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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

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outline
Outline
  • K-Nearest Neighbor algorithm
  • Fuzzy Set theory
  • Classifier Accuracy Measures
chapter 6 classification and prediction
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 Prediction
lazy vs eager learning
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
Lazy Learner: Instance-Based Methods
  • Typical approaches
    • k-nearest neighbor approach
      • Instances represented as points in a Euclidean space.
the k nearest neighbor algorithm
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 algorithm1
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 algorithm2
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)
outline1
Outline
  • K-Nearest Neighbor algorithm
  • Fuzzy Set theory
  • Classifier Accuracy Measures
fuzzy set approaches
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 approaches1
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 approaches2
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 approaches3
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 approaches4
Fuzzy Set Approaches

Another example for temperature

fuzzy set applications
Fuzzy Set Applications
  • http://www.dementia.org/~julied/logic/applications.html
outline2
Outline
  • K-Nearest Neighbor algorithm
  • Fuzzy Set theory
  • Classifier Accuracy Measures
classifier accuracy measures1
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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