scholarly journals Harnessing Matrix Completion to Unify and Extend Viral Serology Studies

2021 ◽  
Author(s):  
Tal Einav ◽  
Brian Cleary
Keyword(s):  
Dimensional Space ◽  
Matrix Completion ◽  
Viral Evolution ◽  
Large Panels ◽  
Successful Prediction ◽  
Low Dimensional ◽  
Incomplete Datasets ◽  
Virus Interactions ◽  
Lower Dimensional Space ◽  
Virus Strains

SummaryCharacterizing the antibody response against large panels of viral variants provides unique insight into key processes that shape viral evolution and host antibody repertoires, and has become critical to the development of new vaccine strategies. Given the enormous diversity of circulating virus strains and antibody responses, exhaustive testing of all antibody-virus interactions is unfeasible. However, prior studies have demonstrated that, despite the complexity of these interactions, their functional phenotypes can be characterized in a vastly simpler and lower-dimensional space, suggesting that matrix completion of relatively few measurements could accurately predict unmeasured antibody-virus interactions. Here, we combine available data from several of the largest-scale studies for both influenza and HIV-1 and demonstrate how matrix completion can substantially expedite experiments. We explore how prediction accuracy evolves as the number of available measurements changes and approximate the number of additional measurements necessary in several highly incomplete datasets (suggesting ∼250,000 measurements could be saved). In addition, we show how the method can be used to combine disparate datasets, even when the number of available measurements is below the theoretical limit for successful prediction. Our results suggest new approaches to improve ongoing experimental design, and could be readily generalized to other viruses or more broadly to other low-dimensional biological datasets.

scholarly journals Predictability and Information Theory. Part II: Imperfect Forecasts

2005 ◽  
Vol 62 (9) ◽  
pp. 3368-3381 ◽  
Author(s):  
Timothy DelSole
Keyword(s):  
Information Theory ◽  
Mutual Information ◽  
Dimensional Space ◽  
Nonlinear Behavior ◽  
Potential Predictability ◽  
Low Dimensional ◽  
Lower Dimensional Space ◽  
True System ◽  
Normally Distributed

Abstract This paper presents a framework for quantifying predictability based on the behavior of imperfect forecasts. The critical quantity in this framework is not the forecast distribution, as used in many other predictability studies, but the conditional distribution of the state given the forecasts, called the regression forecast distribution. The average predictability of the regression forecast distribution is given by a quantity called the mutual information. Standard inequalities in information theory show that this quantity is bounded above by the average predictability of the true system and by the average predictability of the forecast system. These bounds clarify the role of potential predictability, of which many incorrect statements can be found in the literature. Mutual information has further attractive properties: it is invariant with respect to nonlinear transformations of the data, cannot be improved by manipulating the forecast, and reduces to familiar measures of correlation skill when the forecast and verification are joint normally distributed. The concept of potential predictable components is shown to define a lower-dimensional space that captures the full predictability of the regression forecast without loss of generality. The predictability of stationary, Gaussian, Markov systems is examined in detail. Some simple numerical examples suggest that imperfect forecasts are not always useful for joint normally distributed systems since greater predictability often can be obtained directly from observations. Rather, the usefulness of imperfect forecasts appears to lie in the fact that they can identify potential predictable components and capture nonstationary and/or nonlinear behavior, which are difficult to capture by low-dimensional, empirical models estimated from short historical records.

scholarly journals Binary Linear Compression for Multi-label Classification

2017 ◽  
Author(s):  
Wen-Ji Zhou ◽  
Yang Yu ◽  
Min-Ling Zhang
Keyword(s):  
Dimensional Space ◽  
Classification Problem ◽  
Complex Model ◽  
Linear Mapping ◽  
Regression Problem ◽  
Low Dimensional ◽  
The Relationship ◽  
Lower Dimensional Space ◽  
Lower Dimensional ◽  
Linear Compression

In multi-label classification tasks, labels are commonly related with each other. It has been well recognized that utilizing label relationship is essential to multi-label learning. One way to utilizing label relationship is to map labels to a lower-dimensional space of uncorrelated labels, where the relationship could be encoded in the mapping. Previous linear mapping methods commonly result in regression subproblems in the lower-dimensional label space. In this paper, we disclose that mappings to a low-dimensional multi-label regression problem can be worse than mapping to a classification problem, since regression requires more complex model than classification. We then propose the binary linear compression (BILC) method that results in a binary label space, leading to classification subproblems. Experiments on several multi-label datasets show that, employing classification in the embedded space results in much simpler models than regression, leading to smaller structure risk. The proposed methods are also shown to be superior to some state-of-the-art approaches.

Methods for Binary Multidimensional Scaling

2002 ◽  
Vol 14 (5) ◽  
pp. 1195-1232 ◽  
Author(s):  
Douglas L. T. Rohde
Keyword(s):  
Neural Networks ◽  
Multidimensional Scaling ◽  
Dimensional Space ◽  
Discrete Space ◽  
High Dimensional ◽  
Continuous Space ◽  
Low Dimensional ◽  
Set Of Points ◽  
Lower Dimensional Space ◽  
Lower Dimensional

Multidimensional scaling (MDS) is the process of transforming a set of points in a high-dimensional space to a lower-dimensional one while preserving the relative distances between pairs of points. Although effective methods have been developed for solving a variety of MDS problems, they mainly depend on the vectors in the lower-dimensional space having real-valued components. For some applications, the training of neural networks in particular, it is preferable or necessary to obtain vectors in a discrete, binary space. Unfortunately, MDS into a low-dimensional discrete space appears to be a significantly harder problem than MDS into a continuous space. This article introduces and analyzes several methods for performing approximately optimized binary MDS.

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 High Resolution, High Contrast Beamformer Using Minimum Variance and Plane Wave Nonlinear Compounding with Low Complexity

Sensors ◽  
2021 ◽  
Vol 21 (2) ◽  
pp. 394
Author(s):  
Xin Yan ◽  
Yanxing Qi ◽  
Yinmeng Wang ◽  
Yuanyuan Wang
Keyword(s):  
Plane Wave ◽  
Dimensional Space ◽  
Contrast Ratio ◽  
Low Complexity ◽  
Minimum Variance ◽  
Frame Rate ◽  
Channel Noise ◽  
Length Estimation ◽  
Lower Dimensional Space

The plane wave compounding (PWC) is a promising modality to improve the imaging quality and maintain the high frame rate for ultrafast ultrasound imaging. In this paper, a novel beamforming method is proposed to achieve higher resolution and contrast with low complexity. A minimum variance (MV) weight calculated by the partial generalized sidelobe canceler is adopted to beamform the receiving array signals. The dimension reduction technique is introduced to project the data into lower dimensional space, which also contributes to a large subarray length. Estimation of multi-wave receiving covariance matrix is performed and then utilized to determine only one weight. Afterwards, a fast second-order reformulation of the delay multiply and sum (DMAS) is developed as nonlinear compounding to composite the beamforming output of multiple transmissions. Simulations, phantom, in vivo, and robustness experiments were carried out to evaluate the performance of the proposed method. Compared with the delay and sum (DAS) beamformer, the proposed method achieved 86.3% narrower main lobe width and 112% higher contrast ratio in simulations. The robustness to the channel noise of the proposed method is effectively enhanced at the same time. Furthermore, it maintains a linear computational complexity, which means that it has the potential to be implemented for real-time response.

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.

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