scholarly journals Concise and Accessible Representations for Multidimensional Datasets: Introducing a Framework Based on thenD-EVM and Kohonen Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-21
Author(s):  
Ricardo Pérez-Aguila ◽  
Ricardo Ruiz-Rodríguez
Keyword(s):  
Dimensional Space ◽  
Second Step ◽  
Topological Properties ◽  
Color Intensity ◽  
Topological Information ◽  
Spatial Complexity ◽  
Multidimensional Datasets ◽  
Kohonen Networks ◽  
Orthogonal Polytopes ◽  
New Framework

A new framework intended for representing and segmenting multidimensional datasets resulting in low spatial complexity requirements and with appropriate access to their contained information is described. Two steps are going to be taken in account. The first step is to specify (n-1)D hypervoxelizations,n≥2, as Orthogonal Polytopes whosenth dimension corresponds to color intensity. Then, thenD representation is concisely expressed via the Extreme Vertices Model in then-Dimensional Space (nD-EVM). Some examples are presented, which, under our methodology, have storing requirements minor than those demanded by their original hypervoxelizations. In the second step, 1-Dimensional Kohonen Networks (1D-KNs) are applied in order to segment datasets taking in account their geometrical and topological properties providing a non-supervised way to compact even more the proposedn-Dimensional representations. The application of our framework shares compression ratios, for our set of study cases, in the range 5.6496 to 32.4311. Summarizing, the contribution combines the power of thenD-EVM and 1D-KNs by producing very concise datasets’ representations. We argue that the new representations also provide appropriate segmentations by introducing some error functions such that our 1D-KNs classifications are compared against classifications based only in color intensities. Along the work, main properties and algorithms behind thenD-EVM are introduced for the purpose of interrogating the final representations in such a way that it efficiently obtains useful geometrical and topological information.

Search Strategy for Rare Microstructure to Optimize Material Properties of Filled Rubber

2021 ◽  
Author(s):  
Takashi Kojima ◽  
Takashi Washio ◽  
Satoshi Hara ◽  
Masakata Koishi
Keyword(s):  
Gradient Descent ◽  
Search Strategy ◽  
Dimensional Space ◽  
Descent Method ◽  
Coarse Grained ◽  
Replica Exchange ◽  
Second Step ◽  
Gradient Descent Method ◽  
Filled Rubber ◽  
Wide Range

Abstract A shortcut to understand the microstructure-property relationship is sampling and analysis of microstructures that induce the desired material property. In the case of filled rubber, the simulation of complex filler morphology involves hundreds of filler particles. This requires a large amount of iterative sampling, because the number of parameters is when using coordinates of the n particles as the search objective. Furthermore, the morphology that induces the desired property, e.g. extremely high modulus, only occurs rarely. In this paper, we propose an effective three-step search method for the filler morphology. In the first step, the replica exchange Markov chain Monte Carlo (MCMC) was employed to discretely search among a wide range of morphologies. In this step, we reduced the filler morphology space in sampling by introducing distributed filler candidate points and spin function. In the second step, the gradient descent method was applied to search for the desired morphology locally in the high-dimensional space , starting from the morphologies obtained by the replica exchange MCMC. Lastly, the coarse-grained molecular dynamics (CGMD) simulations were performed to validate the morphologies actually show the desired properties, because the surrogate model of CGMD was employed in the first 2 steps for the efficient search. Using the proposed method, we demonstrate the search for morphologies that induce high elastic modulus.

scholarly journals A Mathematical Approach to Establishing Constitutive Models for Geomaterials

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Guang-hua Yang ◽  
Yu-xin Jie ◽  
Guang-xin Li
Keyword(s):  
Mathematical Theory ◽  
Dimensional Space ◽  
Constitutive Models ◽  
Point Of View ◽  
Stress Strain ◽  
Constitutive Theories ◽  
Special Cases ◽  
Strain Relationship ◽  
Strain Space ◽  
New Framework

The mathematical foundation of the traditional elastoplastic constitutive theory for geomaterials is presented from the mathematical point of view, that is, the expression of stress-strain relationship in principal stress/strain space being transformed to the expression in six-dimensional space. A new framework is then established according to the mathematical theory of vectors and tensors, which is applicable to establishing elastoplastic models both in strain space and in stress space. Traditional constitutive theories can be considered as its special cases. The framework also enables modification of traditional constitutive models.

scholarly journals Growing Self-Organizing Maps for Data Analysis

2011 ◽  
pp. 781-787
Author(s):  
Soledad Delgado ◽  
Consuelo Gonzalo ◽  
Estíbaliz Martínez ◽  
Águeda Arquero
Keyword(s):  
Dimensional Space ◽  
Simulated Data ◽  
Multidimensional Data ◽  
Self Organizing Maps ◽  
Research Areas ◽  
Multidimensional Datasets ◽  
Cell Structures ◽  
Growing Cell ◽  
Growing Cell Structures ◽  
Self Organizing

Currently, there exist many research areas that produce large multivariable datasets that are difficult to visualize in order to extract useful information. Kohonen selforganizing maps have been used successfully in the visualization and analysis of multidimensional data. In this work, a projection technique that compresses multidimensional datasets into two dimensional space using growing self-organizing maps is described. With this embedding scheme, traditional Kohonen visualization methods have been implemented using growing cell structures networks. New graphical map displays have been compared with Kohonen graphs using two groups of simulated data and one group of real multidimensional data selected from a satellite scene.

scholarly journals A New Framework for Video Data Retrieval using Hierarchical Clustering Technique

2019 ◽  
Vol 8 (6S3) ◽  
pp. 2052-2055 ◽  
Keyword(s):  
Visual Motion ◽  
Experimental Studies ◽  
Data Retrieval ◽  
Video Data ◽  
Second Step ◽  
Huge Amount ◽  
New Techniques ◽  
Amount Of Information ◽  
Frame Work ◽  
New Framework

The amount of information produced every year is rapidly growing due to many factor among all media, video is a particular media embedding visual, motion, audio and textual information. Given this huge amount of information we need general framework for video data mining to be applied to the raw videos (surveillance videos, news reading, Person reading books in library etc.).We introduce new techniques which are essential to process the video files. The first step of our frame work for mining raw video data in grouping input frames to a set of basic units which are relevant to the structure of the video. The second step is charactering the unit to cluster into similar groups, to detect interesting patterns. To do this we extract some features (object, colors etc.)From the unit. A histogram based color descriptors also introduced to reliably capture and represent the color properties of multiple images. The preliminary experimental studies indicate that the proposed framework is promising

scholarly journals Facial Expressions of Emotion Categories are Embedded within a Dimensional Space of Valence-arousal

2020 ◽  
Author(s):  
Meng Liu ◽  
Yaocong Duan ◽  
Robin A A Ince ◽  
Chaona Chen ◽  
Oliver G. B. Garrod ◽  
...  
Keyword(s):  
Facial Expressions ◽  
Dimensional Space ◽  
Human Perception ◽  
Data Driven ◽  
Facial Expressions Of Emotion ◽  
Complex Emotion ◽  
Valence And Arousal ◽  
Affective Information ◽  
Emotion Representation ◽  
New Framework

One of the longest standing debates in the emotion sciences is whether emotions are represented as discrete categories such as happy or sad or as continuous fundamental dimensions such as valence and arousal. Theories of communication make specific predictions about the facial expression signals that would represent emotions as either discrete or dimensional messages. Here, we address this debate by testing whether facial expressions of emotion categories are embedded in a dimensional space of affective signals, leading to multiplexed communication of affective information. Using a data-driven method based on human perception, we modelled the facial expressions representing the six classic emotion categories – happy, surprise, fear, disgust, anger and sad – and those representing the dimensions of valence and arousal. We then evaluated their embedding by mapping and validating the facial expressions categories onto the valence-arousal space. Results showed that facial expressions of these six classic emotion categories formed dissociable clusters within the valence-arousal space, each located in semantically congruent regions (e.g., happy facial expressions distributed in positively valenced regions). Crucially, we further demonstrated the generalization of the embedding beyond the six classic categories, using a broader set of 19 complex emotion categories (e.g., delighted, fury, and terrified). Together, our results show that facial expressions of emotion categories comprise specific combinations of valence and arousal related face movements, suggesting a multiplexed signalling of categorical and dimensional affective information. Our results unite current theories of emotion representation to form the basis of a new framework of multiplexed communication of affective information.

scholarly journals Computing the Discrete Compactness of Orthogonal Pseudo-Polytopes via Their D-EVM Representation

2010 ◽  
Vol 2010 ◽  
pp. 1-28 ◽  
Author(s):  
Ricardo Pérez-Aguila
Keyword(s):  
Dimensional Space ◽  
Efficient Algorithms ◽  
Video Sequences ◽  
Higher Dimensional ◽  
Discrete Compactness ◽  
Representation Scheme ◽  
2D And 3D ◽  
Orthogonal Polytopes

This work is devoted to present a methodology for the computation of Discrete Compactness in -dimensional orthogonal pseudo-polytopes. The proposed procedures take in account compactness' definitions originally presented for the 2D and 3D cases and extend them directly for considering the D case. There are introduced efficient algorithms for computing discrete compactness which are based on an orthogonal polytopes representation scheme known as the Extreme Vertices Model in the -Dimensional Space (D-EVM). It will be shown the potential of the application of Discrete Compactness in higher-dimensional contexts by applying it, through EVM-based algorithms, in the classification of video sequences, associated to the monitoring of a volcano's activity, which are expressed as 4D orthogonal polytopes in the space-color-time geometry.

scholarly journals Automatic Representation and Segmentation of Video Sequences via a Novel Framework Based on the nD-EVM and Kohonen Networks

2016 ◽  
Vol 2016 ◽  
pp. 1-34
Author(s):  
José-Yovany Luis-García ◽  
Ricardo Pérez-Aguila
Keyword(s):  
Video Segmentation ◽  
Dimensional Space ◽  
Event Analysis ◽  
Self Organizing Maps ◽  
Video Representation ◽  
Guided Surgery ◽  
Frame Sequence ◽  
Video Application ◽  
Discrete Compactness ◽  
Kohonen Networks

Recently in the Computer Vision field, a subject of interest, at least in almost every video application based on scene content, is video segmentation. Some of these applications are indexing, surveillance, medical imaging, event analysis, and computer-guided surgery, for naming some of them. To achieve their goals, these applications need meaningful information about a video sequence, in order to understand the events in its corresponding scene. Therefore, we need semantic information which can be obtained from objects of interest that are present in the scene. In order to recognize objects we need to compute features which aid the finding of similarities and dissimilarities, among other characteristics. For this reason, one of the most important tasks for video and image processing is segmentation. The segmentation process consists in separating data into groups that share similar features. Based on this, in this work we propose a novel framework for video representation and segmentation. The main workflow of this framework is given by the processing of an input frame sequence in order to obtain, as output, a segmented version. For video representation we use the Extreme Vertices Model in the n-Dimensional Space while we use the Discrete Compactness descriptor as feature and Kohonen Self-Organizing Maps for segmentation purposes.

scholarly journals SEGMENTATION OF 2D AND 3D TEXTURES FROM ESTIMATES OF THE LOCAL ORIENTATION

2011 ◽  
Vol 27 (3) ◽  
pp. 183 ◽  
Author(s):  
Dominique Jeulin ◽  
Maxime Moreaud
Keyword(s):  
Dimensional Space ◽  
Lamellar Microstructure ◽  
Second Step ◽  
Fourier Space ◽  
Local Orientation ◽  
3D Images ◽  
Scalar Products ◽  
2D And 3D ◽  
Transmission Electrons ◽  
3D Textures

We use a method to estimate local orientations in the n-dimensional space from the covariance matrix of the gradient, which can be implemented either in the image space or in the Fourier space. In a second step, two methods allow us to detect sudden changes of orientation in images. The first one uses an index of confidence of the estimated orientation, and the second one the detection of minima of scalar products in a neighbourhood. This is illustrated on 2D Transmission Electrons Microscope images of cellulose cryofracture (to display the organisation of cellulose whiskers and the points of germination), and to 3D images of a TA6V alloy (lamellar microstructure) obtained by microtomography.

scholarly journals Predicting miRNA-Disease Associations by Incorporating Projections in Low-Dimensional Space and Local Topological Information

Genes ◽  
2019 ◽  
Vol 10 (9) ◽  
pp. 685 ◽  
Author(s):  
Xuan ◽  
Zhang ◽  
Zhang ◽  
Li ◽  
Zhao
Keyword(s):  
Dimensional Space ◽  
Characteristic Curve ◽  
Feature Space ◽  
Superior Performance ◽  
Topological Information ◽  
Heterogeneous Information ◽  
Feature Representations ◽  
Disease Associations ◽  
Precision Recall Curve ◽  
Low Dimensional

Predicting the potential microRNA (miRNA) candidates associated with a disease helps in exploring the mechanisms of disease development. Most recent approaches have utilized heterogeneous information about miRNAs and diseases, including miRNA similarities, disease similarities, and miRNA-disease associations. However, these methods do not utilize the projections of miRNAs and diseases in a low-dimensional space. Thus, it is necessary to develop a method that can utilize the effective information in the low-dimensional space to predict potential disease-related miRNA candidates. We proposed a method based on non-negative matrix factorization, named DMAPred, to predict potential miRNA-disease associations. DMAPred exploits the similarities and associations of diseases and miRNAs, and it integrates local topological information of the miRNA network. The likelihood that a miRNA is associated with a disease also depends on their projections in low-dimensional space. Therefore, we project miRNAs and diseases into low-dimensional feature space to yield their low-dimensional and dense feature representations. Moreover, the sparse characteristic of miRNA-disease associations was introduced to make our predictive model more credible. DMAPred achieved superior performance for 15 well-characterized diseases with AUCs (area under the receiver operating characteristic curve) ranging from 0.860 to 0.973 and AUPRs (area under the precision-recall curve) ranging from 0.118 to 0.761. In addition, case studies on breast, prostatic, and lung neoplasms demonstrated the ability of DMAPred to discover potential disease-related miRNAs.

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