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[MRG+1] AffinityPropagation damping factor not explained #9335

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Jul 13, 2017
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[MRG+1] AffinityPropagation damping factor not explained #9335

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AffinityPropagation damping factor not explained
SebastinSanty Jul 12, 2017
604cde4
Added for API also
SebastinSanty Jul 12, 2017
3958a42
Add equation for damping
SebastinSanty Jul 12, 2017
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formatting text
SebastinSanty Jul 12, 2017
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SebastinSanty Jul 13, 2017
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11 changes: 10 additions & 1 deletion doc/modules/clustering.rst
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Expand Up @@ -301,7 +301,9 @@ is given.
Affinity Propagation can be interesting as it chooses the number of
clusters based on the data provided. For this purpose, the two important
parameters are the *preference*, which controls how many exemplars are
used, and the *damping factor*.
used, and the *damping factor* which damps the responsibility and
availability messages to avoid numerical oscillations when updating these
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can it be included in the equations below?

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Added.

messages.

The main drawback of Affinity Propagation is its complexity. The
algorithm has a time complexity of the order :math:`O(N^2 T)`, where :math:`N`
Expand Down Expand Up @@ -350,6 +352,13 @@ to be the exemplar of sample :math:`i` is given by:

To begin with, all values for :math:`r` and :math:`a` are set to zero,
and the calculation of each iterates until convergence.
As discussed above, in order to avoid numerical oscillations when updating the
messages, the damping factor :math:`\lambda` is introduced to iteration process:

.. math:: r_{t+1}(i, k) = \lambda\cdot r_{t}(i, k) + (1-\lambda)\cdot r_{t+1}(i, k)
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So to be sure, this means the previous value has to contribute at least half of the new value relative to the incoming message, but can contribute more. Yes?

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Not sure about that. Paper just mentions that damping factor should be between 0 and 1. But, according to scikit's API documentation, yes.

.. math:: a_{t+1}(i, k) = \lambda\cdot a_{t}(i, k) + (1-\lambda)\cdot a_{t+1}(i, k)

where :math:`t` indicates the iteration times.

.. _mean_shift:

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6 changes: 5 additions & 1 deletion sklearn/cluster/affinity_propagation_.py
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Expand Up @@ -197,7 +197,11 @@ class AffinityPropagation(BaseEstimator, ClusterMixin):
Parameters
----------
damping : float, optional, default: 0.5
Damping factor between 0.5 and 1.
Damping factor (between 0.5 and 1) is the extent to
which the current value is maintained relative to
incoming values (weighted 1 - damping). This in order
to avoid numerical oscillations when updating these
values (messages).

max_iter : int, optional, default: 200
Maximum number of iterations.
Expand Down