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K-Nearest Neighbor Learning. Dipanjan Chakraborty. Different Learning Methods. Eager Learning Explicit description of target function on the whole training set Instance-based Learning Learning=storing all training instances Classification=assigning target function to a new instance

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k nearest neighbor learning

K-Nearest Neighbor Learning

Dipanjan Chakraborty

different learning methods
Different Learning Methods
  • Eager Learning
    • Explicit description of target function on the whole training set
  • Instance-based Learning
    • Learning=storing all training instances
    • Classification=assigning target function to a new instance
    • Referred to as “Lazy” learning
different learning methods3
Different Learning Methods
  • Eager Learning

Any random movement

=>It’s a mouse

I saw a mouse!

instance based learning
Instance-based Learning

Its very similar to a

Desktop!!

instance based learning5
Instance-based Learning
  • K-Nearest Neighbor Algorithm
  • Weighted Regression
  • Case-based reasoning
k nearest neighbor
K-Nearest Neighbor
  • Features
    • All instances correspond to points in an n-dimensional Euclidean space
    • Classification is delayed till a new instance arrives
    • Classification done by comparing feature vectors of the different points
    • Target function may be discrete or real-valued
k nearest neighbor9
K-Nearest Neighbor
  • An arbitrary instance is represented by (a1(x), a2(x), a3(x),.., an(x))
    • ai(x) denotes features
  • Euclidean distance between two instances

d(xi, xj)=sqrt (sum for r=1 to n (ar(xi) - ar(xj))2)

  • Continuous valued target function
    • mean value of the k nearest training examples
voronoi diagram
Voronoi Diagram
  • Decision surface formed by the training examples
distance weighted nearest neighbor algorithm
Distance-Weighted Nearest Neighbor Algorithm
  • Assign weights to the neighbors based on their ‘distance’ from the query point
    • Weight ‘may’ be inverse square of the distances
  • All training points may influence a particular instance
    • Shepard’s method
remarks
Remarks

+Highly effective inductive inference method for noisy training data and complex target functions

+Target function for a whole space may be described as a combination of less complex local approximations

+Learning is very simple

- Classification is time consuming

remarks13
Remarks

- Curse of Dimensionality

remarks14
Remarks

- Curse of Dimensionality

remarks15
Remarks

- Curse of Dimensionality

remarks16
Remarks
  • Efficient memory indexing
    • To retrieve the stored training examples (kd-tree)