Generalized Optimization Framework for Graph-based Semi-supervised Learning

Avrachenkov, Konstantin; Gonçalvès, Paulo; Mishenin, Alexey; Sokol, Marina

doi:10.1137/1.9781611972825.83

Cited by 42 publications

(72 citation statements)

References 13 publications

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“…These two types of side-information are typical in semi-supervised clustering applications [13][14][15]. We use BP for subgraph detection to handle these two kinds of side-information.…”

Section: Summary Of Resultsmentioning

confidence: 99%

The Power of Side-Information in Subgraph Detection

Kadavankandy

Avrachenkov

Cottatellucci

et al. 2018

IEEE Trans. Signal Process.

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Abstract:In this work, we tackle the problem of hidden community detection. We consider Belief Propagation (BP) applied to the problem of detecting a hidden Erdős-Rényi (ER) graph embedded in a larger and sparser ER graph, in the presence of side-information. We derive two related algorithms based on BP to perform subgraph detection in the presence of two kinds of sideinformation. The first variant of side-information consists of a set of nodes, called cues, known to be from the subgraph. The second variant of side-information consists of a set of nodes that are cues with a given probability. It was shown in past works that BP without side-information fails to detect the subgraph correctly when an effective signal-to-noise ratio (SNR) parameter falls below a threshold. In contrast, in the presence of non-trivial side-information, we show that the BP algorithm achieves asymptotically zero error for any value of the SNR parameter. We validate our results through simulations on synthetic datasets as well as on a few real world networks.

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“…These two types of side-information are typical in semi-supervised clustering applications [13][14][15]. We use BP for subgraph detection to handle these two kinds of side-information.…”

Section: Summary Of Resultsmentioning

confidence: 99%

The Power of Side-Information in Subgraph Detection

Kadavankandy

Avrachenkov

Cottatellucci

et al. 2018

IEEE Trans. Signal Process.

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“…The general idea of the graph-based semi-supervised learning is to find classification functions so that on the one hand they will be close to the corresponding labeling function and on the other hand they will change smoothly over the graph associated with the similarity matrix. This general idea can be expressed by means of the following optimization formulation [5]:…”

Section: Semi-supervised Learning Methodsmentioning

confidence: 99%

“…We observe that if one takes the method of [1] for detecting local cuts and takes seeds in [1] as the labelled data and considers sweeps as classification functions, then because the degrees of data points in different sweeps are the same, the resulting method will be equivalent to the semi-supervised method proposed in [3]. Recently in [5], the authors proposed a generalized optimization formulation which gives the above mentioned methods as particular cases. In the present work we provide more insights about the differences among the semi-supervised methods based on random walk theory, and give recommendations on how to choose the kernel and labelled points (of course, when there is some freedom in the choice of labelled points).…”

Section: Introductionmentioning

confidence: 99%

On the Choice of Kernel and Labelled Data in Semi-supervised Learning Methods

Avrachenkov¹,

Gonçalvès

Sokol³

2013

Lecture Notes in Computer Science

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Abstract. Semi-supervised learning methods constitute a category of machine learning methods which use labelled points together with unlabelled data to tune the classifier. The main idea of the semi-supervised methods is based on an assumption that the classification function should change smoothly over a similarity graph, which represents relations among data points. This idea can be expressed using kernels on graphs such as graph Laplacian. Different semi-supervised learning methods have different kernels which reflect how the underlying similarity graph influences the classification results. In the present work, we analyse a general family of semi-supervised methods, provide insights about the differences among the methods and give recommendations for the choice of the kernel parameters and labelled points. In particular, it appears that it is preferable to choose a kernel based on the properties of the labelled points. We illustrate our general theoretical conclusions with an analytically tractable characteristic example, clustered preferential attachment model and classification of content in P2P networks.

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“…Our approach is based on a series of works [2]- [4] presenting a generalized expression for G-SSL: this generalization comprehends the different methods, Standard and Normalized Laplacian (SL,NL) and Page Rank (PR) in a unique framework, as we shall display in the following. This generalized expression of the G-SSL [2] reads…”

Section: State Of the Art And Related Workmentioning

confidence: 99%

Fractional graph-based semi-supervised learning

Nigris

Bautista

Abry

et al. 2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-Graph-based semi-supervised learning for classification endorses a nice interpretation in terms of diffusive random walks, where the regularisation factor in the original optimisation formulation plays the role of a restarting probability. Recently, a new type of biased random walks for characterising certain dynamics on networks have been defined and rely on the γ-th power of the standard Laplacian matrix L γ , with γ > 0. In particular, these processes embed long range transitions, the Lévy flights, that are capable of one-step jumps between fardistant states (nodes) of the graph. The present contribution envisions to build upon these volatile random walks to propose a new version of graph based semi-supervised learning algorithms whose classification outcome could benefit from the dynamics induced by the fractional transition matrix.

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Generalized Optimization Framework for Graph-based Semi-supervised Learning

Cited by 42 publications

References 13 publications

The Power of Side-Information in Subgraph Detection

The Power of Side-Information in Subgraph Detection

On the Choice of Kernel and Labelled Data in Semi-supervised Learning Methods

Fractional graph-based semi-supervised learning

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