Fast ISOMAP Based on Minimum Set Coverage

Lei, Yingke; Yu, Xu; Zhang, Shanwen; Ding, Zhiguo

doi:10.1007/978-3-642-14932-0_22

Cited by 10 publications

(7 citation statements)

References 8 publications

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“…Popular choices include the linear Principal Component Analysis [Bishop 2007] algorithm, and the non-linear Isometric Manifold Learning (Isomap) [Tenenbaum et al 2000], Landmark Isomap [De Silva and Tenenbaum 2003], Locally Linear Embedding [Roweis and Saul 2000], and Gaussian Process Latent Variable Model [Lawrence 2003] techniques. Approximation algorithms such as Fast Isomap [Lei et al 2010] have also been proposed recently, in an attempt to minimize the complexity of learning the structure of a highdimensional dataset. Nonlinear manifold learning algorithms capture a wider range of dependencies and are therefore more suited to the motion sequences under analysis.…”

Section: Model-free Algorithmmentioning

confidence: 99%

Latent space segmentation for mobile gait analysis

Valtazanos

Arvind

Ramamoorthy

2013

ACM Trans. Embed. Comput. Syst.

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An unsupervised learning algorithm is presented for segmentation and evaluation of motion data from the on-body Orient wireless motion capture system for mobile gait analysis. The algorithm is model-free and operates on the latent space of the motion, by first aggregating all the sensor data into a single vector, and then modeling them on a low-dimensional manifold to perform segmentation. The proposed approach is contrasted to a basic, model-based algorithm, which operates directly on the joint angles computed by the Orient sensor devices. The latent space algorithm is shown to be capable of retrieving qualitative features of the motion even in the face of noisy or incomplete sensor readings.

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Section: Model-free Algorithmmentioning

confidence: 99%

Latent space segmentation for mobile gait analysis

Valtazanos

Arvind

Ramamoorthy

2013

ACM Trans. Embed. Comput. Syst.

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“…1 ; M kþ1 2 ; μ using Equations ( 21), (22), and (23) 6: Update ρ kþ1 using Equation (24) 7: The computational complexity of the updating equations in Algorithm 1 are presented in Algorithm 1.…”

Section: Algorithm 2 Low-rank Projectionmentioning

confidence: 99%

Low‐rank isomap algorithm

Mehrbani

Kahaei

2022

IET Signal Processing

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Isomap is a well‐known nonlinear dimensionality reduction method that highly suffers from computational complexity. Its computational complexity mainly arises from two stages; a) embedding a full graph on the data in the ambient space, and b) a complete eigenvalue decomposition. Although the reduction of the computational complexity of the graphing stage has been investigated by graph processing methods, the eigenvalue decomposition stage remains a bottleneck in the problem. In this paper, we propose the Low‐Rank Isomap (LRI) algorithm by introducing a projection operator on the embedded graph from the ambient space to a low‐rank latent space to facilitate applying the partial eigenvalue decomposition. This approach leads to reducing the complexity of Isomap to a linear order while preserving the structural information during the dimensionality reduction process as long as the number of observations remains extensively larger than the dimensionality of the ambient space. The superiority of the LRI algorithm compared to some state‐of‐art algorithms is experimentally verified on facial image clustering in terms of speed and accuracy.

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“…Some authors resorted to clustering methods, such as self-organizing map [12] and fuzzy c-means [13], or to weighting schemes defined on the distance between points and their neighbors [14]. An interesting approach based on integer optimization was developed in [15] and effectively applied for analysing protein interactions [16]. It relies on the approximate solution of a minimum set covering problem, which finds a minimum set of landmarks whose neighborhoods cover the entire set of points.…”

Section: Introductionmentioning

confidence: 99%

Landmark Selection for Isometric Feature Mapping Based on Mixed-Integer Optimization

Orsenigo

Vercellis

2013

Modeling Decisions for Artificial Intelligence

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Abstract. Isometric feature mapping (Isomap) demonstrated noteworthy performance for nonlinear dimensionality reduction in a wide range of application domains. To improve the scalability of the algorithm a fast variant, called Landmark Isomap (L-Isomap), has been proposed in which time-consuming computations are performed on a subset of points referred to as landmarks. In this paper we present a novel method for landmark selection to be framed within the L-Isomap procedure. It is based on a mixed-integer problem aimed at finding a set of landmarks which are representative of dense regions of points in the input space which mostly contain samples of the same class. The optimization model is solved by a heuristic algorithm based on Lagrangian relaxation with subgradient method. Computational experiments performed on benchmark data sets highlighted the effectiveness of the proposed landmark selection algorithm which, combined with L-Isomap, provided promising results in terms of classification accuracy and computational effort.

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Fast ISOMAP Based on Minimum Set Coverage

Cited by 10 publications

References 8 publications

Latent space segmentation for mobile gait analysis

Latent space segmentation for mobile gait analysis

Low‐rank isomap algorithm

Landmark Selection for Isometric Feature Mapping Based on Mixed-Integer Optimization

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