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Outline

- K-Nearest Neighbor algorithm
- Fuzzy Set theory
- Classifier Accuracy Measures

Eager Learners: when given a set of training tuples, will construct a generalization model before receiving new tuples to classify

Classification by decision tree induction

Rule-based classification

Classification by back propagation

Support Vector Machines (SVM)

Associative classification

Chapter 6. Classification and PredictionLazy vs. Eager Learning

- Lazy vs. eager learning
- Lazy learning (e.g., instance-based learning): Simply stores training data (or only minor processing) and waits until it is given a test tuple
- Eager learning (the above discussed methods): Given a set of training set, constructs a classification model before receiving new (e.g., test) data to classify

- Lazy: less time in training but more time in predicting

Lazy Learner: Instance-Based Methods

- Typical approaches
- k-nearest neighbor approach
- Instances represented as points in a Euclidean space.

- k-nearest neighbor approach

The k-Nearest Neighbor Algorithm

- All instances correspond to points in the n-D space
- The nearest neighbor are defined in terms of Euclidean distance, dist(X1, X2)
- Target function could be discrete- or real- valued
- For discrete-valued, k-NN returns the most common value among the k training examples nearest to xq

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The k-Nearest Neighbor Algorithm

- k-NN for real-valued prediction for a given unknown tuple
- Returns the mean values of the k nearest neighbors

- Distance-weighted nearest neighbor algorithm
- Weight the contribution of each of the k neighbors according to their distance to the query xq
- Give greater weight to closer neighbors

- Robust to noisy data by averaging k-nearest neighbors

The k-Nearest Neighbor Algorithm

- How can I determine the value of k, the number of neighbors?
- In general, the larger the number of training tuples is, the larger the value of k is

- Nearest-neighbor classifiers can be extremely slow when classifying test tuples O(n)
- By simple presorting and arranging the stored tuples into search tree, the number of comparisons can be reduced to O(logN)

The k-Nearest Neighbor Algorithm

- Example:
K=5

Outline

- K-Nearest Neighbor algorithm
- Fuzzy Set theory
- Classifier Accuracy Measures

Fuzzy Set Approaches

- Rule-based systems for classification have the disadvantage that they involve sharp cutoffs for continuous attributes
- For example:
IF (years_employed>2) AND (income>50K)

THEN credit_card=approved

What if a customer has 10 years employed and income is 49K?

- For example:

Fuzzy Set Approaches

- Instead, we can discretize income into categories such as {low,medium,high}, and then apply fuzzy logic to allow “fuzzy” threshold for each category

Fuzzy Set Approaches

- Fuzzy theory is also known as possibility theory, it was proposed by Lotif Zadeh in 1965
- Unlike the notion of traditional “crisp” sets where an element either belongs to a set S, in fuzzy theory, elements can belong to more than one fuzzy set

Fuzzy Set Approaches

- For example, the income value $49K belongs to both the medium and high fuzzy sets:
Mmedium($49K)=0.15 and

Mhigh($49K)=0.96

Fuzzy Set Approaches

Another example for temperature

Fuzzy Set Applications

- http://www.dementia.org/~julied/logic/applications.html

Outline

- K-Nearest Neighbor algorithm
- Fuzzy Set theory
- Classifier Accuracy Measures

Classifier Accuracy Measures

- Alternative accuracy measures (e.g., for cancer diagnosis)
sensitivity = t-pos/pos

specificity = t-neg/neg

precision = t-pos/(t-pos + f-pos)

accuracy =

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