scholarly journals Laplacian Eigenmaps Dimensionality Reduction Based on Clustering-Adjusted Similarity

Algorithms ◽  
2019 ◽  
Vol 12 (10) ◽  
pp. 210
Author(s):  
Honghu Zhou ◽  
Jun Wang
Keyword(s):  
Dimensionality Reduction ◽  
Euclidean Distance ◽  
Empirical Studies ◽  
Global Structure ◽  
Decision Boundary ◽  
Laplacian Eigenmaps ◽  
Manifold Structure ◽  
Input Parameters

Euclidean distance between instances is widely used to capture the manifold structure of data and for graph-based dimensionality reduction. However, in some circumstances, the basic Euclidean distance cannot accurately capture the similarity between instances; some instances from different classes but close to the decision boundary may be close to each other, which may mislead the graph-based dimensionality reduction and compromise the performance. To mitigate this issue, in this paper, we proposed an approach called Laplacian Eigenmaps based on Clustering-Adjusted Similarity (LE-CAS). LE-CAS first performs clustering on all instances to explore the global structure and discrimination of instances, and quantifies the similarity between cluster centers. Then, it adjusts the similarity between pairwise instances by multiplying the similarity between centers of clusters, which these two instances respectively belong to. In this way, if two instances are from different clusters, the similarity between them is reduced; otherwise, it is unchanged. Finally, LE-CAS performs graph-based dimensionality reduction (via Laplacian Eigenmaps) based on the adjusted similarity. We conducted comprehensive empirical studies on UCI datasets and show that LE-CAS not only has a better performance than other relevant comparing methods, but also is more robust to input parameters.

Improved weighted local linear embedding algorithm based on Laplacian eigenmaps

2021 ◽  
Vol 24 (4) ◽  
pp. 323-330
Author(s):  
Qing Wu ◽  
Rongrong Jing ◽  
En Wang
Keyword(s):  
Theoretical Analysis ◽  
Numerical Experiments ◽  
Euclidean Distance ◽  
Geodesic Distance ◽  
Recognition Rate ◽  
Laplacian Eigenmaps ◽  
Manifold Structure ◽  
Local Linear Embedding ◽  
Local Linear ◽  
Linear Embedding

To solve the shortcomings of local linear embedding (LLE), such as sensitive to noise and poor generalization ability for new samples, an improved weighted local linear embedding algorithm based on Laplacian eigenmaps (IWLLE-LE) is proposed in this paper. In the proposed algorithm, Laplacian eigenmaps are used to reconstruct the objective function of dimensionality reduction. The weights of it are introduced by combining the geodesic distance with Euclidean distance, which can effectively represent the manifold structure of nonlinear data. Compared the existing LLE algorithm, the proposed one better maintains the original manifold structure of the data. The merit of the proposal is enhanced by the theoretical analysis and numerical experiments, where the classification recognition rate is 2%–8% higher than LLE.

scholarly journals Unsupervised Metric Learning Using Low Dimensional Embedding

2018 ◽  
Author(s):  
Parag Jain
Keyword(s):  
Manifold Learning ◽  
Euclidean Distance ◽  
Metric Learning ◽  
Special Property ◽  
Dimensional Manifold ◽  
Laplacian Eigenmaps ◽  
Learning Techniques ◽  
Out Of Sample ◽  
Low Dimensional ◽  
Project Data

Unsupervised metric learning has been generally studied as a byproduct of dimensionality reduction or manifold learning techniques. Manifold learning techniques like Diusion maps, Laplacian eigenmaps has a special property that embedded space is Euclidean. Although laplacian eigenmaps can provide us with some (dis)similarity information it does not provide with a metric which can further be used on out-of-sample data. On other hand supervised metric learning technique like ITML which can learn a metric needs labeled data for learning. In this work propose methods for incremental unsupervised metric learning. In rst approach Laplacian eigenmaps is used along with Information Theoretic Metric Learning(ITML) to form an unsupervised metric learning method. We rst project data into a low dimensional manifold using Laplacian eigenmaps, in embedded space we use euclidean distance to get an idea of similarity between points. If euclidean distance between points in embedded space is below a threshold t1 value we consider them as similar points and if it is greater than a certain threshold t2 we consider them as dissimilar points. Using this we collect a batch of similar and dissimilar points which are then used as a constraints for ITML algorithm and learn a metric. To prove this concept we have tested our approach on various UCI machine learning datasets. In second approach we propose Incremental Diusion Maps by updating SVD in a batch-wise manner.

scholarly journals Electromyography Classification during Reach-to-Grasp Motion using Manifold Learning

2020 ◽  
Author(s):  
Elnaz Lashgari ◽  
Uri Maoz
Keyword(s):  
Dimensionality Reduction ◽  
Cost Effective ◽  
Human Hand ◽  
Reach To Grasp ◽  
K Nearest Neighbors ◽  
Laplacian Eigenmaps ◽  
Non Invasive ◽  
Reduction Methods ◽  
Machine Interface ◽  
Low Dimensional

AbstractElectromyography (EMG) is a simple, non-invasive, and cost-effective technology for sensing muscle activity. However, EMG is also noisy, complex, and high-dimensional. It has nevertheless been widely used in a host of human-machine-interface applications (electrical wheelchairs, virtual computer mice, prosthesis, robotic fingers, etc.) and in particular to measure reaching and grasping motions of the human hand. Here, we developd a more automated pipeline to predict object weight in a reach-and-grasp task from an open dataset relying only on EMG data. In that we shifted the focus from manual feature-engineering to automated feature-extraction by using raw (filtered) EMG signals and thus letting the algorithms select the features. We further compared intrinsic EMG features, derived from several dimensionality-reduction methods, and then ran some classification algorithms on these low-dimensional representations. We found that the Laplacian Eigenmap algorithm generally outperformed other dimensionality-reduction methods. What is more, optimal classification accuracy was achieved using a combination of Laplacian Eigenmaps (simple-minded) and k-Nearest Neighbors (88% for 3-way classification). Our results, using EMG alone, are comparable to others in the literature that used EMG and EEG together. They also demonstrate the usefulness of dimensionality reduction when classifying movement based on EMG signals and more generally the usefulness of EMG for movement classification.

Semi-supervised rough fuzzy Laplacian Eigenmaps for dimensionality reduction

2018 ◽  
Vol 10 (2) ◽  
pp. 397-411 ◽  
Author(s):  
Minghua Ma ◽  
Tingquan Deng ◽  
Ning Wang ◽  
Yanmei Chen
Keyword(s):  
Dimensionality Reduction ◽  
Laplacian Eigenmaps

Optimization of Labyrinth Seal Performance Combining Experimental, Numerical and Data Mining Methods

2012 ◽  
Author(s):  
Erik Braun ◽  
Klaus Dullenkopf ◽  
Hans-Jörg Bauer
Keyword(s):  
Data Mining ◽  
Data Base ◽  
Flow Direction ◽  
Empirical Studies ◽  
Geometry Optimization ◽  
Labyrinth Seal ◽  
Labyrinth Seals ◽  
Research Activities ◽  
Input Parameters ◽  
Mining Methods

Numerous experimental and numerical studies were performed in the past by various authors to reduce the leakage of labyrinth seals and thus increase the performance of turbo machines. Based on the experience of more than 20 years of research activities in this area at the ITS, the authors aim to improve the prediction quality for labyrinth seal performance by combining experimental, numerical and data mining methods. Special emphasis in this work lies on more complex and also worn labyrinth geometries and thus on a more universal optimization tool for labyrinth seals incorporating more realistic engine running conditions as well as wear mechanisms. Better understanding of labyrinth seal behavior based on the new correlations and models will thus lead to optimized geometries and improved designs. The paper contains the results of experiments to determine the discharge coefficients of different straight-through labyrinth seals with three and five fins and two different fin geometries over a large range of pressure ratios as well as results from a stepped labyrinth seal with six fins in convergent and divergent flow direction. The collected data extends an existing data base of labyrinth seal performance already presented in the paper of Pychynski et al. [1]. This data base is used to create models to calculate labyrinth seal performance depending on up to 25 input parameters. The resulting models will be used as a basis for a universal optimization tool for labyrinth seals. In the paper the new and versatile test rig for various kinds of labyrinth and gap seals is presented and an analysis of measurement accuracy will be given. The results of a first set of experiments performed with new (i.e. unworn) geometries are compared to experimental data of similar labyrinth geometries from previous investigations, showing an excellent agreement. The results are then interpreted using Data Mining Methods to identify correlations between different input parameters and the labyrinth seal discharge coefficient. The paper will show that a data based approach can yield similar quality relations as empirical studies but is much less time consuming and more versatile. Several models with different sets of input parameters will be presented and compared as to their applicability in automated geometry optimization using a newly developed optimization tool.

scholarly journals L1-Norm Distance Discriminant Analysis with Multiple Adaptive Graphs and Sample Reconstruction

2021 ◽  
Author(s):  
Guowan Shao ◽  
Chunjiang Peng ◽  
Wenchu Ou ◽  
Kai Duan
Keyword(s):  
Discriminant Analysis ◽  
Classification Performance ◽  
Global Structure ◽  
L1 Norm ◽  
Linear Discriminant ◽  
Manifold Structure ◽  
Discriminative Subspace ◽  
Maximum Margin Criterion ◽  
Distance Discriminant Analysis ◽  
Sample Reconstruction

Linear discriminant analysis (LDA) is sensitive to noise and its performance may decline greatly. Recursive discriminative subspace learning method with an L1-norm distance constraint (RDSL) formulates LDA with the maximum margin criterion and becomes robust to noise by applying L1-norm and slack variables. However, the method only considers inter-class separation and intra-class compactness and ignores the intra-class manifold structure and the global structure of data. In this paper, we present L1-norm distance discriminant analysis with multiple adaptive graphs and sample reconstruction (L1-DDA) to deal with the problem. We use multiple adaptive graphs to preserve intra-class manifold structure and simultaneously apply the sample reconstruction technique to preserve the global structure of data. Moreover, we use an alternating iterative technique to obtain projection vectors. Experimental results on three real databases demonstrate that our method obtains better classification performance than RDSL.

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