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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

Outline

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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

### Lazy 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.

### 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)

• 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?

### 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 =