Analysis and segmentation of higher dimensional data sets with fuzzy operators for representation and visualization

1994 ◽  
Author(s):  
Wolfgang F. Kraske
Keyword(s):  
Data Sets ◽  
Fuzzy Operators ◽  
Higher Dimensional

scholarly journals Functional Imaging with Higher-Dimensional Electrical Data Sets

2018 ◽  
Vol 26 (6) ◽  
pp. 18-27 ◽  
Author(s):  
P. De Wolf ◽  
Z. Huang ◽  
B. Pittenger ◽  
A. Dujardin ◽  
M. Febvre ◽  
...  
Keyword(s):  
Functional Imaging ◽  
Data Sets ◽  
Higher Dimensional ◽  
Image Position ◽  
Electrical Data

Abstract

Directionally Independent Failure Prediction of End-Milling Tools by Tracking Increasing Chaotic Noise at the Machining Frequencies Due to Wear

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Christopher A. Suprock ◽  
John T. Roth
Keyword(s):  
Discrete Cosine Transform ◽  
End Milling ◽  
Dimensional Space ◽  
Data Sets ◽  
Cosine Transform ◽  
Modal Reduction ◽  
Milling Operations ◽  
Higher Dimensional ◽  
System Energy ◽  
Fourier Type

Accurate on-line forecasting of a tool’s condition during end-milling operations is advantageous to the functionality and reliability of automated industrial processes. The ability to disengage the tool prior to catastrophic failure reduces manufacturing costs, excessive machine deterioration, and personnel hazards. Rapid computational feedback describing the system’s state is critical for realizing a practical failure forecasting model. To this end, spectral analysis by fast Fourier type algorithms allows a rapid computational response. The research described herein explores the development of nontraditional real fast Fourier transform (discrete cosine transform) based algorithms performed in unique higher-dimensional states of observed data sets. Moreover, the developed Fourier algorithm quantifies chaotic noise rather than relying on the more traditional observation of system energy. By increasing the vector dimensionality of the discrete cosine transform, the respective linear transform basis more effectively cross correlates the transform data into fewer (more significant) transform coefficients. Thus, a single vector in orthogonally higher-dimensional space is observed instead of multiple orthogonal vectors in single-dimensional space. More specifically, a novel modal reduction technique is utilized to track trends measured from triaxial force dynamometer signals. This transformation effectively achieves both modal reduction and directional independence by observing the chaotic noise instead of system energy. Algorithm output trends from six end-milling life tests are tracked from both linear and pocketing maneuvers in order to demonstrate the technique’s capabilities. In all six tests, the algorithm predicts impending tool failure with sufficient time for tool removal.

Families of Triangular Norm-Based Kernel Functions and Their Application to Kernel k-Means

2017 ◽  
Vol 21 (3) ◽  
pp. 534-542
Author(s):  
Kazushi Okamoto ◽  
Keyword(s):  
Feature Space ◽  
Kernel Functions ◽  
Rand Index ◽  
Adjusted Rand Index ◽  
Data Sets ◽  
Linear Kernel ◽  
Triangular Norm ◽  
Higher Dimensional ◽  
Rbf Kernel ◽  
Map Data

This study proposes the concept of families of triangular norm (t-norm)-based kernel functions, and discusses their positive-definite property and the conditions for applicable t-norms. A clustering experiment with kernel k-means is performed in order to analyze the characteristics of the proposed concept, as well as the effects of the t-norm and parameter selections. It is evaluated that the clusters obtained in terms of the adjusted rand index and the experimental results suggested the following : (1) the adjusted rand index values obtained by the proposed method were almost the same or higher than those produced using the linear kernel for all of the data sets; (2) the proposed method slightly improved the adjusted rand index values for some data sets compared with the radial basis function (RBF) kernel; (3) the proposed method tended to map data to a higher dimensional feature space than the linear kernel but the dimension was lower than that using the RBF kernel.

scholarly journals Robustifying the multivariate chain-ladder method: A comparison of two methods

2016 ◽  
Vol 5 (1) ◽  
pp. 70-77
Author(s):  
Martine Van Wouwe ◽  
Nattakorn Phewchean
Keyword(s):  
Life Insurance ◽  
Higher Dimensions ◽  
Data Sets ◽  
Multiple Constraints ◽  
Insurance Company ◽  
Life Insurance Company ◽  
Robust Solutions ◽  
Higher Dimensional ◽  
Chain Ladder Method ◽  
Chain Ladder

The expected result of a non-life insurance company is usually determined for its activity in different business lines as a whole. This implies that the claims reserving problem for a portfolio of several (perhaps correlated) subportfolios is to be solved. A popular technique for studying such a portfolio is the chain-ladder method. However, it is well known that the chain-ladder method is very sensitive to outlying data. For the bivariate situation, we have already developed robust solutions for the chain-ladder method by introducing two techniques for detecting and correcting outliers. In this article we focus on higher dimensions. Being subjected to multiple constraints (no graphical plots available), the goal of our research is to find solutions to detect and smooth the influence of outlying data on the outstanding claims reserve in higher dimensional data sets. The methodologies are illustrated and computed for real examples from the insurance practice.

scholarly journals Cortical Spatiotemporal Dimensionality Reduction for Visual Grouping

2015 ◽  
Vol 27 (6) ◽  
pp. 1252-1293 ◽  
Author(s):  
Giacomo Cocci ◽  
Davide Barbieri ◽  
Giovanna Citti ◽  
Alessandro Sarti
Keyword(s):  
Spectral Clustering ◽  
Geometric Model ◽  
Visual Stimuli ◽  
Main Idea ◽  
Cognitive Tasks ◽  
Data Sets ◽  
Cell Level ◽  
Geometric Information ◽  
Visual Grouping ◽  
Higher Dimensional

The visual systems of many mammals, including humans, are able to integrate the geometric information of visual stimuli and perform cognitive tasks at the first stages of the cortical processing. This is thought to be the result of a combination of mechanisms, which include feature extraction at the single cell level and geometric processing by means of cell connectivity. We present a geometric model of such connectivities in the space of detected features associated with spatiotemporal visual stimuli and show how they can be used to obtain low-level object segmentation. The main idea is to define a spectral clustering procedure with anisotropic affinities over data sets consisting of embeddings of the visual stimuli into higher-dimensional spaces. Neural plausibility of the proposed arguments will be discussed.

scholarly journals Systematic exploration of unsupervised methods for mapping behavior

2016 ◽  
Author(s):  
Jeremy G. Todd ◽  
Jamey S. Kain ◽  
Benjamin L. de Bivort
Keyword(s):  
Gaussian Mixture ◽  
Data Sets ◽  
Clustering Methods ◽  
Cluster Assignment ◽  
Data Set ◽  
Behavioral Transitions ◽  
Assignment Algorithm ◽  
Higher Dimensional ◽  
Systematic Exploration ◽  
Components Analysis

AbstractTo fully understand the mechanisms giving rise to behavior, we need to be able to precisely measure it. When coupled with large behavioral data sets, unsupervised clustering methods offer the potential of unbiased mapping of behavioral spaces. However, unsupervised techniques to map behavioral spaces are in their infancy, and there have been few systematic considerations of all the methodological options. We compared the performance of seven distinct mapping methods in clustering a data set consisting of the x-and y-positions of the six legs of individual flies. Legs were automatically tracked by small pieces of fluorescent dye, while the fly was tethered and walking on an air-suspended ball. We find that there is considerable variation in the performance of these mapping methods, and that better performance is attained when clustering is done in higher dimensional spaces (which are otherwise less preferable because they are hard to visualize). High dimensionality means that some algorithms, including the non-parametric watershed cluster assignment algorithm, cannot be used. We developed an alternative watershed algorithm which can be used in high-dimensional spaces when the probability density estimate can be computed directly. With these tools in hand, we examined the behavioral space of fly leg postural dynamics and locomotion. We find a striking division of behavior into modes involving the fore legs and modes involving the hind legs, with few direct transitions between them. By computing behavioral clusters using the data from all flies simultaneously, we show that this division appears to be common to all flies. We also identify individual-to-individual differences in behavior and behavioral transitions. Lastly, we suggest a computational pipeline that can achieve satisfactory levels of performance without the taxing computational demands of a systematic combinatorial approach.AbbreviationsGMM: Gaussian mixture model; PCA: principal components analysis; SW: sparse watershed; t-SNE: t-distributed stochastic neighbor embedding

scholarly journals Quaternionic Assessment of EEG Traces on Nervous Multidimensional Hyperspheres

2020 ◽  
Author(s):  
Arturo Tozzi ◽  
James F. Peters ◽  
Norbert Jausovec ◽  
Irina Legchenkova ◽  
Edward Bormashenko
Keyword(s):  
Nervous Activity ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Data Sets ◽  
Operational Procedure ◽  
Higher Dimensional ◽  
Spatial Dimensions ◽  
The Brain ◽  
Real Experimental Data ◽  
Operational Assessment

The nervous activity of the brain takes place in higher-dimensional functional spaces. Indeed, recent claims advocate that the brain might be equipped with a phase space displaying four spatial dimensions plus time, instead of the classical three plus time. This suggests the possibility to investigate global visualization methods for exploiting four-dimensional maps of real experimental data sets. Here we asked whether, starting from the conventional neuro-data available in three dimensions plus time, it is feasible to find an operational procedure to describe the corresponding four-dimensional trajectories. In particular, we used quaternion orthographic projections for the assessment of electroencephalographic traces (EEG) from scalp locations. This approach makes it possible to map three-dimensional EEG traces to the surface of a four-dimensional hypersphere, which has an important advantage, since quaternionic networks make it feasible to enlighten temporally far apart nervous trajectories equipped with the same features, such as the same frequency or amplitude of electric oscillations. This leads to an incisive operational assessment of symmetries, dualities and matching descriptions hidden in the very structure of complex neuro-data signals.

scholarly journals SWeeP: representing large biological sequences datasets in compact vectors

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Camilla Reginatto De Pierri ◽  
Ricardo Voyceik ◽  
Letícia Graziela Costa Santos de Mattos ◽  
Mariane Gonçalves Kulik ◽  
Josué Oliveira Camargo ◽  
...  
Keyword(s):  
Phylogenetic Trees ◽  
Computational Cost ◽  
Large Data ◽  
Data Sets ◽  
Biological Sequences ◽  
Biological Sequence ◽  
Sequence Comparisons ◽  
Alignment Free ◽  
Higher Dimensional ◽  
Sequence Representation

AbstractVectoral and alignment-free approaches to biological sequence representation have been explored in bioinformatics to efficiently handle big data. Even so, most current methods involve sequence comparisons via alignment-based heuristics and fail when applied to the analysis of large data sets. Here, we present “Spaced Words Projection (SWeeP)”, a method for representing biological sequences using relatively small vectors while preserving intersequence comparability. SWeeP uses spaced-words by scanning the sequences and generating indices to create a higher-dimensional vector that is later projected onto a smaller randomly oriented orthonormal base. We constructed phylogenetic trees for all organisms with mitochondrial and bacterial protein data in the NCBI database. SWeeP quickly built complete and accurate trees for these organisms with low computational cost. We compared SWeeP to other alignment-free methods and Sweep was 10 to 100 times quicker than the other techniques. A tool to build SWeeP vectors is available at https://sourceforge.net/projects/spacedwordsprojection/.

LARGE DYNAMICAL SYMMETRY OF QUASI-SPHERICAL GRAVITATIONAL COLLAPSE WITH RADIAL AND TANGENTIAL PRESSURES AND ANISOTROPY AND INHOMOGENEITY OF SPACE–TIME

2006 ◽  
Vol 15 (09) ◽  
pp. 1531-1544 ◽  
Author(s):  
SUBENOY CHAKRABORTY ◽  
SANJUKTA CHAKRABORTY
Keyword(s):  
Initial Data ◽  
Gravitational Collapse ◽  
Naked Singularity ◽  
Dynamical Symmetry ◽  
Physical Parameters ◽  
Data Sets ◽  
Final State ◽  
Data Set ◽  
Higher Dimensional

A detailed study of higher-dimensional quasi-spherical gravitational collapse with radial and tangential stresses has been done and the role of initial data, anisotropy and inhomogeneity has been investigated in determining the end state of collapse. By linear scaling the initial data set and the area radius, it is found that the dynamics of quasi-spherical collapse remains invariant. In other words, the linear transformation identifies an equivalence class of data sets for which physical parameters like density, pressures (radial and tangential), shear remain invariant and the final state of collapse is identical (black hole or naked singularity). Finally, the role of anisotropy and inhomogeneity has been studied by proving some propositions.

Sign in / Sign up

Export Citation Format

Share Document