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Related Concept Videos

Orthogonal Trajectories01:26

Orthogonal Trajectories

Orthogonal trajectories describe the geometric relationship between two families of curves that intersect each other at right angles. One illustrative case involves a family of parabolas that open sideways along the x-axis. These curves share a common shape but differ by a scaling parameter, resulting in a set of curves that all pass through the origin and widen at different rates.Determining Orthogonal TrajectoriesTo identify the orthogonal trajectories for these parabolas, the first step...
Kinematic Equations - III01:18

Kinematic Equations - III

The first two kinematic equations have time as a variable, but the third kinematic equation is independent of time. This equation expresses final velocity as a function of the acceleration and distance over which it acts. The fourth kinematic equation does not have an acceleration term and provides the final position of the object at time t in terms of the initial and final velocities. This equation is useful when the value of the constant acceleration is unknown.
Using the kinematic equations,...
Kinematic Equations: Problem Solving01:15

Kinematic Equations: Problem Solving

When analyzing one-dimensional motion with constant acceleration, the problem-solving strategy involves identifying the known quantities and choosing the appropriate kinematic equations to solve for the unknowns. Either one or two kinematic equations are needed to solve for the unknowns, depending on the known and unknown quantities. Generally, the number of equations required is the same as the number of unknown quantities in the given example. Two-body pursuit problems always require two...
Kinematic Equations - II01:17

Kinematic Equations - II

The second kinematic equation expresses the final position of an object in terms of its initial position, the distance traveled with the initial constant velocity, and the distance traveled due to a change in velocity. Similar to the first kinematic equation, this equation is also only valid when the acceleration is constant throughout the motion of an object.
Suppose a car merges into freeway traffic on a 200 m long ramp. If its initial velocity is 10 m/s and it accelerates at 2 m/s2, then the...
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
Cluster Sampling Method01:20

Cluster Sampling Method

Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...

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Related Experiment Video

Updated: May 17, 2026

Trajectory Data Analyses for Pedestrian Space-time Activity Study
16:14

Trajectory Data Analyses for Pedestrian Space-time Activity Study

Published on: February 25, 2013

KmL3D: a non-parametric algorithm for clustering joint trajectories.

C Genolini1, J B Pingault, T Driss

  • 1INSERM, Université Paul Sabatier, Toulouse III, France. genolini@u-paris10.fr

Computer Methods and Programs in Biomedicine
|November 7, 2012
PubMed
Summary
This summary is machine-generated.

Clustering joint-variable trajectories in cohort studies reveals homogeneous patterns of evolution. The KmL3D R package facilitates this analysis, handling missing data and offering visualization tools for co-evolutionary patterns.

Related Experiment Videos

Last Updated: May 17, 2026

Trajectory Data Analyses for Pedestrian Space-time Activity Study
16:14

Trajectory Data Analyses for Pedestrian Space-time Activity Study

Published on: February 25, 2013

Area of Science:

  • Biostatistics
  • Data Science
  • Epidemiology

Background:

  • Cohort studies involve repeated measurements, generating trajectory data for multiple variables.
  • Analyzing joint-variable trajectories is crucial for understanding co-evolutionary patterns but lacks dedicated methods.
  • Existing methods for joint-trajectory clustering are suboptimal, failing to capture inter-variable dependencies.

Purpose of the Study:

  • Introduce KmL3D, an R package for clustering joint-variable trajectories.
  • Address limitations in current methods for analyzing co-evolution in cohort data.
  • Provide tools for managing missing data and visualizing joint-trajectory patterns.

Main Methods:

  • KmL3D implements a k-means algorithm specifically adapted for joint-trajectory clustering.
  • The package supports handling missing values within trajectories.
  • It offers various quality criteria for partition selection and a graphical interface for user guidance.

Main Results:

  • KmL3D enables clustering of multiple joint-variable trajectories, accounting for co-evolution.
  • For two joint trajectories, 3D visualization and dynamic graph export to PDF are available.
  • The package facilitates the identification of homogeneous patterns in the joint evolution of variables.

Conclusions:

  • KmL3D offers a novel and effective approach to clustering joint-variable trajectories in cohort studies.
  • The package enhances the analysis of co-evolutionary patterns by considering inter-variable relationships.
  • KmL3D provides valuable tools for biostatisticians and data scientists working with complex longitudinal data.