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Related Concept Videos

Quantifying and Rejecting Outliers: The Grubbs Test01:02

Quantifying and Rejecting Outliers: The Grubbs Test

Sometimes, a data set can have a recorded numerical observation that greatly  deviates from the rest of the data. Assuming that the data is normally distributed, a statistical method called the Grubbs test can be used to determine whether the observation is truly an outlier.  To perform a two-tailed Grubbs test, first, calculate the absolute difference between the outlier and the mean. Then, calculate the ratio between this difference and the standard deviation of the sample. This number is...
What Are Outliers?01:12

What Are Outliers?

Outliers are observed data points that are far from the least squares line. They have unusual values and need to be examined carefully. Though an outlier may result from erroneous data, at other times, it may hold valuable information about the population under study and should be included in the data. Hence, it is crucial to examine what causes a data point to be an outlier.
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Outliers and Influential Points01:08

Outliers and Influential Points

An outlier is an observation of data that does not fit the rest of the data. It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500), while others may indicate that something unusual is happening. Outliers are present far from the least squares line in the vertical direction. They have large "errors," where the "error" or residual is the vertical...
Modified Boxplots00:57

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Detection of Gross Error: The Q Test01:00

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When one or more data points appear far from the rest of the data, there is a need to determine whether they are outliers and whether they should be eliminated from the data set to ensure an accurate representation of the measured value. In many cases, outliers arise from gross errors (or human errors) and do not accurately reflect the underlying phenomenon. In some cases, however, these apparent outliers reflect true phenomenological differences. In these cases, we can use statistical methods...
Depth Perception and Spatial Vision01:15

Depth Perception and Spatial Vision

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Related Experiment Videos

Outlier detection with the kernelized spatial depth function.

Yixin Chen1, Xin Dang, Hanxiang Peng

  • 1Department of Computer and Information Science, University of Mississippi, University, MS 38677, USA. ychen@cs.olemiss.edu

IEEE Transactions on Pattern Analysis and Machine Intelligence
|December 27, 2008
PubMed
Summary
This summary is machine-generated.

We introduce the kernelized spatial depth (KSD), a novel statistical depth function for multidimensional data. KSD effectively detects outliers by generalizing spatial depth, capturing local data structures for improved outlier detection performance.

Related Experiment Videos

Area of Science:

  • Statistics
  • Machine Learning
  • Data Mining

Background:

  • Statistical depth functions offer a way to order multidimensional data from the center outwards.
  • Depth functions are crucial for identifying outliers, which are observations significantly different from the rest of the data.
  • Spatial depth is a computationally efficient and mathematically tractable depth measure, but it may fail to capture local data structures.

Purpose of the Study:

  • To propose a novel statistical depth measure, the kernelized spatial depth (KSD), which generalizes spatial depth.
  • To develop a new outlier detection algorithm based on the KSD.
  • To demonstrate KSD's ability to capture local data structures where spatial depth fails.

Main Methods:

  • Generalizing spatial depth using positive definite kernels to create the kernelized spatial depth (KSD).
  • Developing an outlier detection algorithm where observations with KSD below a threshold are classified as outliers.
  • Analyzing the false alarm probability of the depth-based detector and providing upper bounds for threshold determination.

Main Results:

  • The KSD successfully captures local data structures, as shown with half-moon and ring-shaped data.
  • The proposed KSD-based outlier detection algorithm is effective in both one-class learning and missing label scenarios.
  • The algorithm demonstrated competitive performance against existing outlier detection methods in extensive experiments.

Conclusions:

  • The kernelized spatial depth (KSD) offers a powerful generalization of spatial depth for outlier detection.
  • The KSD-based outlier detection algorithm is robust, parameter-efficient, and performs competitively.
  • KSD provides a valuable tool for identifying extreme observations in complex datasets.