《 data mining 》 National Defense University of science and technology
《 data mining 》 Qingdao University
《 Data mining and python practice 》

Understanding of data mining

1. Data and information

** data (data)** Is the result of fact or observation , It is a logical induction of objective things , It is used to express objective things Unprocessed raw material .

In computer system , Various letters 、 Combination of numbers and symbols 、 voice 、 graphics 、 Images and the like are collectively referred to as data , After data processing become Information .

2. Data object and attribute type

Data set from Data objects form , A data object corresponds to an entity , Data objects can also be Tuples .
Data fields used to represent the characteristics or functions of data objects are called attribute .
Attribute types ：

1. Nominal properties nominal： States can be enumerated
   special ： Binary properties ,（0,1）
   · Symmetric binary ： The quantity is equal to
   · Asymmetric binary ： The quantity gap is large
2. Ordinal property ordinal： Meaningful order , Ruda 、 in 、 Small
3. Interval scaling attribute interval scaled： Measure in order of unit length , Value order , No zero point , Multiples are meaningless
4. Ratio scale attribute ratio scaled： Numerical properties with fixed zeros , Ordered and computable multiples
   （ Nominal and narrative attributes are qualitative , Interval scaling attribute and ratio scaling attribute are quantitative ）

Discrete properties (Discrete Attribute)& Continuous attributes (Continuous Attribute)

2. Data statistics

Concentration trend

1. mean value mean
2. Median median
3. The number of mode
   Empirical formula ：mean - mode = 3×(mean - median)

Discrete trends 【 A measure of the degree of variation 】

1. range （range, Full range ）： The difference between the maximum and the minimum
2. variance （Variance）： The difference between the data value and the average
   
3. Standard deviation （Standard deviation）： The positive square root of variance
4. Coefficient of variation ： A measure of the magnitude of the standard deviation relative to the mean
   

quantile

Four percentile （quartile）: Q1 (25th Percentiles percentile), Q3 (75th percentile)
Middle quartile range （Inter-quartile range）: IQR = Q3 – Q1
Five numbers sum up : min, Q1, median, Q3, max

3. Data visualization

Data visualization 、 Process visualization 、 Result visualization
Basic statistical chart ：

1. boxplot / Box chart （Box plot）： It can analyze the distribution difference of multiple attribute data
   
   outliers ： Usually higher or lower than 1.5 IQR Value
2. Histogram ： It can analyze the change distribution of a single attribute in each interval
3. Scatter plot ： It can be used to display the correlation distribution of two sets of data , positive correlation 、 negative correlation 、 Unrelated

4. Data similarity

Data matrix ：N×p,N Data ,p Dimensions
Dissimilarity matrix ,N Data points , Record the distance between two points , Lower triangular matrix

Similarity measure

1. Similarity degree similarity：[0,1], The larger the value, the more similar
2. The degree of difference dissimilarity/distance： The smaller the value, the more similar
3. Proximity proximity （ Similarity or dissimilarity ）

（1） Proximity measurement of nominal attributes

For binary attributes ：

（2） Proximity measurement of ordinal attributes

（3） Proximity measurement of numerical attributes
① Minkowski distance Minkovski distance


Manhattan distance Manhattan Distance：L1 norm
Euclidean distance Euclidean Distance：L2 norm
Supremum distance / Chebyshev distance Supremum Distance：L_max,L_∞ norm （ Between all attributes , The biggest difference is the distance between the two objects ）
② Z-score（ Standardization ）
③ Cosine similarity
cos(d1, d2) = (d1 • d2) /||d1|| ||d2||

（4） Proximity measurement of mixed attributes