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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

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

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?

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