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Related Concept Videos

Distance Problem01:29

Distance Problem

When an object's velocity changes over time, the total distance traveled can be determined by summing small displacement intervals over short increments. This approach approximates the true distance through numerical summation and the use of integral calculus. An estimate of the total displacement can be obtained by measuring velocity at regular intervals and multiplying each value by the corresponding time step.If a runner accelerates over the first three seconds of a race, speed measurements...
Distance Corrections01:15

Distance Corrections

To achieve precise distance measurements, especially in surveying and construction, certain corrections must be applied to account for potential sources of error like the standardization errors, temperature variations, and slope adjustments.Standardization error emerges when measurement equipment undergoes changes, such as wear, repairs, or weather impacts. To address this, surveyors compare the equipment’s readings to a standard. This process identifies any deviation that might lead to...
The Distance Formula01:20

The Distance Formula

In geometry, measuring the direct distance between two points on a plane is essential in various practical and theoretical applications. Whether in navigation, engineering, or computer graphics, determining the shortest path between two locations involves using the distance formula. This formula is derived from the Pythagorean Theorem, which relates the lengths of the sides of a right triangle. On a coordinate plane, the horizontal and vertical distances between two points serve as the legs of...
Distance Measurements by Taping01:18

Distance Measurements by Taping

Tapes are essential in surveying for accurate, durable, and short-distance measurements. Made from lightweight, nylon-coated steel, they offer flexibility and strength for rugged outdoor use. The nylon coating protects against rust and wear, extending the tape's life. Standard lengths, around 30 meters, are marked in meters and millimeters for precision.Surveyors select tapes based on site conditions and accuracy needs. Lightweight, nylon-coated tapes are commonly used for ease of handling and...
Vectors in 2D: Problem Solving01:29

Vectors in 2D: Problem Solving

A plane traveling due north at 180 km/h in still air was found to be 80 km off-course after 30 minutes, deviating approximately 5 degrees east of north. This deviation means the influence of a crosswind alters the plane’s intended trajectory. The actual ground path formed a diagonal, suggesting that the aircraft’s effective ground speed was reduced to 160 km/h and directed slightly to the east due to the wind.By analyzing the displacement from the intended path, the velocity contributed by the...
Design Example: Measuring Distance Between Two Points with Obstructions01:10

Design Example: Measuring Distance Between Two Points with Obstructions

When measuring distances in areas with physical obstructions, such as a lake in a field, surveyors must employ techniques to calculate accurate lengths without direct line measurements. One effective method is the offset technique, which allows for precise distance estimation over inaccessible stretches.In this scenario, a surveyor must measure a side of an area that crosses a lake. Since the measuring tape cannot span the lake, the surveyor begins by establishing a baseline that aligns with...

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Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations
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Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations

Published on: February 15, 2017

Supervised distance matrices.

Katherine S Pollard1, Mark J van der Laan

  • 1University of California, San Francisco, USA. kpollard@gladstone.ucsf.edu

Statistical Applications in Genetics and Molecular Biology
|December 4, 2008
PubMed
Summary
This summary is machine-generated.

We introduce a novel supervised distance matrix to measure variable similarity related to an outcome. This method aids in identifying predictive variable groups and sample subpopulations in high-dimensional data.

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Area of Science:

  • Statistics
  • Machine Learning
  • Bioinformatics

Background:

  • High-dimensional data analysis presents challenges in identifying meaningful relationships between variables and outcomes.
  • Existing methods may not effectively capture variable associations influenced by a specific outcome.
  • Discovering patterns in complex datasets requires novel statistical approaches.

Purpose of the Study:

  • To introduce a new statistical concept: the supervised distance matrix.
  • To provide a method for quantifying pairwise variable similarity based on outcome association.
  • To enable the identification of predictive variable groups and sample subpopulations.

Main Methods:

  • The supervised distance matrix is constructed in two stages: data transformation and distance computation.
  • Data transformation involves using working models for association, such as regression residuals or influence curves.
  • Pairwise distances are calculated on transformed data, with consistent estimators and an inverse probability of censoring weighted estimator for censored outcomes.

Main Results:

  • The study demonstrates the utility of supervised distance matrices through simulations.
  • Application to gene expression data with a censored survival outcome showcases its effectiveness.
  • The method successfully identifies groups of similarly predictive variables and subpopulations of related samples.

Conclusions:

  • Supervised distance matrices offer a powerful tool for analyzing high-dimensional data.
  • This approach facilitates the discovery of variable relationships and sample structures driven by specific outcomes.
  • The methods are broadly applicable across various scientific fields, including genomics.