Learning notes on Data Mining: Part 1

What is Data Mining

Knowledge Discovery from Data.

Iterative step:

• Data cleaning
• Data integrating(from multiple source)
• Data selecting
• Data transforming
• Data mining
• Pattern evaluating
• Knowledge representing

Tasks

Descriptive

Data characterization: Summarize main features on target class.

Data discrimination: Compare main features of target classes.

Frequent pattern discovery: frequent item set

ordered: sequence pattern

structured: structure pattern

Predictive

Classification & Regression

Clustering: have no knowledge of class.

Outlier analysis

What is interesting

• Easy to understand or interpretable
• Vaildation when meet the objective criteria like

$$ \text{support}(X \Rightarrow Y) := P(X \lor Y) $$

$$ \text{confidence}(X \Rightarrow Y) := P(Y | X) $$

or subjective ones

• Potential useful
• Novel

Challanges

• Ways of mining
• Effectiveness and scalability
• Visualizaion
• Multiple types of data
• Its impact about society

Data attributes

Categorical

mode only

• Binary: limited to 2

Symmetric: carried same weight

Asymmetric: not equally important

• Ordinal: have order

mode and median

Numeric

mean, mode and median

• interval-scaled: allow data go to negative and zero only represent numeric meaning

ratio is meaningless here

• ratio-scaled: data never fall below or reach zero and zero has the property of absolute.

contrary to the one above

Data description

Central tendency measurement

• Mean

Imbalanced importance: weighted mean

Sensitive to outlier: trimmed mean

• Median

For imbalanced data.

For large dataset, the interpolation way to calculate is as follows.

$$ \text{median} = L + \left( \frac{N}{2} + \sum_{l} freq_l \right) \frac{width}{freq_{\text{median}}} $$

where L is the low bound of the range of median, N is the count of data, sum(freq)_l is the sum of all frequency of ranges which is lower than median range, freq_median is the frequency of the median range and width is the width of of median range.

• Mode

May exists multiple mode

Data distribution

• Range = max - min
• Quantile

Selected data that split total data equally in size.

Median is a specialized version of this.

Interquartile range (IQR): Q3 - Q1

Five-number summary: ordered(min, Q1, median, Q3, max) vis=boxplot

• Variance

$$ \left(\frac{\sum(xi^2)}{N}\right)^2 - x_{mean}^2 $$

• Standart deviation

Square root of variance

Graph

• Quantile plot

univariable

x: percentage

y: value

• Quantile-quantile plot

bivariable

• Histogram

Bar chart: categotical

Histogram: Numerical

• Scatter plot

Visualization

• Pixel-oriented technique

Not suitable for high dimension data

Space-filling curve

Hilbert, Grey, Z

Detailed explaination

Circle segment techinique

TODO

• Geomertic projection

Scatter matrix: half is enough

Parallel coordinates

TODO

• Icon-based

Too wired

Chernoff faces

Stick figure

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