Unsupervised Learning

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Unsupervised Learning

• G.Anuradha

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Contents

• Introduction
• Competitive Learning networks
• Kohenen self-organizing networks
• Learning vector quantization
• Hebbian learning

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Introduction

• When no external teacher or critics information
  is available, only input vectors are used for
  learning
• Learning without supervision-unsupervised
  learning
• Learning evolves to extract features or
  regularities in presented patterns, without being
  told about the output classes
• Frequently employed in data clustering, feature
  extraction, similarity detection

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Introduction

• Unsupervised learning NNs learn to respond to
  different input patterns with different parts of
  the network
• Trained to strengthen firing to respond to
  frequently occurring patterns
• Based on this concept we have competitive
  learning and kohenen self-organizing feature maps

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Competitive learning networks
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Competitive learning networks

• Weights in this case are updated based on the
  input pattern alone.
• The no. of inputs is the input dimension, while
  the no. of outputs is equal to the number of
  clusters that the data are to be divided into.
• Cluster center positionweight vector connected
  to the corresponding output unit.

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Learning algorithm

• Learning algorithn used in most of these nets is
  known as kohonen learning
• The units update their weights by forming a new
  weight vector, which is a linear combination of
  the old weight vector and the new input vector.
• The weight updation formula for output cluster
  unit j is given by
• wk(t1)wk(t) ?(x(t)-wk(t))

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Learning algorithm

• There are 2 methods to determine the winner of
  the network during competition
• Euclidian distance method
• Dot product method
• Euclidean distance method-
• the square of Euclidean distance between the
  input vector and the weight vector is computed
• The unit whose weight vector is at the smallest
  Euclidean distance from the input vector is
  chosen as the winner

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Learning algorithm

• The dot product method-
• The dot product between the input vector and
  weight vector is computed
• aj
• The output unit with the highest activation must
  be selected for further processing (competitive)
• The weights of this unit are updated
  (Winner-take-all)
• In this case the weight updations are given by

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What happens in a dot product method?

• In the case of a dot product finding a minimum of
  x-wi is nothing but finding the maximum among the
  m scalar products

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• Competitive learning network performs an on-line
  clustering process on the input patterns
• When process is complete the input data is
  divided into disjoint clusters
• With euclidean distance the update formula is
  actually an online gradient descent that
  minimizes the objective function

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Competitive learning with unit-length vectors
The dots represent the input vectors and the
crosses denote the weight vectors for the four
output units As the learning continues, the four
weight vectors rotate toward the centers of the
four input clusters
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Limitations of competitive learning

• Weights are initialized to random values which
  might be far from any input vector and it never
  gets updated
• Can be prevented by initializing the weights to
  samples from the input data itself, thereby
  ensuring that all weights get updated when all
  the input patterns are presented
• Or else the weights of winning as well as losing
  neurons can be updated by tuning the learning
  constant by using a significantly smaller
  learning rate for the losers. This is called as
  leaky learning
• Note- Changing ? is generally desired. An
  initial value of ? explores the data space
  widely. Later on progressively smaller value
  refines the weights. Similar to the cooling
  schedule in simulated annealing.

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Limitations of competitive learning

• Lacks the capability to add new clusters when
  deemed necessary
• If ? is constant no stability of clusters
• If ? is decreasing with time may become too small
  to update cluster centers
• This is called as stability-plasticity dilemma
  (Solved using adaptive resonance theory (ART))

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• If the output units are arranged in the form of a
  vector or matrix then the weights of winners as
  well as neighbouring losers can be updated.
  (Kohenen feature maps)
• After learning the input space is divided into a
  number of disjoint clusters. These cluster
  centers are known as template or code book
• For any input pattern presented we can use an
  appropriate code book vector (Vector
  Quantization)
• This vector quantization is used in data
  compression in IP and communication systems.

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Kohenen Self-Organizing networks
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• Also known as Kohenen Feature maps or
  topology-preserving maps
• Learning procedure of Kohenen feature maps is
  similar to that of competitive learning networks.
• Similarity (dissimilarity) measure is selected
  and the winning unit is considered to be the one
  with the largest (smallest) activation
• The weights of the winning neuron as well as the
  neighborhood around the winning units are
  adjusted.
• Neighborhood size decreases slowly with every
  iteration.

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Training of kohenon self organizing network

• Select the winning output unit as the one with
  the largest similarity measure between all wi and
  xi . The winning unit c satisfies the equation
• x-wcminx-wi where the index c refers to
  the winning unit (Euclidean distance)
• Let NBc denote a set of index corresponding to a
  neighborhood around winner c. The weights of the
  winner and it neighboring units are updated by
• ?wi?(x-wi) ieNBc

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• A neighborhood function around the winning unit
  can be used instead of defining the neighborhood
  of a winning unit.
• A Gaussian function can be used as neighborhood
  function

Where pi and pc are the positions of the output
units i and c respectively and s reflects the
scope of the neighborhood.
The update formula using neighborhood function is
given by
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For Each i/p X
Initialize Weights, Learning rate
Initialize Topological Neighborhood params
Start
For i1 to n
For j1 to m
D(j)?(xi-wij)2
Winning unit index J is computed D(J)minimum
Weights of winning unit
continue
continue
Stop
Test (t1) Is reduced
Reduce learning rate
Reduce radius Of network
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Learning Vector Quantization

• LVQ

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• It is an adaptive data classification method
  based on training data with desired class
  information
• It is actually a supervised training method but
  employs unsupervised data-clustering techniques
  to preprocess the data set and obtain cluster
  centers
• Resembles a competitive learning network except
  that each output unit is associated with a class.

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Network representation of LVQ
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Possible data distributions and decision
boundaries
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LVQ learning algorithm

• Step 1 Initialize the cluster centers by a
  clustering method
• Step 2 Label each cluster by the voting method
• Step 3 Randomly select a training input vector x
  and find k such that x-wk is a minimum
• Step 4 If x and wk belong to the same class
  update wk by

else
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• The parameters used for the training process of a
  LVQ include the following
• xtraining vector (x1,x2,xn)
• Tcategory or class for the training vector x
• wj weight vector for j th output unit
  (w1j,wij.wnj)
• cj cluster or class or category associated with
  jth output unit
• The Euclidean distance of jth output unit is
  D(j)?(xi-wij)2

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For each i/p x
Y
Initialize weight Learning rate
Calculate winner Winner min D(j)
Start
Input T
A
If TCj
B
Y
N
wj(n)wj(o) ?x-wj(o)
wj(n)wj(o) - ?x-wj(o)
A
Reduce ? ?(t1)0.5 ?(t)
If ? reduces negligible
Y
Stop
B