Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Collisions in Multiple Dimensions: Introduction01:05

Collisions in Multiple Dimensions: Introduction

5.5K
It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a...
5.5K
Collisions in Multiple Dimensions: Problem Solving01:06

Collisions in Multiple Dimensions: Problem Solving

4.3K
In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...
4.3K
Problem Solving: Dimensional Analysis01:08

Problem Solving: Dimensional Analysis

3.5K
Every mathematical equation that connects separate distinct physical quantities must be dimensionally consistent, which implies it must abide by two rules. For this reason, the concept of dimension is crucial. The first rule is that an equation's expressions on either side of an equality must have the exact same dimension, i.e., quantities of the same dimension can be added or removed. The second rule stipulates that all popular mathematical functions, such as exponential, logarithmic, and...
3.5K
Dimensional Analysis02:19

Dimensional Analysis

15.5K
The concept of dimension is important because every mathematical equation linking physical quantities must be dimensionally consistent, implying that mathematical equations must meet the following two rules. The first rule is that, in an equation, the expressions on each side of the equal sign must have the same dimensions. This is fairly intuitive since we can only add or subtract quantities of the same type (dimension). The second rule states that, in an equation, the arguments of any of the...
15.5K
Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

14.3K
It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
14.3K
Downsampling01:20

Downsampling

217
When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
217

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Optimization in Sparse 2D to Dense 3D Weakly Supervised Learning: Application to Multi-Label Segmentation of Large ex vivo MRI Data.

ArXiv·2026
Same author

Tobacco Use and Cessation Strategies Among Individuals Recently Diagnosed with Cancer.

Nicotine & tobacco research : official journal of the Society for Research on Nicotine and Tobacco·2026
Same author

Batch Effect Correction for Neuroimaging Data with Heterogeneous Spatial Correlations.

bioRxiv : the preprint server for biology·2026
Same author

Rejoinder to the discussion on "INTACT: A method for integration of longitudinal physical activity data from multiple sources".

Biometrics·2026
Same author

An open, fully-processed data resource for studying mood and sleep variability in the developing brain.

Aperture neuro·2026
Same author

INTACT: a method for integration of longitudinal physical activity data from multiple sources.

Biometrics·2026
Same journal

A human-specific genetic modifier reconfigures large-scale cortical network dynamics underlying behavioral performance.

bioRxiv : the preprint server for biology·2026
Same journal

<i>Staphylococcus aureus</i> uses a eukaryotic-like uridyltransferase to make UDP-GlcNAc for cell wall synthesis.

bioRxiv : the preprint server for biology·2026
Same journal

Dynamic redistribution of eIF4F controls cap-dependent translation initiation.

bioRxiv : the preprint server for biology·2026
Same journal

When does additional information improve accuracy of RNA secondary structure prediction?

bioRxiv : the preprint server for biology·2026
Same journal

Normative brain-state trajectories reveal deviation from healthy aging in Alzheimer's disease.

bioRxiv : the preprint server for biology·2026
Same journal

Noradrenergic infraslow rhythm during sleep is the critical link between heart-rate dynamics and memory consolidation.

bioRxiv : the preprint server for biology·2026
See all related articles

Related Experiment Video

Updated: Aug 12, 2025

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

2.6K

Deconfounded Dimension Reduction via Partial Embeddings.

Andrew A Chen1,2, Kelly Clark1, Blake Dewey3

  • 1Penn Statistics in Imaging and Visualization Center, Department of Biostatistics, Epidemiology, and Informatics, University of Pennsylvania, Philadelphia, PA.

Biorxiv : the Preprint Server for Biology
|January 30, 2023
PubMed
Summary
This summary is machine-generated.

Dimension reduction methods like t-SNE and UMAP can reveal biological patterns but struggle with confounding effects. The new partial embedding (PARE) framework effectively removes unwanted variables from these analyses.

Keywords:
Dimension reductionconfounding effectsembeddingsgenomicsneuroimaging

More Related Videos

An Operant Intra-/Extra-dimensional Set-shift Task for Mice
08:35

An Operant Intra-/Extra-dimensional Set-shift Task for Mice

Published on: January 22, 2016

12.3K
Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness
03:14

Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness

Published on: December 6, 2024

659

Related Experiment Videos

Last Updated: Aug 12, 2025

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

2.6K
An Operant Intra-/Extra-dimensional Set-shift Task for Mice
08:35

An Operant Intra-/Extra-dimensional Set-shift Task for Mice

Published on: January 22, 2016

12.3K
Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness
03:14

Augmenting Large Language Models via Vector Embeddings to Improve Domain-Specific Responsiveness

Published on: December 6, 2024

659

Area of Science:

  • Computational Biology
  • Data Science
  • Bioinformatics

Background:

  • High-dimensional biological data, such as single-cell sequencing and neuroimaging, often contain complex patterns obscured by confounding factors.
  • Existing dimension reduction techniques, including t-distributed Stochastic Neighbor Embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP), excel at preserving data structure but do not inherently account for unwanted sources of variation.

Approach:

  • We introduce the partial embedding (PARE) framework, a novel method designed to remove confounding effects from any distance-based dimension reduction technique.
  • PARE is integrated with popular methods to create partial t-SNE and partial UMAP, enabling the isolation of biological signals from technical or clinical variability.
  • The framework is applied to diverse high-dimensional datasets, including genomic and neuroimaging data, to demonstrate its versatility and effectiveness.

Key Points:

  • The PARE framework successfully removes batch effects in single-cell RNA sequencing data, a common challenge in genomics.
  • In neuroimaging, PARE effectively separates clinical variability from technical noise, improving the interpretability of brain data.
  • Partial dimension reduction methods developed using PARE highlight biologically relevant patterns while mitigating the influence of confounding variables.

Conclusions:

  • The PARE framework provides a robust and generalizable approach to enhance existing dimension reduction tools by removing unwanted effects.
  • This methodology allows for a clearer visualization and analysis of biological patterns of interest in high-dimensional data.
  • PARE represents a significant advancement in computational biology and data analysis, enabling more accurate insights from complex biological datasets.