Semi-Supervised Learning

Zhou, Xueyuan; Belkin, Mikhail

doi:10.1016/b978-0-12-396502-8.00022-x

Cited by 78 publications

(41 citation statements)

References 14 publications

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“…Zhou and Schölkopf in their papers [84][83] [82] formulated a theory of non-local operators that is related to the discrete graph Laplacian described in Section 2.1. Buades, Coll, and Morel applied this non-local theory to denoising algorithms in their work [16].…”

Section: Non-local Means Methods For Rgb Imagementioning

confidence: 99%

Hyperspectral Image Classification Using Graph Clustering Methods

Zhang¹,

Merkurjev²,

Koniges³

et al. 2017

Image Processing on Line

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Hyperspectral imagery is a challenging modality due to the dimension of the pixels which can range from hundreds to over a thousand frequencies depending on the sensor. Most methods in the literature reduce the dimension of the data using a method such as principal component analysis, however this procedure can lose information. More recently methods have been developed to address classification of large datasets in high dimensions. This paper presents two classes of graph-based classification methods for hyperspectral imagery. Using the full dimensionality of the data, we consider a similarity graph based on pairwise comparisons of pixels. The graph is segmented using a pseudospectral algorithm for graph clustering that requires information about the eigenfunctions of the graph Laplacian but does not require computation of the full graph. We develop a parallel version of the Nyström extension method to randomly sample the graph to construct a low rank approximation of the graph Laplacian. With at most a few hundred eigenfunctions, we can implement the clustering method designed to solve a variational problem for a graph-cut-based semi-supervised or unsupervised classification problem. We implement OpenMP directive-based parallelism in our algorithms and show performance improvement and strong, almost ideal, scaling behavior. The method can handle very large datasets including a video sequence with over a million pixels, and the problem of segmenting a data set into a pre-determined number of classes. Source CodeThe reviewed source code and documentation for this algorithm are available from the web page of this article 1 . Compilation and usage instructions are included in the README.txt file of the archive.

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Section: Non-local Means Methods For Rgb Imagementioning

confidence: 99%

Hyperspectral Image Classification Using Graph Clustering Methods

Zhang¹,

Merkurjev²,

Koniges³

et al. 2017

Image Processing on Line

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“…Zhou and Schölkopf in their papers [67,64,66,65] formulated a theory of nonlocal operators that is related to the discrete graph Laplacian described in section 2.2. Buades, Coll, and Morel applied this nonlocal theory to denoising algorithms in their work [9].…”

Section: Nonlocal Operatorsmentioning

confidence: 99%

An MBO Scheme on Graphs for Classification and Image Processing

Merkurjev¹,

Kostic²,

Bertozzi³

2013

SIAM J. Imaging Sci.

128

266

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Abstract. In this paper we present a computationally efficient algorithm utilizing a fully or seminonlocal graph Laplacian for solving a wide range of learning problems in binary data classification and image processing. In their recent work [Multiscale Model. Simul., 10 (2012) 1. Introduction. This work develops a fast algorithm for a recent variational method in a graph setting. The method is inspired by diffuse interface models that have been used in a variety of problems, such as those in fluid dynamics and materials science. We consider data represented as nodes in a weighted graph, and each edge is assigned a numerical value describing the similarity between the nodes. In spectral graph theory, this approach is successfully used to perform various learning tasks in imaging and data clustering. The standard techniques of the theory are thoroughly described in [13,45], and the graph Laplacian, which is discussed in more detail in section 2.2, is introduced as one of the fundamental concepts. In imaging, spectral methods are often used in image segmentation applications, as shown in [54,33,14].We are particularly interested in nonlocal total variation methods, as they are a link between spectral graph theory and diffuse interface models and thus can be used as a motivation for our algorithm. These methods are used in numerous image processing applications. They were initially developed as methods for image denoising [9,29] but were successfully applied to many other image processing problems such as inpainting and reconstruction in [30,63,49], image deblurring in [40], and manifold processing in [18].Bertozzi and Flenner introduce a graph-based model based on the Ginzburg-Landau func-

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“…The first is called an inductive learning; the second is a transductive learning. Vapnik [21,22] defined the semi-supervised learning as a principle of transduction.…”

Section: Semi Supervised Learningmentioning

confidence: 99%

CAD system for classification of mammographic abnormalities using transductive semi supervised learning algorithm and heterogeneous features

Zemmal

Azizi

Sellami

2015

2015 12th International Symposium on Programming and Systems (ISPS)

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Breast cancer is the most frequently diagnosed cancer in women worldwide and the leading cause of cancer death among females. Currently the most effective method for early detection and screening of breast abnormalities is mammography. In particular, the breast mass diagnosis and classification arouse nowadays a great interest. Various researches have proven that the computer-aided diagnosis (CAD) of breast abnormalities is becoming increasingly a necessity given the exponential growth of performed. Hence, it can reduce the cost for double screening process A generic CAD system includes segmentation, feature extraction, and classification stages in order to have a final decision. However, such a system is usually characterized by the large volume of the acquired data. This data must be labeled in a specific way that leads to a major problem which is the necessity of an expert to make the labeling operation. To overcome this constraint, statistical learning propose semi-supervised learning (SSL) algorithm as alternative in order to beneficiate to the all dataset images. In this paper, a CAD system for the breast abnormalities classification is proposed basing on Transductive semi-supervised learning technique using TSVM with these different kernel functions and heterogeneous features families. Experimental results based on DDSM dataset are very encouraging.

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Semi-Supervised Learning

Cited by 78 publications

References 14 publications

Hyperspectral Image Classification Using Graph Clustering Methods

Hyperspectral Image Classification Using Graph Clustering Methods

An MBO Scheme on Graphs for Classification and Image Processing

CAD system for classification of mammographic abnormalities using transductive semi supervised learning algorithm and heterogeneous features

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