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      sym.py

            This is ttv1 code (Timm tools, version 1).

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Maintains summaries of symbols. Can be used incrementally, or in batch.

Example of incremental usage:

   words = # some long list of quotes
   words = re.sub(r'[-,\.\n]'," ",words).split()

   s=sym()
   for i,x in enumerate(words):
       s + x
       if i % 25 == 0: print(s) 
   print(s)

   # output:
   {:n   1 :most  1 :mode You :ent 0}
   {:n  26 :most  3 :mode is  :ent 4.1329}
   {:n  51 :most  4 :mode is  :ent 5.0546}
   {:n  76 :most  5 :mode is  :ent 5.495}
   {:n 101 :most  7 :mode the :ent 5.8595}
   {:n 126 :most  7 :mode the :ent 6.2548}
   {:n 151 :most 10 :mode is  :ent 6.2816}
   {:n 176 :most 12 :mode is  :ent 6.3449}
   {:n 199 :most 13 :mode is  :ent 6.5374}

Example of batch usage:

  print( sym( x for x in words ))

  # output:
  {:n 199 :most 13 :mode is :ent 6.5374}

Also, can be used to:

  • compute distance between symbols (used in nearest-neighbor calculations);
  • compute likelihood a symbol belongs to a sample (used in Bayes classifiers).

Programmer's Guide

from math import log
# 
class sym:
#

Initialization

  def __init__(i,inits=[]):
    i.n, i.most, i.mode, i.counts = 0,0,None,{}
    [i + x for x in inits]
#

Reporting

  def __repr__(i):
    return '{:n %s :most %s :mode %s :ent %.5g}' % (i.n,i.most,i.mode,i.ent())
#

Updating. If we find a new most frequent symbol, update mode.

  def __add__(i,x):
    i.n += 1
    count= i.counts[x] = i.counts.get(x,0) + 1
    if count > i.most:
      i.most,i.mode=count,x
    return x
#

Entropy calculation (guesstimate of the number of bits required to encode this distribution).

  def ent(i):
    e = 0
    for _,v in i.counts.items():
      p  = v/i.n
      e -= p*log(p,2)
    return e
#

Distance calculations


    

  

  

  

    

      

        #
      

      
Distance between two symbols, defined as per p42 of Aha et al., 1991
(when faced with unknown values, assume maximal distance).

    

    

      
  def dist(i,x,y,miss="?"):
    if   x == miss and y == miss : return None
    elif x == miss or  y == miss : return 1
    else:
      return 0 if x==y else 1

    

  

  

  

    

      

        #
      

      
Calculates how likely is it that symbol x belongs to this distribution (used in Bayes classifiers).
Adds certain magic factors to the numerator and denominator to handle low frequency events.
From Section 3 of Yang and Webb,2002.

    

    

      
  def like(i,x,prior=0,m=2):
     return (i.counts.get(x,0) + m*prior)/(i.n + m)

    

  

  

  

    

      

        #
      

      




Copyleft


Copyright © 2016,2017 Tim Menzies tim@menzies.us, MIT license v2.


Permission is hereby granted, free of charge, to any person obtaining
a copy of this software and associated documentation files (the
"Software"), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject
to the following conditions:


The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.


THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR
ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF
CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.


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