Transcript Lecture 2 Slides
Chapter 2 Overview of the Data Mining Process
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Introduction
• • Data Mining – Predictive analysis • • Tasks of Classification & Prediction Core of Business Intelligence Data Base Methods – OLAP – SQL – Do not involve statistical modeling 2
Core Ideas in Data Mining
• Analytical Methods Used in Predictive Analytics – Classification • Used with categorical response variables • E.g. Will purchase be made / not made?
– Prediction • Predict (estimate) value of continuous response variable • Prediction used with categorical as well – Association Rules • Affinity analysis – “what goes with what” • Seeks correlations among data 3
Core Ideas in Data Mining
• • • Data Reduction – Reduce variables – Group together similar variables Data Exploration – View data as evidence – Get “a feel” for the data Data Visualization – Graphical representation of data – Locate tends, correlations, etc.
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Supervised Learning
• • “Supervised learning" algorithms are those used in classification and prediction . – Data is available in which the value of the outcome of interest is known . “Training data" are the data from which the classification or prediction algorithm “learns," or is “trained," about the relationship between predictor variables and the outcome variable . • This process results in a “model” – – Classification Model Predictive Model 5
Supervised Learning
• Model is then run with another sample of data – – – “validation data" the outcome is known but we wish to see how well the model performs If many different models are being tried out, a third sample of known outcomes -“test data” is used with the final, selected model to predict how well it will do. • The model can then be used to classify or predict the outcome of interest in new cases where the outcome is unknown. 6
Supervised Learning
• Linear regression analysis is an example of supervised Learning – The Y variable is the (known) outcome variable – – The X variable is some predictor variable. A regression line is drawn to minimize the sum of squared deviations between the actual Y values and the values predicted by this line. – The regression line can now be used to predict Y values for new values of X for which we do not know the Y value. 7
Unsupervised Learning
• No outcome variable to predict or classify • No “learning” from cases • Unsupervised leaning methods – – – Association Rules Data Reduction Methods Clustering Techniques 8
The Steps in Data Mining
• • 1. Develop an understanding of the purpose of the data mining project – – It is a one-shot effort to answer a question or questions or Application (if it is an ongoing procedure).
2. Obtain the dataset to be used in the analysis. – Random sampling from a large database to capture records to be used in an analysis – Pulling together data from different databases. • Internal (e.g. Past purchases made by customers) • External (credit ratings). – Usually the analysis to be done requires only thousands or tens of thousands of records.
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The Steps in Data Mining
• 3. Explore, clean, and preprocess the data – – – Verifying that the data are in reasonable condition. How missing data should be handled? Are the values in a reasonable range, given what you would expect for each variable? – Are there obvious “outliers?" – Data are reviewed graphically – • For example, a matrix of scatter plots showing the relationship of each variable with each other variable. – Ensure consistency in the definitions of fields, units of measurement, time periods, etc.
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The Steps in Data Mining
• • • 4. Reduce the data – If supervised training is involved separate them into training, validation and test datasets. – Eliminating unneeded variables, • Transforming variables – Turning “money spent" into “spent > $100" vs. “Spent · $100"), • Creating new variables – A variable that records whether at least one of several products was purchased – Make sure you know what each variable means, and whether it is sensible to include it in the model.
5. Determine the data mining task – Classification, prediction, clustering, etc.
6. Choose the data mining techniques to be used – Regression, neural nets, hierarchical clustering, etc.
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• • •
The Steps in Data Mining
7. Use algorithms to perform the task. – Iterative process - trying multiple variants, and often using multiple variants of the same algorithm (choosing different variables or settings within the algorithm). – When appropriate, feedback from the algorithm's performance on validation data is used to refine the settings.
8. Interpret the results of the algorithms. – Choose the best algorithm to deploy, – Use final choice on the test data to get an idea how well it will perform. 9. Deploy the model. – Integrate the model into operational systems – Run it on real records to produce decisions or actions. – For example, the model might be applied to a purchased list of possible customers, and the action might be “include in the mailing if the predicted amount of purchase is > $10." 12
Preliminary Steps
• • • Organization of datasets – Records in rows – Variables in columns • In supervised learning one of these will be the outcome variable • Labels the first or last column Sampling from a database – Use a samples to create, validate, & test model Oversampling rare events – If response variable value is seldom found in data then sample size increase – Adjust algorithm as necessary 13
Preliminary Steps (Pre-processing and Cleaning the Data)
• Types of variables – Continuous – assumes a any real numerical value (generally within a specified range) – Categorical – assumes one of a limited number of values • • • Text (e.g. Payments e {current, not current, bankrupt} Numerical (e.g. Age e {0 … 120} ) Nominal (payments) • Ordinal (age) 14
• •
Preliminary Steps (Pre-processing and Cleaning the Data)
Handling categorical variables – If categorical is ordered then it can be used as continuous variable (e.g. Age, level of credit, etc.) – Use of “dummy” variables when range of values not large • e.g. Variable occupation e {student, unemployed, employed, retired} • Create binary (yes/no) dummy variables – Student – yes/no – Unemployed – yes/no – – Employed – yes/no Retired – yes/no Variable selection – The more predictor variables the more records need to build the model – Reduce number of variables whenever appropriate 15
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Preliminary Steps (Pre-processing and Cleaning the Data)
Overfitting – Building a model - describe relationships among variables in order to predict future outcome (dependent) values on the basis of future predictor (independent) values.
– Avoid “explaining“ variation in the data that was nothing more than chance variation. Avoid mislabeling “noise” in the data as if it were a “signal” – Caution - if the dataset is not much larger than the number of predictor variables, then it is very likely that a spurious relationship like this will creep into the model 16
Overfitting
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•
Preliminary Steps (Pre-processing and Cleaning the Data)
How many variables & how much data • A good rule of thumb is to have ten records for every predictor variable. • For classification procedures – – At least 6xmxp records, Where m = number of outcome classes, and p = number of variables • Compactness or parsimony is a desirable feature in a model. • • A matrix of x-y plots can be useful in variable selection. Can see at a glance x-y plots for all variable combinations. – A straight line would be an indication that one variable is exactly correlated with another. – We would want to include only one of them in our model. • • Weed out irrelevant and redundant variables from our model Consult domain expert whenever possible 18
Preliminary Steps (Pre-processing and Cleaning the Data)
• Outliers – Values that lie far away from the bulk of the data are called outliers – no statistical rule can tell us whether such an outlier is the result of an error – these are judgments best made by someone with “domain" knowledge – if the number of records with outliers is very small, they might be treated as missing data.
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•
Preliminary Steps (Pre-processing and Cleaning the Data)
Missing values – If the number of records with missing values is small, those records might be omitted – The more variables, the more records to dropped • Solution - use average value computed from records with valid data for variable with missing data • Reduces variability in data set – Human judgment can be used to determine best way to handle missing data 20
Preliminary Steps (Pre-processing and Cleaning the Data)
• Normalizing (standardizing) the data – To normalize the data, we subtract the mean from each value, and divide by the standard deviation of the resulting deviations from the mean • Expressing each value as “number of standard deviations away from the mean“ – the z-score • Needed if variables are in different units e.G. Hours, thousands of dollars, etc.
– Clustering algorithms measure variables values in distance from each other – need a standard value for distance.
– Data mining software, including XLMiner, typically has an option that normalizes the data in those algorithms where it may be required 21
Preliminary Steps
• Use and creation of partition – Training partition • The largest partition • Contains the data used to build the various models • Same training partition is generally used to develop multiple models.
– Validation partition • Used to assess the performance of each model, • Used to compare models and pick the best one. • In classification and regression trees algorithms the validation partition may be used automatically to tune and improve the model.
– Test partition • Sometimes called the “holdout" or “evaluation" partition is used to assess the performance of a chosen model with new data.
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The Three Data Partitions and Their Role in the Data Mining Process
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A CRIM 0.006
0.027
0.027
0.032
0.069
0.030
0.088
0.145
0.211
0.170
B
Example – Linear Regression
D
Boston Housing Data
E F G H I J K L M C N ZN INDUS CHAS 18 0 2.31
7.07
0 0 12.5
12.5
12.5
12.5
0 0 0 0 7.07
2.18
2.18
2.18
7.87
7.87
7.87
7.87
0 0 0 0 0 0 0 0 NOX 0.54
0.47
0.47
0.46
0.46
0.46
0.52
0.52
0.52
0.52
RM 6.58
6.42
7.19
7.00
7.15
6.43
6.01
6.17
5.63
6.00
AGE 65.2
78.9
61.1
45.8
54.2
58.7
66.6
96.1
100 85.9
DIS RAD 4.09
4.97
1 2 4.97
6.06
6.06
6.06
5.56
5.95
6.08
6.59
2 3 3 3 5 5 5 5 TAX PTRATIO 296 242 15.3
17.8
242 222 222 222 311 311 311 311 17.8
18.7
18.7
18.7
15.2
15.2
15.2
15.2
B LSTAT 397 397 5 9 393 395 397 394 396 397 387 387 4 3 5 5 12 19 30 17 O MEDV CAT. MEDV 24 21.6
34.7
33.4
36.2
28.7
22.9
27.1
16.5
18.9
0 0 1 1 1 0 0 0 0 0 24
CRIM per capita crime rate by town ZN proportion of residential land zoned for lots over 25,000 sq.ft. INDUS proportion of non-retail business acres per town. CHAS Charles River dummy variable (1 if tract bounds river; 0 otherwise) NOX nitric oxides concentration (parts per 10 million) RM average number of rooms per dwelling AGE proportion of owner-occupied units built prior to 1940 DIS weighted distances to five Boston employment centres RAD index of accessibility to radial highways TAX full-value property-tax rate per $10,000 PTRATIO pupil-teacher ratio by town B 1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town LSTAT % lower status of the population MEDV Median value of owner-occupied homes in $1000 25
Partitioning the data
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Using XLMiner for Multiple Linear Regression 27
Specifying Output
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Row Id.
10 12 17 18 1 4 5 6 9
Prediction of Training Data
Predicted Value
30.24690555
28.61652272
27.76434086
25.6204032
11.54583087
19.13566187
21.95655773
20.80054199
16.94685562
Actual Value Residual
24 -6.246905549
33.4
4.783477282
36.2
28.7
16.5
8.435659135
3.079596801
4.954169128
18.9 -0.235661871
18.9
-3.05655773
23.1
17.5
2.299458015
0.553144385
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Prediction of Validation Data
Row Id.
8 11 13 14 15 16 2 3 7
Predicted Value
25.03555247
30.1845219
23.39322259
19.58824389
18.83048747
21.20113865
19.81376359
19.42217211
19.63108414
Actual Value Residual
21.6 -3.435552468
34.7
4.515478101
22.9 -0.493222593
27.1
7.511756109
15 -3.830487466
21.7
20.4
0.498861352
0.586236414
18.2 -1.222172107
19.9
0.268915856
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Summary of errors
Training Data scoring - Summary Report Total sum of squared errors
6977.106
RMS Error Average Error
4.790720883
3.11245E-07
Validation Data scoring - Summary Report Total sum of squared errors
4251.582211
RMS Error Average Error
4.587748542
-0.011138034
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RMS error
• • • Error = actual - predicted RMS = Root-mean-squared error = Square root of average squared error • In previous example, sizes of training and validation sets differ, so only RMS Error and Average Error are comparable 32
Using Excel and XLMiner for Data Mining
• • • • Excel is limited in data capacity However, the training and validation of DM models can be handled within the modest limits of Excel and XLMiner Models can then be used to score larger databases XLMiner has functions for interacting with various databases (taking samples from a database, and scoring a database from a developed model) 33
Simple Regression Example
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Simple Regression Model
• • Make prediction about the starting salary of a current college graduate Data set of starting salaries of recent college graduates
Data Set Compute Average Salary How certain are of this prediction?
There is variability in the data.
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•
Simple Regression Model
Use total variation as an index of uncertainty about our prediction
Compute Total Variation
• The smaller the amount of total variation the more accurate (certain) will be our prediction.
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•
Simple Regression Model
How “explain” the variability - Perhaps it depends on the student’s GPA Salary GPA 37
Simple Regression Model
• • Find a linear relationship between GPA and starting salary As GPA increases/decreases starting salary increases/decreases 38
•
Simple Regression Model
Least Squares Method to find regression model – Choose a and b in regression model (equation) so that it minimizes the sum of the squared deviations – actual Y value minus predicted Y value (Y-hat) 39
•
Simple Regression Model
How good is the model?
a= 4,779 & b = 5,370 A computer program computed these values u-hat is a “residual” value The sum of all u-hats is zero The sum of all u-hats squared is the total variance not explained by the model “unexplained variance” is 7,425,926 40
Simple Regression Model
Total Variation = 23,000,000 41
Simple Regression Model
Total Unexplained Variation = 7,425,726 42
Simple Regression Model
• • Relative Goodness of Fit – Summarize the improvement in prediction using regression model Compute R 2 – coefficient of determination Regression Model (equation) a better predictor than guessing the average salary The GPA is a more accurate predictor of starting salary than guessing the average R 2 is the “performance measure“ for the model.
Predicted Starting Salary = 4,779 + 5,370 * GPA 43
Detailed Regression Example
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Obs #
1 2 3 4 5 6 7 8 9 10
Salary
20000 24500 23000 25000 20000 22500 27500 19000 24000 28500
Data Set
GPA
2.8 3.4 3.2 3.8 3.2 3.4 4.0 2.6 3.2 3.8
Months Work
48 24 24 24 48 36 20 48 36 12 45
Scatter Plot - GPA vs Salary
4,5 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 0,0 0 5000 10000 15000 20000 25000 30000 46
60 50 40 30 20 10 0 0
Scatter Plot - Work vs Salary
5000 10000 15000 20000 25000 30000 47
Pearson Correlation Coefficients -1 <= r <= 1
Salary GPA Months Work
Salary
1 0.898007
-0.93927
GPA
1 -0.82993
Months Work
1 48
Three Regressions
• • • • Salary = f(GPA) Salary = f(Work) Salary = f(GPA, Work) Interpret Excel Output 49
Interpreting Results
• • Regression Statistics – Multiple R, – R 2 , – R 2 adj – Standard Error S y Statistical Significance – t-test – p-value – F test 50
Regression Statistics Table
• • • • Multiple R – R = square root of R 2 R 2 – Coefficient of Determination R 2 adj – used if more than one x variable Standard Error S y – This is the sample estimate of the standard deviation of the error (actual – predicted) 51
ANOVA Table
• • • • Table 1 gives the F statistic Tests the claim – there is no significant relationship between your all of your independent and dependent variables The significance F value is a p-value should reject the claim: – –
Of NO significant relationship between your independent and dependent variables if p<
Generally = 0.05
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Regression Coefficients Table
• Coefficients Column gives – – – b 1 value is next to your independent variable x 1 – The b 0 is the intercept b 2 is next to your independent variable x 2 .
– b 0 , b 1, , b 2 , … , b n values for the regression equation. b 3 is next to your independent variable x 3 53
Regression Coefficients Table
• • • p values for individual t tests each independent variables t test - tests the claim that there is no relationship between the independent variable (in the corresponding row) and your dependent variable.
Should reject the claim •
Of NO significant relationship between your independent variable (in the corresponding row) and dependent variable if p<
.
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Regression Statistics
Multiple R R Square Adjusted R Square Standard Error Observations
Salary = f(GPA)
f(GPA)
0.898006642
0.806415929
0.78221792
1479.019946
10 ANOVA Regression Residual Total
df
1 8 9
SS
72900000 17500000 90400000
MS
72900000 2187500
F
33.32571
Significance F
0.00041792
Intercept GPA
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
1928.571429 3748.677 0.514467 0.620833 -6715.89326 10573.04
6428.571429 1113.589 5.772843 0.000418 3860.63173 8996.511
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Salary = f(Work)
Regression Statistics
Multiple R R Square Adjusted R Square Standard Error Observations
f(Work)
0.939265177
0.882219073
0.867496457
1153.657002
10 ANOVA Regression Residual Total
df
1 8 9
SS
79752604.17
10647395.83
90400000
MS
79752604 1330924
F
59.92271
Significance F
5.52993E-05
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 30691.66667 1010.136344 30.38369 1.49E-09 28362.28808 33021.0453
Months Work -227.864583 29.43615619 -7.74098 5.53E-05 295.7444812 -159.98469
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Salary = f(GPA, Work)
Regression Statistics
Multiple R R Square Adjusted R Square Standard Error Observations
f(GPA,Work)
0.962978985
0.927328525
0.906565246
968.7621974
10 ANOVA Regression Residual Total Intercept GPA Months Work
df
2 7 9
SS
83830499 6569501 90400000
MS
41915249 938500.2
F
44.66195
Significance F
0.00010346
Coefficients Standard Error
19135.92896 5608.184
2725.409836 1307.468
t Stat
3.412144
2.084495
-151.2124317 44.30826
-3.41274
P-value Lower 95% Upper 95%
0.011255 5874.682112 32397.176
0.075582 -366.2602983 5817.08
0.011246 -255.9848174
46.440046
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Compare Three “Models”
Regression Statistics f(GPA)
Multiple R R Square Adjusted R Square Standard Error Observations 0.898006642
0.806415929
0.78221792
1479.019946
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Regression Statistics
Multiple R R Square Adjusted R Square Standard Error Observations
f(Work)
0.939265177
0.882219073
0.867496457
1153.657002
10
Regression Statistics
Multiple R R Square Adjusted R Square Standard Error Observations
f(GPA,Work)
0.962978985
0.927328525
0.906565246
968.7621974
10 58