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Related Concept Videos

Quantifying and Rejecting Outliers: The Grubbs Test01:02

Quantifying and Rejecting Outliers: The Grubbs Test

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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...
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What Are Outliers?01:12

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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.
The z score is used to find outliers or unusual values. It should be noted that any values beyond -2 and +2 are...
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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...
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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...
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Modified Boxplots00:57

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A standard box and whisker plot informs us about the spread of the data in a given sample. One can identify the minimum value, maximum value, first quartile value, second quartile or median value, and third quartile.
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Fisher's exact test is a statistical significance test widely used to analyze 2x2 contingency tables, particularly in situations where sample sizes are small. Unlike the chi-squared test, which approximates P-values and assumes minimum expected frequencies of at least five in each cell, Fisher's exact test calculates the exact probability (P-value) of observing the data or more extreme results under the null hypothesis. This feature makes it especially valuable when the assumptions of...
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A one-class kernel fisher criterion for outlier detection.

Franck Dufrenois

    IEEE Transactions on Neural Networks and Learning Systems
    |July 23, 2014
    PubMed
    Summary

    A new kernelized Fisher's linear discriminant method efficiently separates normal data from outliers. This approach simplifies model selection by using a Gaussian kernel's contrast measure to find the optimal kernel width, avoiding complex cross-validation.

    Area of Science:

    • Machine Learning
    • Data Mining
    • Statistical Pattern Recognition

    Background:

    • Outlier detection is crucial for data integrity.
    • Fisher's linear discriminant (FLD) is effective for classification.
    • Previous FLD methods for outlier detection required iterative optimization.

    Purpose of the Study:

    • To introduce a kernelized version of Dufrenois and Noyer's one-class Fisher's linear discriminant.
    • To simplify the optimization process by decoupling subspace selection and clustering.
    • To develop an efficient model selection strategy for kernelized outlier detection.

    Main Methods:

    • Formulated label vector estimation as an unconstrained binary linear problem (UBLP).
    • Solved UBLP using an iterative perturbation method.

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  • Obtained optimal projection subspace via a generalized eigenvalue problem.
  • Utilized a Gaussian kernel's contrast measure for kernel width selection.

    • Main Results:

    • The kernelized criterion decouples subspace selection and clustering.
    • The proposed method efficiently estimates the label vector and optimal subspace.
    • The Gaussian kernel's contrast measure effectively guides kernel width selection, simplifying model selection.
    • The algorithm demonstrates competitive performance against existing novelty detection methods on synthetic and real datasets.

    Conclusions:

    • The kernelized Fisher's linear discriminant offers an efficient approach to outlier detection.
    • The integrated model selection strategy significantly reduces computational cost.
    • This method provides a robust and simplified alternative for identifying anomalies in data.