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Related Concept Videos

Time-Series Graph00:54

Time-Series Graph

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A time-series graph is a line graph with repeated measurements taken at successive intervals of time. It is also called a time series chart. To construct a time-series graph, one must look at both pieces of a paired data set. The horizontal axis is used to plot the time increments, and the vertical axis is used to plot the values of the variable that one is measuring. By using the axes in this way, each point on the graph will correspond to time and a measured quantity. The points on the graph...
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Transformations of Functions III01:20

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Transformations modify the graphical representation of a function without changing its fundamental form. One common transformation is reflection, which flips the graph across a designated axis. When the vertical coordinates of all points are multiplied by the negative one, the entire graph is mirrored over the horizontal axis. This transformation reverses the vertical orientation of peaks and troughs, akin to signal inversion in electrical systems, where a waveform is flipped, but the timing of...
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Transformations of Functions I01:29

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A function's graph can be modified by changing its position or size without altering its overall shape. These transformations allow the graph to be moved across the coordinate plane while preserving its pattern and structure. One of the most common transformations is shifting, which repositions the graph without distorting it.When the output of a function is adjusted by adding or subtracting a constant, the graph shifts vertically. A positive value moves the graph upward, while a negative value...
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Transformations of Functions II01:29

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Transformations in mathematics alter the position or orientation of a function’s graph while preserving its fundamental shape. One important type of transformation is the horizontal shift, which involves modifying the input variable within a function’s equation. This operation affects where outputs occur along the horizontal axis but does not alter the function’s overall structure.A horizontal shift is achieved by replacing the input variable x with either x + c or x - c,...
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Velocity and Position by Graphical Method01:34

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Velocity and position can be calculated from the known function of acceleration as a function of time. The total area under the acceleration-time graph and the velocity-time graph gives the change in velocity and position, respectively. In the case of an airplane, its acceleration is tracked using the inertial navigation system. The pilot provides the input of the airplane's initial position and velocity before takeoff. The inertial navigation system then uses the acceleration data to...
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Multiple Bar Graph01:07

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As the name suggests, a multiple bar graph is the same as a bar graph but has multiple bars to depict relationships between different data values. One can include as many parameters as possible. However, each parameter must have the same unit of measurement.
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Related Experiment Video

Updated: Apr 4, 2026

Trajectory Data Analyses for Pedestrian Space-time Activity Study
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Fast transformation from time series to visibility graphs.

Xin Lan1, Hongming Mo1, Shiyu Chen1

  • 1School of Computer and Information Science, Southwest University, Chongqing 400715, China.

Chaos (Woodbury, N.Y.)
|September 3, 2015
PubMed
Summary

This study introduces a faster algorithm for creating visibility graphs from time series data. The new method significantly improves efficiency compared to older techniques, aiding complex network analysis.

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Area of Science:

  • Complex Networks
  • Time Series Analysis
  • Network Science

Background:

  • The visibility graph method transforms time series data into complex network representations.
  • Efficient algorithms are crucial for analyzing large time series datasets.

Purpose of the Study:

  • To propose a fast transform algorithm for generating visibility graphs.
  • To improve the computational efficiency of visibility graph construction.

Main Methods:

  • The study employs a "divide and conquer" strategy.
  • A novel fast transform algorithm is developed for visibility graph creation.

Main Results:

  • The proposed algorithm achieves a time complexity of O(n log n).
  • This represents a significant improvement over the basic algorithm's O(n^2) time complexity.

Conclusions:

  • The developed algorithm offers a more efficient approach to visibility graph construction.
  • This advancement facilitates more scalable analysis of time series data using complex network methods.