Selection of the optimal parameter value for the Isomap algorithm

Samko, Oksana; Marshall, A. David; Rosin, Paul L.

doi:10.1016/j.patrec.2005.11.017

Cited by 118 publications

(68 citation statements)

References 12 publications

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“…These are the presence of minimal shortcuts and a smooth embedding curve. Typically, dimensionality reduction using Isomap is sensitive to κ, the number of nearest neigbhors, and there are several methods in the literature that aim to locate the optimal choice [59]. While we do not claim to have addressed the problem of sensitivity to κ, we do provide a supervision step by successively increasing the temporal weighting parameter λ to obtain an acceptable low-dimensional embedding for a for a given value of κ.…”

Section: Discussionmentioning

confidence: 99%

Analysis and classification of collective behavior using generative modeling and nonlinear manifold learning

Butail

Bollt

Porfiri

2013

Journal of Theoretical Biology

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In this paper, we build a framework for the analysis and classification of collective behavior using methods from generative modeling and nonlinear manifold learning. We represent an animal group with a set of finite-sized particles and vary known features of the group structure and motion via a class of generative models to position each particle on a two-dimensional plane. Particle positions are then mapped onto training images that are processed to emphasize the features of interest and match attainable far-field videos of real animal groups. The training images serve as templates of recognizable patterns of collective behavior and are compactly represented in a low-dimensional space called embedding manifold. Two mappings from the manifold are derived: the manifold-to-image mapping serves to reconstruct new and unseen images of the group and the manifold-to-feature mapping allows frame-by-frame classification of raw video. We validate the combined framework on datasets of growing level of complexity. Specifically, we classify artificial images from the generative model, interacting self-propelled particle model, and raw overhead videos of schooling fish obtained from the literature.

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Section: Discussionmentioning

confidence: 99%

Analysis and classification of collective behavior using generative modeling and nonlinear manifold learning

Butail

Bollt

Porfiri

2013

Journal of Theoretical Biology

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“…MDS(MultiDimensional Scaling), PCA(Principal Component Analysis) [9], ISOMAP(Isometric Feature Mapping), LLE, Hessian LLE, Laplacian Eigenmap, Diffusion maps are some of the manifold learning techniques. [2,8].…”

Section: Manifold Learning Techniquesmentioning

confidence: 99%

Similarity Consideration for Visualization and Manifold Geometry Preservation

Mishra¹,

Pradhan²

2011

IJCA

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Manifold learning techniques are used to preserve the original geometry of dataset after reduction by preserving the distance among data points. MDS (Multidimensional Scaling), ISOMAP (Isometric Feature Mapping), LLE (Locally Linear Embedding) are some of the geometrical structure preserving dimension reduction methods. In this paper, we have compared MDS and ISOMAP and considered similarity as an approach to find the reduced representation of original data using ISOMAP.

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“…To compute the geodesic distances, we need decide on the number of nearest neighbors, k. If k is too large, it would cause the short circuit edges that shortcut the true geometry of a manifold reecting the non-linear structure of data; if k is too small, it will causes the manifold to fragment into a large number of disconnected clusters. Following Samko et al (2006), we choose k by maximizing |ρ(D, Φ k,p )|, where D and Φ k,p are the matrices of the Euclidean distances between a pair of points in the original space and the feature space, respectively, and ρ(·, ·) is the linear correlation coecient. Note that Φ k,p depends on p, the dimension of the space of the embeddings.…”

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confidence: 99%

“…Note that Φ k,p depends on p, the dimension of the space of the embeddings. Samko et al (2006) argued that the data set has its intrinsic dimension, and subsequently, they showed empirically that p does not change even if k changes. Hence, we decide to rst estimate p for an arbitrary (but reasonable) choice of k and then choose the optimal k with this p.…”

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confidence: 99%

A multistage, semi-automated procedure for analyzing the morphology of nanoparticles

et al. 2012

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This paper presents a multi-stage, semi-automated procedure that can expedite the morphology analysis of nanoparticles. Material scientists have long conjectured that morphology of nanoparticles has a profound impact on the properties of the hosting material but a bottleneck is the lack of a reliable and automated morphology analysis of the particles based on their image measurements. This paper attempts to ll in this critical void. One particular challenge in nano morphology analysis is how to analyze the overlapped nanoparticles, a problem not well addressed by the existing methods but eectively tackled by our proposed method. Our proposed method entails multiple stages of operations, executed sequentially, and is considered semi-automated due to the inclusion of a semi-supervised clustering step. Our method was applied to several images of gold nanoparticles, producing the needed statistical characterization of their morphology.

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Selection of the optimal parameter value for the Isomap algorithm

Cited by 118 publications

References 12 publications

Analysis and classification of collective behavior using generative modeling and nonlinear manifold learning

Analysis and classification of collective behavior using generative modeling and nonlinear manifold learning

Similarity Consideration for Visualization and Manifold Geometry Preservation

A multistage, semi-automated procedure for analyzing the morphology of nanoparticles

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