On the Initialisation of Sammon’s Nonlinear Mapping

Lerner, Boaz; Guterman, Hugo; Aladjem, Mayer; Dinstein, I.

doi:10.1007/s100440050006

Cited by 14 publications

(4 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Some authors (Mao and Jain 1995;Lerner et al 2000) suggest using the scores of the first two components of an ordination method, such as the principal component analysis. In this study, however, Sammon's mapping did not arrive at a higher squared correlation coefficient of the distance matrices of 0.58, which was achieved by using the scores of the first two components.…”

Section: Pearson Correlation Of Distance Matrices Of Sammon's Mappingmentioning

confidence: 99%

Non-linear visualization and analysis of large water quality data sets: a model-free basis for efficient monitoring and risk assessment

Lischeid

2008

Stoch Environ Res Risk Assess

View full text Add to dashboard Cite

Environmental monitoring programs provide large multivariate data sets that usually cover considerable spatial and temporal variabilities. The apparent complexity of these data sets requires sophisticated tools for their processing. Usually, fixed schemes are followed, including the application of numerical models, which are increasingly implemented in decision support systems. However, these schemes are too rigid with respect to detecting unexpected features, like the onset of subtle trends, nonlinear relationships or patterns that are restricted to limited sub-samples of the total data set. In this study, an alternative approach is followed. It is based on an efficient nonlinear visualization of the data. Visualization is the most powerful interface between computer and human brain.

show abstract

Section: Pearson Correlation Of Distance Matrices Of Sammon's Mappingmentioning

confidence: 99%

Non-linear visualization and analysis of large water quality data sets: a model-free basis for efficient monitoring and risk assessment

Lischeid

2008

Stoch Environ Res Risk Assess

View full text Add to dashboard Cite

show abstract

“…The 3D plots could be moved around and rotated to give a better sense of the landscape of the data points, since MATLAB (R2016b, MATLAB, Natick, MA, USA) was used for all the work done in this exercise. The Sammon's nonlinear mapping [15], which is a popular nonmetric MDS, was employed for the multi-dimensional scaling as a way to preserve, as much as possible, the inherent structure of the data when the patterns are projected from a higher-dimensional space to a lower-dimensional space by maintaining the distances between the patterns under projection [28]. The simplest technique for dimensionality reduction is a straightforward linear projection, such as the principal components of the data, which maximizes the variance present in the transformed dataset, albeit without the preservation of the geometrical structure of the data that is not detectable by the human senses.…”

Section: Normalization Sammon's Nonlinear Mapping and Classical Mdsmentioning

confidence: 99%

Optimal Clustering and Cluster Identity in Understanding High-Dimensional Data Spaces with Tightly Distributed Points

Chikumbo¹,

Granville²

2019

MAKE

View full text Add to dashboard Cite

The sensitivity of the elbow rule in determining an optimal number of clusters in high-dimensional spaces that are characterized by tightly distributed data points is demonstrated. The high-dimensional data samples are not artificially generated, but they are taken from a real world evolutionary many-objective optimization. They comprise of Pareto fronts from the last 10 generations of an evolutionary optimization computation with 14 objective functions. The choice for analyzing Pareto fronts is strategic, as it is squarely intended to benefit the user who only needs one solution to implement from the Pareto set, and therefore a systematic means of reducing the cardinality of solutions is imperative. As such, clustering the data and identifying the cluster from which to pick the desired solution is covered in this manuscript, highlighting the implementation of the elbow rule and the use of hyper-radial distances for cluster identity. The Calinski-Harabasz statistic was favored for determining the criteria used in the elbow rule because of its robustness. The statistic takes into account the variance within clusters and also the variance between the clusters. This exercise also opened an opportunity to revisit the justification of using the highest Calinski-Harabasz criterion for determining the optimal number of clusters for multivariate data. The elbow rule predicted the maximum end of the optimal number of clusters, and the highest Calinski-Harabasz criterion method favored the number of clusters at the lower end. Both results are used in a unique way for understanding high-dimensional data, despite being inconclusive regarding which of the two methods determine the true optimal number of clusters.

show abstract

“…It is difficult for us to use these methods to discover nonlinear structure in the fault data, resulting, from the point of view of fault classification, in low accuracy fault identification or misjudgment. Among traditional nonlinear mapping methods, Sammon mapping [ 6 ] and the neuroscale method [ 7 ] are used. The former uses an iterative process that results in intensive computation, while the latter uses a radial basis function network and has similar shortcomings as neural networks.…”

Section: Introductionmentioning

confidence: 99%

Bearing Fault Diagnosis Based on Statistical Locally Linear Embedding

Wang

Zheng

Zhao

et al. 2015

Sensors

128

View full text Add to dashboard Cite

Fault diagnosis is essentially a kind of pattern recognition. The measured signal samples usually distribute on nonlinear low-dimensional manifolds embedded in the high-dimensional signal space, so how to implement feature extraction, dimensionality reduction and improve recognition performance is a crucial task. In this paper a novel machinery fault diagnosis approach based on a statistical locally linear embedding (S-LLE) algorithm which is an extension of LLE by exploiting the fault class label information is proposed. The fault diagnosis approach first extracts the intrinsic manifold features from the high-dimensional feature vectors which are obtained from vibration signals that feature extraction by time-domain, frequency-domain and empirical mode decomposition (EMD), and then translates the complex mode space into a salient low-dimensional feature space by the manifold learning algorithm S-LLE, which outperforms other feature reduction methods such as PCA, LDA and LLE. Finally in the feature reduction space pattern classification and fault diagnosis by classifier are carried out easily and rapidly. Rolling bearing fault signals are used to validate the proposed fault diagnosis approach. The results indicate that the proposed approach obviously improves the classification performance of fault pattern recognition and outperforms the other traditional approaches.

show abstract

On the Initialisation of Sammon’s Nonlinear Mapping

Cited by 14 publications

References 9 publications

Non-linear visualization and analysis of large water quality data sets: a model-free basis for efficient monitoring and risk assessment

Non-linear visualization and analysis of large water quality data sets: a model-free basis for efficient monitoring and risk assessment

Optimal Clustering and Cluster Identity in Understanding High-Dimensional Data Spaces with Tightly Distributed Points

Bearing Fault Diagnosis Based on Statistical Locally Linear Embedding

Contact Info

Product

Resources

About