ISOLLE: Locally Linear Embedding with Geodesic Distance

Varini, Claudio; Degenhard, Andreas; Nattkemper, Tim Wilhelm

doi:10.1007/11564126_34

Cited by 10 publications

(10 citation statements)

References 10 publications

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“…The algorithm includes five general steps as follows. Research has shown that the Geodesic distance is superior to the default setting of Euclidean distance in LLE, and can eliminate the "short circuit" problem and lead to a more faithful representation of the global structure of the underlying manifold [56]. The Geodesic distance is approximated as the length of shortest path between a pair of data points in a weighted graph 𝐺 ]^& , which can be computed as in [57].…”

Section: Linear Neighborhood Propagationmentioning

confidence: 99%

Measuring relative opinion from location-based social media: A case study of the 2016 U.S. presidential election

et al. 2020

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Social media has become an emerging alternative to opinion polls for public opinion collection, while it is still posing many challenges as a passive data source, such as structurelessness, quantifiability, and representativeness. Social media data with geotags provide new opportunities to unveil the geographic locations of users expressing their opinions. This paper aims to answer two questions: 1) whether quantifiable measurement of public opinion can be obtained from social media and 2) whether it can produce better or complementary measures compared to opinion polls. This research proposes a novel approach to measure the relative opinion of Twitter users towards public issues in order to accommodate more complex opinion structures and take advantage of the geography pertaining to the public issues. To ensure that this new measure is technically feasible, a modeling framework is developed including building a training dataset by adopting a state-of-the-art approach and devising a new deep learning method called Opinion-Oriented Word Embedding. With a case study of tweets on the 2016 U.S. presidential election, we demonstrate the predictive superiority of our relative opinion approach and we show how it can aid visual analytics and support opinion predictions. Although the relative opinion measure is proved to be more robust than polling, our study also suggests that the former can advantageously complement the latter in opinion prediction.

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Section: Linear Neighborhood Propagationmentioning

confidence: 99%

Measuring relative opinion from location-based social media: A case study of the 2016 U.S. presidential election

et al. 2020

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“…The premise of manifold learning is based on a priori assumptions. Different from the previous works, we explore the geometry of data distribution through the manifold constraint technique by presenting a neighbor-preserving embedding algorithm [40] and then utilize it as an added regularization term to discover the manifold estimates. This formalization method is similar to LLE [41] in calculating the weights in dimension reduction.…”

Section: Related Workmentioning

confidence: 99%

“…As described in LLE algorithm [28], a focal point on a manifold can be expressed by a small and dense set of K nearest neighbors to approximate ISOMAP(Isometric Feature Mapping) [42]. Obviously, the Geodesic distance which is employed in ISOMAP [40] is another available technique to detect the neighbors in a linear embedding.…”

Section: Related Workmentioning

confidence: 99%

ManiDec: Manifold Constrained Low-Rank and Sparse Decomposition

Liu

Zeng

et al. 2019

IEEE Access

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Low-rank and sparse decomposition based image alignment has recently become an important research topic in the computer vision community. However, the reconstruction process often suffers from the perturbations caused by variations of the input samples. The reason behind is that the consistency of the learned low-rank and sparse structures for similar input samples is not well addressed in the existing literature. In this paper, a novel framework that embeds the manifold constraint into low-rank and sparse decomposition is proposed. Particularly, the proposed approach attempts to solve the original optimization problem directly and force the optimization process to satisfy the structure preservation requirement. Therefore, this novel manifold constrained low-rank and sparse decomposition (ManiDec) can consistently integrate the manifold constraint during the non-convex optimization process, and it can contribute a better solution which is robust to the variance of the input samples. Numerical comparisons between our proposed ManiDec and some state-of-the-art solvers, on several accessible databases, are presented to demonstrate its efficiency and effectiveness. In fact, to the best of our knowledge, this is the first time to integrate the manifold constraint into a non-convex framework, which has demonstrated the superiority of performance. INDEX TERMS Low-rank and sparse decomposition, image alignment, manifold constraint, non-convex optimization.

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“…Differently, in our method data is embedded into a manifold not known a priori but learned from the very same data. Now we formalize the manifold by introducing a neighbor-preserving embedding [20,5], which aims to find an estimation of the manifold. Such a formalization is similar to [5] which calculates the weights in the process of dimension reduction by LLE [18].…”

Section: Meadmmmentioning

confidence: 99%

“…As shown in LLE [21], a local point on a manifold can be represented by a small and compact set of K nearest neighbors to approximate ISOMAP. In [20], it has been shown that the Geodesic distance used in ISOMAP is another effective way to locate the neighbors for a linear embedding. We first follow the idea in [15] to estimate the manifold dimension by PCA.…”

mentioning

confidence: 99%

Manifold Constrained Low-Rank Decomposition

Chen

Zhang

Bue

et al. 2017

2017 IEEE International Conference on Computer Vision Workshops (ICCVW)

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Low-rank decomposition (LRD) is a state-of-the-art method for visual data reconstruction and modelling. However, it is a very challenging problem when the image data contains significant occlusion, noise, illumination variation, and misalignment from rotation or viewpoint changes. We leverage the specific structure of data in order to improve the performance of LRD when the data are not ideal. To this end, we propose a new framework that embeds manifold priors into LRD. To implement the framework, we design an alternating direction method of multipliers (ADMM) method which efficiently integrates the manifold constraints during the optimization process. The proposed approach is successfully used to calculate low-rank models from face images, hand-written digits and planar surface images. The results show a consistent increase of performance when compared to the state-of-the-art over a wide range of realistic image misalignments and corruptions.

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ISOLLE: Locally Linear Embedding with Geodesic Distance

Cited by 10 publications

References 10 publications

Measuring relative opinion from location-based social media: A case study of the 2016 U.S. presidential election

Measuring relative opinion from location-based social media: A case study of the 2016 U.S. presidential election

ManiDec: Manifold Constrained Low-Rank and Sparse Decomposition

Manifold Constrained Low-Rank Decomposition

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