國立虎尾科技大學 |

Sampling and Filtering of Signals on Graphs With Applications to Active Learning and Image Processing.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Sampling and Filtering of Signals on Graphs With Applications to Active Learning and Image Processing./
作者:	Gadde, Akshay.
面頁冊數:	1 online resource (112 pages)
附註:	Source: Dissertation Abstracts International, Volume: 79-06(E), Section: B.
Contained By:	Dissertation Abstracts International79-06B(E).
標題:	Electrical engineering. -
電子資源:	click for full text (PQDT)

Sampling and Filtering of Signals on Graphs With Applications to Active Learning and Image Processing.
Gadde, Akshay.

Sampling and Filtering of Signals on Graphs With Applications to Active Learning and Image Processing. - 1 online resource (112 pages)

Source: Dissertation Abstracts International, Volume: 79-06(E), Section: B.

Thesis (Ph.D.)--University of Southern California, 2017.

Includes bibliographical references

Graph signals provide a natural representation for data in many applications such as social networks, web information analysis, sensor networks and machine learning. Traditional data such as images and videos can also be represented as signals on graphs. A frequency domain representation for graph signals can be obtained using the eigenvectors and eigenvalues of operators that measure the variation in signals taking into account the underlying connectivity in the graph. Based on this, we develop a sampling theory for graph signals that answers the following questions: 1. When can we uniquely and stably reconstruct a bandlimited graph signal from its samples on a subset of the nodes? 2. What is the best subset of nodes for sampling a signal so that the resulting bandlimited reconstruction is most stable? 3. How to compute a bandlimited reconstruction efficiently from a subset of samples? The algorithms developed for sampling set selection and reconstruction do not require explicit eigenvalue decomposition of the variation operator and admit efficient, localized implementation. Using graph sampling theory, we propose effective graph based active semi-supervised learning techniques. We also give a probabilistic interpretation of graph sampling. Based on this interpretation, we generalize the framework of sampling on graphs using Bayesian methods to give an adaptive sampling method in which the future choice of nodes to be sampled depends on the samples observed in the past. Additionally, we study the problem of constructing a sparse graph efficiently from given data and a kernel function that measures pairwise similarity between data points. The proposed graph construction method leads to graph based learning and clustering algorithms that outperform the conventional k-nearest neighbor methods. We also use the proposed graph construction method to provide an efficient alternative to the well-known bilateral filter by representing an image as a sparse graph in which the nodes correspond to the pixels in the image.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

Subjects--Topical Terms:

596380
Electrical engineering.
Index Terms--Genre/Form:

554714
Electronic books.

Sampling and Filtering of Signals on Graphs With Applications to Active Learning and Image Processing.
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300 $a 1 online resource (112 pages)
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500 $a Source: Dissertation Abstracts International, Volume: 79-06(E), Section: B.
500 $a Adviser: Antonio Ortega.
502 $a Thesis (Ph.D.)--University of Southern California, 2017.
504 $a Includes bibliographical references
520 $a Graph signals provide a natural representation for data in many applications such as social networks, web information analysis, sensor networks and machine learning. Traditional data such as images and videos can also be represented as signals on graphs. A frequency domain representation for graph signals can be obtained using the eigenvectors and eigenvalues of operators that measure the variation in signals taking into account the underlying connectivity in the graph. Based on this, we develop a sampling theory for graph signals that answers the following questions: 1. When can we uniquely and stably reconstruct a bandlimited graph signal from its samples on a subset of the nodes? 2. What is the best subset of nodes for sampling a signal so that the resulting bandlimited reconstruction is most stable? 3. How to compute a bandlimited reconstruction efficiently from a subset of samples? The algorithms developed for sampling set selection and reconstruction do not require explicit eigenvalue decomposition of the variation operator and admit efficient, localized implementation. Using graph sampling theory, we propose effective graph based active semi-supervised learning techniques. We also give a probabilistic interpretation of graph sampling. Based on this interpretation, we generalize the framework of sampling on graphs using Bayesian methods to give an adaptive sampling method in which the future choice of nodes to be sampled depends on the samples observed in the past. Additionally, we study the problem of constructing a sparse graph efficiently from given data and a kernel function that measures pairwise similarity between data points. The proposed graph construction method leads to graph based learning and clustering algorithms that outperform the conventional k-nearest neighbor methods. We also use the proposed graph construction method to provide an efficient alternative to the well-known bilateral filter by representing an image as a sparse graph in which the nodes correspond to the pixels in the image.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
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