Clustering in Low-Dimensional Space

1993 ◽  
pp. 162-173 ◽  
Author(s):  
Willem J. Heiser
Keyword(s):  
Dimensional Space ◽  
Low Dimensional

scholarly journals A Generative-Discriminative Framework that Integrates Imaging, Genetic, and Diagnosis into Coupled Low Dimensional Space

NeuroImage ◽  
2021 ◽  
pp. 118200
Author(s):  
Sayan Ghosal ◽  
Qiang Chen ◽  
Giulio Pergola ◽  
Aaron L. Goldman ◽  
William Ulrich ◽  
...  
Keyword(s):  
Dimensional Space ◽  
Low Dimensional

scholarly journals Artifacts in Simultaneous hdEEG/fMRI Imaging: A Nonlinear Dimensionality Reduction Approach

Sensors ◽  
2019 ◽  
Vol 19 (20) ◽  
pp. 4454 ◽  
Author(s):  
Marek Piorecky ◽  
Vlastimil Koudelka ◽  
Jan Strobl ◽  
Martin Brunovsky ◽  
Vladimir Krajca
Keyword(s):  
Data Structure ◽  
Spatial Clustering ◽  
Dimensional Space ◽  
Head Movements ◽  
Nonlinear Dimensionality Reduction ◽  
Space Resolution ◽  
Additional Information ◽  
Nonlinear Dimension ◽  
The Time Domain ◽  
Low Dimensional

Simultaneous recordings of electroencephalogram (EEG) and functional magnetic resonance imaging (fMRI) are at the forefront of technologies of interest to physicians and scientists because they combine the benefits of both modalities—better time resolution (hdEEG) and space resolution (fMRI). However, EEG measurements in the scanner contain an electromagnetic field that is induced in leads as a result of gradient switching slight head movements and vibrations, and it is corrupted by changes in the measured potential because of the Hall phenomenon. The aim of this study is to design and test a methodology for inspecting hidden EEG structures with respect to artifacts. We propose a top-down strategy to obtain additional information that is not visible in a single recording. The time-domain independent component analysis algorithm was employed to obtain independent components and spatial weights. A nonlinear dimension reduction technique t-distributed stochastic neighbor embedding was used to create low-dimensional space, which was then partitioned using the density-based spatial clustering of applications with noise (DBSCAN). The relationships between the found data structure and the used criteria were investigated. As a result, we were able to extract information from the data structure regarding electrooculographic, electrocardiographic, electromyographic and gradient artifacts. This new methodology could facilitate the identification of artifacts and their residues from simultaneous EEG in fMRI.

scholarly journals Optimizing the structure and movement of a robotic bat with biological kinematic synergies

2018 ◽  
Vol 37 (10) ◽  
pp. 1233-1252 ◽  
Author(s):  
Jonathan Hoff ◽  
Alireza Ramezani ◽  
Soon-Jo Chung ◽  
Seth Hutchinson
Keyword(s):  
Principal Component Analysis ◽  
Topological Structure ◽  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Principal Component ◽  
Biologically Inspired ◽  
Wing Kinematics ◽  
Wing Motion ◽  
Kinematic Synergies ◽  
Low Dimensional

In this article, we present methods to optimize the design and flight characteristics of a biologically inspired bat-like robot. In previous, work we have designed the topological structure for the wing kinematics of this robot; here we present methods to optimize the geometry of this structure, and to compute actuator trajectories such that its wingbeat pattern closely matches biological counterparts. Our approach is motivated by recent studies on biological bat flight that have shown that the salient aspects of wing motion can be accurately represented in a low-dimensional space. Although bats have over 40 degrees of freedom (DoFs), our robot possesses several biologically meaningful morphing specializations. We use principal component analysis (PCA) to characterize the two most dominant modes of biological bat flight kinematics, and we optimize our robot’s parametric kinematics to mimic these. The method yields a robot that is reduced from five degrees of actuation (DoAs) to just three, and that actively folds its wings within a wingbeat period. As a result of mimicking synergies, the robot produces an average net lift improvesment of 89% over the same robot when its wings cannot fold.

Reduced $$k$$ k -means clustering with MCA in a low-dimensional space

2014 ◽  
Vol 30 (2) ◽  
pp. 463-475 ◽  
Author(s):  
Masaki Mitsuhiro ◽  
Hiroshi Yadohisa
Keyword(s):  
Dimensional Space ◽  
Low Dimensional

scholarly journals Season- and Trend-aware Symbolic Approximation for Accurate and Efficient Time Series Matching

2021 ◽  
Author(s):  
Lars Kegel ◽  
Claudio Hartmann ◽  
Maik Thiele ◽  
Wolfgang Lehner
Keyword(s):  
Time Series ◽  
State Of The Art ◽  
Dimensional Space ◽  
Symbolic Aggregate Approximation ◽  
Current State ◽  
Optimal Representation ◽  
Symbolic Approximation ◽  
Low Dimensional ◽  
Deterministic Behavior ◽  
Support Time

AbstractProcessing and analyzing time series datasets have become a central issue in many domains requiring data management systems to support time series as a native data type. A core access primitive of time series is matching, which requires efficient algorithms on-top of appropriate representations like the symbolic aggregate approximation (SAX) representing the current state of the art. This technique reduces a time series to a low-dimensional space by segmenting it and discretizing each segment into a small symbolic alphabet. Unfortunately, SAX ignores the deterministic behavior of time series such as cyclical repeating patterns or a trend component affecting all segments, which may lead to a sub-optimal representation accuracy. We therefore introduce a novel season- and a trend-aware symbolic approximation and demonstrate an improved representation accuracy without increasing the memory footprint. Most importantly, our techniques also enable a more efficient time series matching by providing a match up to three orders of magnitude faster than SAX.

scholarly journals Neuroimaging: into the Multiverse

2020 ◽  
Author(s):  
Jessica Dafflon ◽  
Pedro F. Da Costa ◽  
František Váša ◽  
Ricardo Pio Monti ◽  
Danilo Bzdok ◽  
...  
Keyword(s):  
Active Learning ◽  
Statistical Power ◽  
Predictive Power ◽  
Dimensional Space ◽  
Graph Theoretic ◽  
Processing Pipeline ◽  
Regression Approach ◽  
Low Dimensional ◽  
Sequential Analyses ◽  
Processing Steps

AbstractFor most neuroimaging questions the huge range of possible analytic choices leads to the possibility that conclusions from any single analytic approach may be misleading. Examples of possible choices include the motion regression approach used and smoothing and threshold factors applied during the processing pipeline. Although it is possible to perform a multiverse analysis that evaluates all possible analytic choices, this can be computationally challenging and repeated sequential analyses on the same data can compromise inferential and predictive power. Here, we establish how active learning on a low-dimensional space that captures the inter-relationships between analysis approaches can be used to efficiently approximate the whole multiverse of analyses. This approach balances the benefits of a multiverse analysis without the accompanying cost to statistical power, computational power and the integrity of inferences. We illustrate this approach with a functional MRI dataset of functional connectivity across adolescence, demonstrating how a multiverse of graph theoretic and simple pre-processing steps can be efficiently navigated using active learning. Our study shows how this approach can identify the subset of analysis techniques (i.e., pipelines) which are best able to predict participants’ ages, as well as allowing the performance of different approaches to be quantified.

scholarly journals Network Embedding via a Bi-Mode and Deep Neural Network Model

2017 ◽  
Author(s):  
Yang Fang ◽  
Xiang Zhao ◽  
Zhen Tan
Keyword(s):  
Neural Network ◽  
Deep Neural Network ◽  
Semantic Information ◽  
Dimensional Space ◽  
Relation Extraction ◽  
Network Embedding ◽  
Structure Information ◽  
Second Mode ◽  
Real World Datasets ◽  
Low Dimensional

Network Embedding (NE) is an important method to learn the representations of network via a low-dimensional space. Conventional NE models focus on capturing the structure information and semantic information of vertices while neglecting such information for edges. In this work, we propose a novel NE model named BimoNet to capture both the structure and semantic information of edges. BimoNet is composed of two parts, i.e., the bi-mode embedding part and the deep neural network part. For bi-mode embedding part, the first mode named add-mode is used to express the entity-shared features of edges and the second mode named subtract-mode is employed to represent the entity-specific features of edges. These features actually reflect the semantic information. For deep neural network part, we firstly regard the edges in a network as nodes, and the vertices as links, which will not change the overall structure of the whole network. Then we take the nodes' adjacent matrix as the input of the deep neural network as it can obtain similar representations for nodes with similar structure. Afterwards, by jointly optimizing the objective function of these two parts, BimoNet could preserve both the semantic and structure information of edges. In experiments, we evaluate BimoNet on three real-world datasets and task of relation extraction, and BimoNet is demonstrated to outperform state-of-the-art baseline models consistently and significantly.

Community detection in complex network by network embedding and density clustering

2021 ◽  
pp. 1-12
Author(s):  
JinFang Sheng ◽  
Huaiyu Zuo ◽  
Bin Wang ◽  
Qiong Li
Keyword(s):  
Complex Network ◽  
Community Detection ◽  
Dimensional Space ◽  
Detection Algorithm ◽  
Superior Performance ◽  
Network Embedding ◽  
Detection Algorithms ◽  
Density Clustering ◽  
Community Detection Algorithm ◽  
Low Dimensional

 In a complex network system, the structure of the network is an extremely important element for the analysis of the system, and the study of community detection algorithms is key to exploring the structure of the complex network. Traditional community detection algorithms would represent the network using an adjacency matrix based on observations, which may contain redundant information or noise that interferes with the detection results. In this paper, we propose a community detection algorithm based on density clustering. In order to improve the performance of density clustering, we consider an algorithmic framework for learning the continuous representation of network nodes in a low-dimensional space. The network structure is effectively preserved through network embedding, and density clustering is applied in the embedded low-dimensional space to compute the similarity of nodes in the network, which in turn reveals the implied structure in a given network. Experiments show that the algorithm has superior performance compared to other advanced community detection algorithms for real-world networks in multiple domains as well as synthetic networks, especially when the network data chaos is high.

Learning Manifolds

2012 ◽  
pp. 374-402
Author(s):  
Diana Mateus ◽  
Christian Wachinger ◽  
Selen Atasoy ◽  
Loren Schwarz ◽  
Nassir Navab
Keyword(s):  
Manifold Learning ◽  
Domain Knowledge ◽  
Dimensional Space ◽  
Human Motion ◽  
Motion Modeling ◽  
Learning Methods ◽  
Data Representations ◽  
Non Linear ◽  
Data Points ◽  
Low Dimensional

Computer aided diagnosis is often confronted with processing and analyzing high dimensional data. One alternative to deal with such data is dimensionality reduction. This chapter focuses on manifold learning methods to create low dimensional data representations adapted to a given application. From pairwise non-linear relations between neighboring data-points, manifold learning algorithms first approximate the low dimensional manifold where data lives with a graph; then, they find a non-linear map to embed this graph into a low dimensional space. Since the explicit pairwise relations and the neighborhood system can be designed according to the application, manifold learning methods are very flexible and allow easy incorporation of domain knowledge. The authors describe different assumptions and design elements that are crucial to building successful low dimensional data representations with manifold learning for a variety of applications. In particular, they discuss examples for visualization, clustering, classification, registration, and human-motion modeling.

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