weather forecasts.
Neural Network Applications in High-Resolution Atmospheric RemoteSensing
Development of a Real Time Remote Sensing Network to MonitorSmall Fluctuations in Urban Air Quality
Network clustering by graph coloring: An application to astronomicalimages
Astronomical image segmentation by Networks and wavelets
Machine learning method to analyse galaxy images
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 21
/ 32
Possible Applications outside and in Astronomy
Remote Sensing Network for Time-Sensitive Detection of Fine ScaleDamage to Transportation Infrastructure
Expoiting existing ground-based remote sensing Networks to improveHigh-resolution weather forecasts.
Neural Network Applications in High-Resolution Atmospheric RemoteSensing
Development of a Real Time Remote Sensing Network to MonitorSmall Fluctuations in Urban Air Quality
Network clustering by graph coloring: An application to astronomicalimages
Astronomical image segmentation by Networks and wavelets
Machine learning method to analyse galaxy images
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 21
/ 32
Pictures to:
Machine learning: to ”teach” a machine to analyse galaxy images
1 Picture 1: Hubble Space Telescope image of the cluster of galaxiesMACS0416.1-2403, one of the Hubble ‘Frontier Fields’. Bright yellow‘elliptical’ galaxies can be seen, surrounded by numerous blue spiraland amorphous (star-forming) galaxies
2 Picture 2: Visualisation of the (neural) network representing the‘brain’ of the machine learning algorithm. The intersections of linesare called nodes, and these represent a map of the input data. Nodesthat are closer to each other represent similarity
3 Picture 3: A zoom-in of part of the network described above.Credit: J. Geach / A. Hocking
4 Picture 4: Image showing the MACS0416.1-2403 cluster, highlightingparts of the image that the algorithm has identified as ‘star-forming’galaxies. Credit: NASA / ESA / J. Geach / A. Hocking
5 Picture 5: Image showing the MACS0416.1-2403 cluster, highlightingparts of the image that the algorithm has identified as ‘elliptical’galaxies. Credit: NASA / ESA / J. Geach / A. Hocking
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 22
/ 32
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 23
/ 32
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 24
/ 32
Continued - Network approximation
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 25
/ 32
Cont’d - zoomed part
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 26
/ 32
Cont’d - ”star forming” galaxies
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 27
/ 32
Cont’d – ”elliptical” galaxies
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 28
/ 32
Deep Learning and Wavelets approach
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 29
/ 32
References and Credits
Hammond, Vandergheynst, R. Gribonval, Wavelets on graphs viaspectral graph theory, 2009 in arxiv; 2011 in IEEE.
R. Lambiotte, J.-C. Delvenne and M. Barahona, Laplacian Dynamicsand Multiscale Modular Structure in Networks, 2009, arxiv.
R. Lambiotte, J.-C. Delvenne and M. Barahona, Random Walks,Markov Processes and the Multiscale Modular Organization ofComplex Networks, IEEE TRANSACTIONS ON NETWORK SCIENCEAND ENGINEERING, VOL. 1, NO. 2, JULY-DECEMBER, 2014
Leonardi, N., D. Van De Ville, Tight wavelet frames on multislicegraphs, IEEE, 2013
M. Mitrovic and B. Tadic, “Spectral and dynamical properties inclasses of sparse networks with mesoscopic inhomogeneities,” Phys.Rev. E, vol. 80, p. 026123, Aug 2009.
Raif M. Rustamov & Leonidas Guibas, Wavelets on Graphs via DeepLearning, 2013.
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 30
/ 32
Credits
A. Sandryhaila and J. Moura, Big data analysis with signal processingon graphs, IEEE Signal processing Magazine, September, 2014.
D. Shuman, Ch. Wiesmeyr, N. Hoighaus, P. Vandergheynst,Spectrum-adapted tight graph wavelet and vertex-frequency frames,IEEE, 2015.
D. Shuman, Pierre Vandergheynst, and Pascal Frossard, ChebyshevPolynomial Approximation for Distributed Signal Processing, IEEE,2011
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 31
/ 32
Credits
David I Shuman, Sunil K. Narang, Pascal Frossard, Antonio Ortega,and Pierre Vandergheynst, The Emerging Field of Signal Processingon Graphs, IEEE SIGNAL PROCESSING MAGAZINE, May 2013.
Tremblay, N., P. Borgnat, Graph wavelets for multiscale communitymining, IEEE, 2014.
Tremblay, N., P. Borgnat, Multiscale community mining in networksusing spectral graph wavelets, 2013.
R. Carmona, W.L. Hwang, and B. Torresani, Practical Time-frequencyanalysis, Academic press, 1998.
Ognyan Kounchev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, IZKS-University of Bonn)Network Methods for Big Data: Applications to AstroinformaticsSupported by the Humboldt Foundation and Project between Serbian and Bulgarian Academy of Sciences X Serbian-Bulgarian Astronomical Conference, Belgrade, 2016 32
/ 32