scholarly journals Brain Density Clustering Analysis: A New Approach to Brain Functional Dynamics

2021 ◽  
Vol 15 ◽  
Author(s):  
Ashkan Faghiri ◽  
Eswar Damaraju ◽  
Aysenil Belger ◽  
Judith M. Ford ◽  
Daniel Mathalon ◽  
...  
Keyword(s):  
Time Series ◽  
Dimensional Space ◽  
Real Data ◽  
High Dimensional ◽  
Data Set ◽  
High Dimensional Space ◽  
New Approach ◽  
Oscillatory Pattern ◽  
Functional Dynamics ◽  
Novel Approach

BackgroundA number of studies in recent years have explored whole-brain dynamic connectivity using pairwise approaches. There has been less focus on trying to analyze brain dynamics in higher dimensions over time.MethodsWe introduce a new approach that analyzes time series trajectories to identify high traffic nodes in a high dimensional space. First, functional magnetic resonance imaging (fMRI) data are decomposed using spatial ICA to a set of maps and their associated time series. Next, density is calculated for each time point and high-density points are clustered to identify a small set of high traffic nodes. We validated our method using simulations and then implemented it on a real data set.ResultsWe present a novel approach that captures dynamics within a high dimensional space and also does not use any windowing in contrast to many existing approaches. The approach enables one to characterize and study the time series in a potentially high dimensional space, rather than looking at each component pair separately. Our results show that schizophrenia patients have a lower dynamism compared to healthy controls. In addition, we find patients spend more time in nodes associated with the default mode network and less time in components strongly correlated with auditory and sensorimotor regions. Interestingly, we also found that subjects oscillate between state pairs that show opposite spatial maps, suggesting an oscillatory pattern.ConclusionOur proposed method provides a novel approach to analyze the data in its native high dimensional space and can possibly provide new information that is undetectable using other methods.

Geometric Algebra Neuron for SAR Automation Target Recognition

2011 ◽  
Vol 187 ◽  
pp. 319-325
Author(s):  
Wen Ming Cao ◽  
Xiong Feng Li ◽  
Li Juan Pu
Keyword(s):  
Geometric Algebra ◽  
Target Recognition ◽  
Dimensional Space ◽  
Feature Space ◽  
Automatic Target Recognition ◽  
High Dimensional ◽  
Small Data ◽  
Data Set ◽  
High Dimensional Space ◽  
Stationary Target

Biometric Pattern Recognition aim at finding the best coverage of per kind of sample’s distribution in the feature space. This paper employed geometric algebra to determine local continuum (connected) direction and connected path of same kind of target of SAR images of the complex geometrical body in high dimensional space. We researched the property of the GA Neuron of the coverage body in high dimensional space and studied a kind of SAR ATR(SAR automatic target recognition) technique which works with small data amount and result to high recognizing rate. Finally, we verified our algorithm with MSTAR (Moving and Stationary Target Acquisition and Recognition) [1] data set.

An Error Minimizing Partitioning Method for the Nearest Neighbor Search

2013 ◽  
Vol 321-324 ◽  
pp. 2165-2170
Author(s):  
Seung Hoon Lee ◽  
Jaek Wang Kim ◽  
Jae Dong Lee ◽  
Jee Hyong Lee
Keyword(s):  
Nearest Neighbor ◽  
Dimensional Space ◽  
Computational Cost ◽  
Nearest Neighbor Search ◽  
High Dimensional ◽  
Index Structures ◽  
Cost Index ◽  
Data Set ◽  
High Dimensional Space ◽  
Neighbor Search

The nearest neighbor search in high-dimensional space is an important operation in many applications, such as data mining and multimedia databases. Evaluating similarity in high-dimensional space requires high computational cost; index-structures are frequently used for reducing computational cost. Most of these index-structures are built by partitioning the data set. However, the partitioning approaches potentially have the problem of failing to find the nearest neighbor that is caused by partitions. In this paper, we propose the Error Minimizing Partitioning (EMP) method with a novel tree structure that minimizes the failures of finding the nearest neighbors. EMP divides the data into subsets with considering the distribution of data sets. For partitioning a data set, the proposed method finds the line that minimizes the summation of distance to data points. The method then finds the median of the data set. Finally, our proposed method determines the partitioning hyper-plane that passes the median and is perpendicular to the line. We also make a comparative study between existing methods and the proposed method to verify the effectiveness of our method.

A New Outlier Detection Algorithms Based on Markov Chain

2011 ◽  
Vol 366 ◽  
pp. 456-459 ◽  
Author(s):  
Jun Yang ◽  
Ying Long Wang
Keyword(s):  
Markov Chain ◽  
Outlier Detection ◽  
High Dimensional Data ◽  
Weighted Graph ◽  
Real Data ◽  
Curse Of Dimensionality ◽  
High Dimensional ◽  
Large Set ◽  
Data Set ◽  
Novel Approach

Detecting outliers in a large set of data objects is a major data mining task aiming at finding different mechanisms responsible for different groups of objects in a data set. In high-dimensional data, these approaches are bound to deteriorate due to the notorious “curse of dimensionality”. In this paper, we propose a novel approach named ODMC (Outlier Detection Based On Markov Chain)，the effects of the “curse of dimensionality” are alleviated compared to purely distance-based approaches. A main advantage of our new approach is that our method is to use a major feature of an undirected weighted graph to calculate the outlier degree of each node, In a thorough experimental evaluation, we compare ODMC to the ABOD and FindFPOF for various artificial and real data set and show ODMC to perform especially well on high-dimensional data.

Neural networks trained with high-dimensional functions approximation data in high-dimensional space

2021 ◽  
pp. 1-12
Author(s):  
Jian Zheng ◽  
Jianfeng Wang ◽  
Yanping Chen ◽  
Shuping Chen ◽  
Jingjin Chen ◽  
...  
Keyword(s):  
Neural Networks ◽  
Dimensional Space ◽  
Data Distribution ◽  
High Dimensional ◽  
Sufficient Information ◽  
Sufficient Data ◽  
High Dimensional Space ◽  
Positive Effects ◽  
The Neural Networks ◽  
Using Data

Neural networks can approximate data because of owning many compact non-linear layers. In high-dimensional space, due to the curse of dimensionality, data distribution becomes sparse, causing that it is difficulty to provide sufficient information. Hence, the task becomes even harder if neural networks approximate data in high-dimensional space. To address this issue, according to the Lipschitz condition, the two deviations, i.e., the deviation of the neural networks trained using high-dimensional functions, and the deviation of high-dimensional functions approximation data, are derived. This purpose of doing this is to improve the ability of approximation high-dimensional space using neural networks. Experimental results show that the neural networks trained using high-dimensional functions outperforms that of using data in the capability of approximation data in high-dimensional space. We find that the neural networks trained using high-dimensional functions more suitable for high-dimensional space than that of using data, so that there is no need to retain sufficient data for neural networks training. Our findings suggests that in high-dimensional space, by tuning hidden layers of neural networks, this is hard to have substantial positive effects on improving precision of approximation data.

scholarly journals A System to Assess the Semantic Content of Student Essays

2001 ◽  
Vol 24 (3) ◽  
pp. 305-320 ◽  
Author(s):  
Benoit Lemaire ◽  
Philippe Dessus
Keyword(s):  
Latent Semantic Analysis ◽  
Semantic Analysis ◽  
Dimensional Space ◽  
Semantic Content ◽  
High Dimensional ◽  
High Dimensional Space

This paper presents Apex, a system that can automatically assess a student essay based on its content. It relies on Latent Semantic Analysis, a tool which is used to represent the meaning of words as vectors in a high-dimensional space. By comparing an essay and the text of a given course on a semantic basis, our system can measure how well the essay matches the text. Various assessments are presented to the student regarding the topic, the outline and the coherence of the essay. Our experiments yield promising results.

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