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Related Concept Videos

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.
The z score is used to find outliers or unusual values. It should be noted that any values beyond -2 and +2 are...
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...
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...
Detection of Gross Error: The Q Test01:00

Detection of Gross Error: The Q Test

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...
Modified Boxplots00:57

Modified Boxplots

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.
However, the box plot does not tell the reader about outliers - values that lie far from the center of the data. We can modify the standard box and whisker plot to identify the outliers and visualize the actual spread of the data in a sample.
Initially, we calculate the adjusted...
Trimmed Mean01:10

Trimmed Mean

While measuring the mean of a data set, care needs to be taken when associating the mean to its central tendency. The same goes for the arithmetic mean, the geometric mean, or the harmonic mean. This is because the presence of a single outlier data value can significantly affect the mean. That is, the mean is sensitive to fluctuations in the data set.
Although certain measures of central tendency are not sensitive to outliers, there are alternative versions of the mean that get around the...

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Related Experiment Video

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Competitive Genomic Screens of Barcoded Yeast Libraries
11:59

Competitive Genomic Screens of Barcoded Yeast Libraries

Published on: August 11, 2011

Closest string with outliers.

Christina Boucher1, Bin Ma

  • 1David R Cheriton School of Computer Science, University of Waterloo, Waterloo, ON. cabouche@cs.uwaterloo.ca

BMC Bioinformatics
|February 24, 2011
PubMed
Summary
This summary is machine-generated.

The closest string with outliers (CSWO) problem refines pattern finding by allowing for a specified number of outlier strings. This approach identifies a central pattern and potential outliers in datasets, crucial for bioinformatics applications.

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Area of Science:

  • Computational biology
  • Bioinformatics algorithms
  • Stringology

Background:

  • The standard closest string problem seeks a center string within a fixed Hamming distance (d) of all input strings.
  • This model is sensitive to outliers, which can significantly impact results.
  • Identifying common patterns in datasets with potential noise is a key challenge.

Purpose of the Study:

  • To introduce and analyze the closest string with outliers (CSWO) problem.
  • To develop algorithms for finding a representative string and identifying outliers in datasets.
  • To extend existing models for pattern discovery in biological sequences.

Main Methods:

  • Formalized the closest string with outliers (CSWO) problem, allowing for k outliers.
  • Developed fixed-parameter tractable algorithms for CSWO with respect to parameters d and k.
  • Analyzed the computational complexity for both bounded and unbounded alphabets.

Main Results:

  • The CSWO model successfully identifies a center string within distance d of at least n-k input strings.
  • Algorithms were provided for CSWO, demonstrating its computability.
  • The problem was shown to be W[1]-hard for unbounded alphabets concerning n-k, ℓ, and d.

Conclusions:

  • The CSWO model provides a robust method for finding common patterns in datasets containing outliers.
  • The study initiates the investigation into the computability and parameter sensitivity of CSWO.
  • Further research is suggested on open problems related to this refined model.