Domain adaptation via transferring spectral properties of label functions on graphs

Pilanci, Mehmet; Vural, Elif

doi:10.1109/ivmspw.2016.7528188

Cited by 5 publications

(16 citation statements)

References 7 publications

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“…Given the source and the target samples The bound (2) on the target error suggests that when learning a pair of graphs, the parameters κ, B and B should be kept small, whereas small values for w min should be avoided. The expression in (5) shows that the parameters λ R and ∆ α should be kept small. Meanwhile, in the expression of ρ max in (6), we observe that the terms A, M s , and M t are determined by the geometry of the data manifolds and these are independent of the graphs.…”

Section: Problem Formulationmentioning

confidence: 99%

“…The simplified objective 2 in (8) is in fact the same as the objective of the SDA algorithm proposed in [5]. As the problem is quadratic and convex in α s and α t , its solution can be analytically found by setting the gradient equal to 0 , which gives [5]…”

Section: Problem Formulationmentioning

confidence: 99%

“…These methods are applied to problems such as clustering and 3D shape analysis. Our recent work [5] also relies on representations with graph Fourier bases, but in the context of domain adaptation.…”

Section: Related Workmentioning

confidence: 99%

“…The expression in Eq. (5) shows that the parameters λ R and ∆ α should be kept small. Meanwhile, in the expression of ρ max in Eq.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Then, the purpose of graph domain adaptation is to transfer this information to a target graph that contains very few labels and estimate the unknown class labels. We studied this problem in our previous work [5], where we proposed a method called spectral domain adaptation (SDA). In order to optimize the performance of graph domain adaptation methods, it is important to theoretically characterize their performance limits.…”

Section: Introductionmentioning

confidence: 99%

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Domain adaptation on graphs by learning graph topologies: theoretical analysisand an algorithm

Vural¹

2019

Turk J Elec Eng & Comp Sci

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Traditional machine learning algorithms assume that the training and test data have the same distribution, while this assumption does not necessarily hold in real applications. Domain adaptation methods take into account the deviations in the data distribution. In this work, we study the problem of domain adaptation on graphs. We consider a source graph and a target graph constructed with samples drawn from data manifolds. We study the problem of estimating the unknown class labels on the target graph using the label information on the source graph and the similarity between the two graphs. We particularly focus on a setting where the target label function is learnt such that its spectrum is similar to that of the source label function. We first propose a theoretical analysis of domain adaptation on graphs and present performance bounds that characterize the target classification error in terms of the properties of the graphs and the data manifolds. We show that the classification performance improves as the topologies of the graphs get more balanced, i.e., as the numbers of neighbors of different graph nodes become more proportionate, and weak edges with small weights are avoided. Our results also suggest that graph edges between too distant data samples should be avoided for good generalization performance. We then propose a graph domain adaptation algorithm inspired by our theoretical findings, which estimates the label functions while learning the source and target graph topologies at the same time. The joint graph learning and label estimation problem is formulated through an objective function relying on our performance bounds, which is minimized with an alternating optimization scheme. Experiments on synthetic and real data sets suggest that the proposed method outperforms baseline approaches.

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Section: Problem Formulationmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

“…The expression in Eq. (5) shows that the parameters λ R and ∆ α should be kept small. Meanwhile, in the expression of ρ max in Eq.…”

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Domain adaptation on graphs by learning graph topologies: theoretical analysisand an algorithm

Vural¹

2019

Turk J Elec Eng & Comp Sci

Self Cite

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Semisupervised charting for spectral multimodal manifold learning and alignment

Pournemat

Adibi

Chanussot

2021

Pattern Recognition

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Domain Adaptation on Graphs by Learning Aligned Graph Bases

Pilanci

Vural

2022

IEEE Trans. Knowl. Data Eng.

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A common assumption in semi-supervised learning with graph models is that the class label function varies smoothly on the data graph, resulting in the rather strict prior that the label function has low-frequency content. Meanwhile, in many classification problems, the label function may vary abruptly in certain graph regions, resulting in high-frequency components. Although the semi-supervised estimation of class labels is an ill-posed problem in general, in several applications it is possible to find a source graph on which the label function has similar frequency content to that on the target graph where the actual classification problem is defined. In this paper, we propose a method for domain adaptation on graphs motivated by these observations. Our algorithm is based on learning the spectrum of the label function in a source graph with many labeled nodes, and transferring the information of the spectrum to the target graph with fewer labeled nodes. While the frequency content of the class label function can be identified through the graph Fourier transform, it is not easy to transfer the Fourier coefficients directly between the two graphs, since no one-to-one match exists between the Fourier basis vectors of independently constructed graphs in the domain adaptation setting. We solve this problem by learning a transformation between the Fourier bases of the two graphs that flexibly "aligns" them. The unknown class label function on the target graph is then reconstructed such that its spectrum matches that on the source graph while also ensuring the consistency with the available labels. The proposed method is tested in the classification of image, online product review, and social network data sets. Comparative experiments suggest that the proposed algorithm performs better than recent domain adaptation methods in the literature in most settings.

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Domain adaptation via transferring spectral properties of label functions on graphs

Cited by 5 publications

References 7 publications

Domain adaptation on graphs by learning graph topologies: theoretical analysisand an algorithm

Domain adaptation on graphs by learning graph topologies: theoretical analysisand an algorithm

Semisupervised charting for spectral multimodal manifold learning and alignment

Domain Adaptation on Graphs by Learning Aligned Graph Bases

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