Data Mining and KD at TU München

Flashcards and summaries for Data Mining and KD at the TU München

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Scales for numerical measurements

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How do you represent data  when there is no feature vector for the objects

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What does Fourier analysis allow us?

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Fuzzy histogram

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Histogram

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Sammon mapping

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MDS - what is it?

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Why do we need data transformation?


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Exponential filter

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Asymmetric windows

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Symmetric filtering

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Inlier - how to detect?

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Exemplary flashcards for Data Mining and KD at the TU München on StudySmarter:

Data Mining and KD

Scales for numerical measurements

Ratio 

= > < + –  * /

21 years, 273 Kelvin

Generalized mean

Interval

= > < + – 
2015 A.D, 20 C 

Mean

Ordinal

> < = 

A,B,C,D,F

Median

Nominal

Alice, Bob, Carol

Mode

Data Mining and KD

How do you represent data  when there is no feature vector for the objects

the relation of all pairs of objects can often be quantified and written as a square matrix


Each relation may refer to a degree of:

  • similarity, dissimilarity,
  • compatibility, incompatibility, 
  • proximity or distance

Data Mining and KD

What does Fourier analysis allow us?

Given time series data, Fourier analysis allows us to compute the 

  • amplitude spectrum Y (y1….ym) and the 
  • phase spectrum P (p1….pm)

that represent the:

frequencies, amplitudes, and phase angles of the spectral components of the time series.

Data Mining and KD

Fuzzy histogram

  • partially counts data for several neighboring bins
  • For example, a number at the border between two bins may be counted as half for one and a half for the other bin

Data Mining and KD

Histogram

  • Equally sized intervals
  • The left and right borders of each bar represent the lower and upper limits of the corresponding data interval. 
  • The height of each bar

    represents the interval count.

Data Mining and KD

Sammon mapping

Idea: map a dataset X to a data set Y

like MDS,


it simply provides a measure of how well the result of a transformation reflects the structure present in the original dataset, in the sense described above.

In other words, we are attempting not to find an optimal mapping to apply to the original data, but rather to construct a new lower-dimensional dataset, which has structure as similar to the first dataset as possible.

Data Mining and KD

MDS - what is it?

MDS of a feature data set X yields the same results as PCA.

More than PCA:

produce an (approximate) feature space representation Y for relational data specified
by a Euclidean distance matrix D.

Data Mining and KD


Why do we need data transformation?


  • incorrect results may be obtained IF the ranges of the feature are so different
  • Also the choice of the feature units might be arbitrary. 

Data Mining and KD

Exponential filter

  • The exponential filter works best with slow changes of the filtered data
  • for time series
  • The current filter output is affected by each past filter output  with the multiplier so the filter exponentially forgets previous filter outputs, hence the name exponential filter.
  • The outlier suppression is much
    weaker than with the median filter

Data Mining and KD

Asymmetric windows

  • Even order
  • Asymmetric windows are also suitable for online filtering and are able to provide each filter output yk as soon as xk is known.

Data Mining and KD

Symmetric filtering

odd order q=(3; 5; 7…..)

Symmetric windows are only suitable for offline filtering when the future values of the series are already known

Data Mining and KD

Inlier - how to detect?

  • They are local outliers
  • Can be  detected when considering the differential change of subsequent values

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