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Re: Joint Entropy
*To*: mathgroup at smc.vnet.net
*Subject*: [mg65587] Re: Joint Entropy
*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
*Date*: Mon, 10 Apr 2006 02:31:07 -0400 (EDT)
*Organization*: The Open University, Milton Keynes, UK
*References*: <e1agqs$ro$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Sensei wrote:
> Hi! I'm writing some functions to analyze the informative content of
> sequences, and I've stopped trying to produce the joint entropy.
>
> These are my auxiliary functions:
>
> (* Generates a sequence of random numbers *)
> In[2]:=
> RandomSequence[nsamples_,min_,max_]:=Table[
> Random[Integer,{min,max}], {nsamples}
> ]
>
> (* Alphabet of a sequence *)
> In[3]:=
> SignalAlphabet[signal_]:=Union[signal]
>
> (* Gives the probability of a symbol *)
> In[13]:=
> SymbolProbability[symbol_,signal_]:=Count[signal,symbol]/Length[signal]
>
> (* Gives the list of all symbols and their probabilities *)
> In[20]:=
> SignalProbabilityList[signal_]:=Map[
> {#,SymbolProbability[#,signal]}&,
> SignalAlphabet[signal]]
>
> (* Calculates the entropy *)
> In[24]:=
> SignalEntropy[signal_]:=-1*Fold[Plus, 0,
> Map[Log[2,Last[#]]&,SignalProbability[signal]]]
>
>
> Now, my question is, how to produce the joint probability of two
> sequences ``mathematica style''? So, given X and Y, I can produce the
> alphabet of XY, that is the cartesian product of the two alphabets
> (using CartesianProduct), but... well, I don't know how to make a
> good code! As I said previously, I'm new to mathematica... How should
> I proceed?
Hi Sensei,
Could anything like the following may be of any help (the Cartesian
product is implemented with the *Outer* built-in function)?
In[1]:=
X = {a, b, c, d};
Y = {d, e, f};
Outer[List, X, Y]
Out[3]=
{{{a, d}, {a, e}, {a, f}}, {{b, d}, {b, e}, {b, f}},
{{c, d}, {c, e}, {c, f}}, {{d, d}, {d, e}, {d, f}}}
In[4]:=
Flatten[%]
Out[4]=
{a, d, a, e, a, f, b, d, b, e, b, f, c, d, c, e, c,
f, d, d, d, e, d, f}
In[5]:=
Union[%]
Out[5]=
{a, b, c, d, e, f}
Best regards,
Jean-Marc
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