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Data Mining DataLecture Notes for Chapter 2IntroducOllieShoresna
Data Mining: Data
Lecture Notes for Chapter 2
Introduction to Data Mining
by
Tan, Steinbach, Kumar
What is Data?Collection of data objects and their attributes
An attribute is a property or characteristic of an objectExamples: eye color of a person, temperature, etc.Attribute is also known as variable, field, characteristic, or featureA collection of attributes describe an objectObject is also known as record, point, case, sample, entity, or instance
Attributes
Objects
Attribute ValuesAttribute values are numbers or symbols assigned to an attribute
Distinction between attributes and attribute valuesSame attribute can be mapped to different attribute values Example: height can be measured in feet or meters
Different attributes can be mapped to the same set of values Example: Attribute values for ID and age are integers But properties of attribute values can be different
ID has no limit but age has a maximum and minimum value
Types of Attributes There are different types of attributesNominalExamples: ID numbers, eye color, zip codesOrdinalExamples: rankings (e.g., taste of potato chips on a scale from 1-10), grades, height in {tall, medium, short}IntervalExamples: calendar dates, temperatures in Celsius or Fahrenheit.RatioExamples: temperature in Kelvin, length, time, counts
Properties of Attribute Values The type of an attribute depends on which of the following properties it possesses:Distinctness: = Order: < > Addition: + - Multiplication: * /
Nominal attribute: distinctnessOrdinal attribute: distinctness & orderInterval attribute: distinctness, order & additionRatio attribute: all 4 properties
Attribute Type
Description
Examples
Operations
Nominal
The values of a nominal attribute are just different names, i.e., nominal attributes provide only enough information to distinguish one object from another. (=, )
zip codes, employee ID numbers, eye color, sex: {male, female}
mode, entropy, contingency correlation, 2 test
Ordinal
The values of an ordinal attribute provide enough information to order objects. (<, >)
hardness of minerals, {good, better, best},
grades, street numbers
median, percentiles, rank correlation, run tests, sign tests
Interval
For interval attributes, the differences between values are meaningful, i.e., a unit of measurement exists.
(+, - )
calendar dates, temperature in Celsius or Fahrenheit
mean, standard deviation, Pearson's correlation, t and F tests
Ratio
For ratio variables, both differences and ratios are meaningful. (*, /)
temperature in Kelvin, monetary quantities, counts, age, mass, length, electrical current
geometric mean, harmonic mean, percent variation
Attribute Level
Transformation
Comments
Nominal
Any permutation of values
If all employee ID numbers were reassigned, would it make any difference?
Ordinal
An order preserving change of values, i.e.,
new_value = f(old_value)
where f is a monotonic function.
An attribut ...
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8. Signature of transform()
§ Invocation 1:
§ Resulting metadata: # distinct values in categorical columns, list of distinct values with their
recoded IDs, number of bins, bin width, etc.
§ An existing transformation can be applied to new data using the metadata generated in an
earlier invocation
§ Invocation 2:
8
output = transform (target = input,
spec = specification,
transformPath = "/path/to/metadata“);
output = transform (target = input,
transformPath = "/path/to/new_metadata“
applyTransformPath = "/path/to/metadata“);
11. Pre-Processing Training and
Testing Data
Training phase
Testing phase
11
Train = read ("/user/ml/trainset.csv");
Spec = read("/user/ml/tf.spec.json“, data_type = "scalar",
value_type = "String");
trainD = transform (target = Train,
transformSpec = Spec,
transformPath = "/user/ml/train_tf_metadata");
# Build a predictive model using trainD
...
Test = read ("/user/ml/testset.csv");
testD = transform (target = Test,
transformPath = "/user/ml/test_tf_metadata",
applyTransformPath = "/user/ml/train_tf_metdata");
# Test the model using testD
...
12. Cross Validation
K-fold Cross Validation:
1. Shuffle the data points
2. Divide the data points into 𝑘 folds of (roughly)
the same size
3. For 𝑖 = 1, … , 𝑘:
• Train each model on all the data points that
do not belong to fold 𝑖
• Test each model on all the examples in fold 𝑖
and compute the test error
4. Select the model with the minimum average test
over all 𝑘 folds
5. (Train the winning model on all the data points)
12
Testing Training
Example: 𝑘 = 5
14. Univariate Statistics
14
Row Name of Statistic Scale Category
1 Minimum +
2 Maximum +
3 Range +
4 Mean +
5 Variance +
6 Standard deviation +
7 Standard error of mean +
8 Coefficient of variation +
9 Skewness +
10 Kurtosis +
11 Standard error of skewness +
12 Standard error of Kurtosis +
13 Median +
14 Intequartilemean +
15 Number of categories +
16 Mode +
17 Number of modes +
Central tendency measures
Dispersion measures
Shape measures
Categorical measures
20. Nominal-vs-Scale Statistics
𝐹 statistic
§ A measure for the strength of association between a categorical feature and a scale
feature
§ Assumptions (𝑥 categorical, 𝑦 scale):
§ 𝑦 ~ 𝑁𝑜𝑟𝑚𝑎𝑙 𝜇, 𝜎)
- same variance for all 𝑥
§ 𝑥 has small value domain with large frequency counts, 𝑥A non-random
§ All records are iid
§ Under independence assumption 𝐹 distributed approximately 𝐹(𝑘 − 1, 𝑛 − 𝑘)
20
𝐹 =
∑ 𝑓𝑟𝑒𝑞 𝑥 𝑦B 𝑥 − 𝑦k )/(𝑘 − 1)5
∑ 𝑦A − 𝑦B 𝑥A
)/(𝑛 − 𝑘)C
AD0
=
𝜂)(𝑛 − 𝑘)
1 − 𝜂)(𝑘 − 1)
ESS: Explained Sum of Squares
RSS
Degrees of freedom
Degrees of freedom