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LURE: superrange

Supervised discretization

tim@menzies.us
August, 2017

This code is a supervised discretizer. Numbers in a list are sorted, then broken according to where a dependent variable starts to change.

This code works by first generating ranges using unsupervised discretization (using ranges.lua). Adjacent ranges are then combined if there is little change in the class diversity across the range.

 
require "show"
local the=require "config"
local NUM=require "num"
local SYM=require "sym"
local RANGE=require "range"
local LST= require "lists"
local STR=require "str"
local replace = STR.replace_char

pretty print

 
local function labels(nums)
  local out={}
  for i =1,#nums do
    out[#out+1] =  {
      most  = nums[i],
      label  =i } end --replace(i,string.rep("_",#nums),

string.char(64+i))} end

 
  return out end

covenient short cuts

 
local function same(_)    return _ end
local function sd(_)      return _.sd end
local function ent(_)     return sym.ent(_)  end
local function below(x,y) return x*the.tree.ish < y end
local function above(x,y) return x              > y*the.tree.ish end

External interface

  • things (REQUIRED) is a list of lists of items..
  • x (REQUIRED) is a function that extracts a number from an item (defaults to same).
  • y (OPTIONAL) is a function that extracts the dependent variable used to control the discretization
  • nump (OPTIONAL) is true if our dependent variable is numeric. Note that if the dependent variable is numeric,symbolic then we will emasure diversity using standard deviation, entropy (respectively).
  • lessp (OPTIONAL) is true if lower values are better.
 
return function (things,x,y,   nump, lessp)
  y    = y or LST.last -- klass is last arg
  nump = nump==nil  and true or nump 
  lessp= lessp==nil and true or lessp
  local better= lessp and below or above
  local what  = nump and NUM or sym 
  local z     = nump and sd or ent
  local breaks,ranges = {},RANGE(things,x) -- breaks is the output

Tedious detail #1: range holds its data as samples so the actual data is accessed via `.all.all1

 
       local function data(j) return ranges[j]._all._all end

Tedious detail #2: We'll always be counting right and left from current pos. So, to save time, pre-compute and cache the left and right stats.

 
       local function memo(here,stop,_memo,    b4,inc)
         if stop > here then inc=1 else inc=-1 end
         if here ~= stop then 
            b4=  LST.copy( memo(here+inc, stop, _memo)) end
         _memo[here] = what.updates(data(here), y, b4)
         return _memo[here] 
       end

Combine is a recursive bi-clusterer. 

       local function combine(lo,hi,all,bin,lvl)   
             local best = z(all)
             local lmemo,rmemo = {},{}
             memo(hi,lo, lmemo) -- summarize i+1 using i
             memo(lo,hi, rmemo) -- summarize i using i+1
             local cut, lbest, rbest
             for j=lo,hi-1 do
               local l = lmemo[j]
               local r = rmemo[j+1]
               local tmp= l.n/all.n*z(l) + r.n/all.n*z(r)
               if better(tmp, best) then
                 cut  = j
                 best = tmp
                 lbest = LST.copy(l)
                 rbest = LST.copy(r)
               end 
             end
             if cut then
               bin = combine(lo,   cut, lbest, bin, lvl+1) + 1
               bin = combine(cut+1, hi, rbest, bin, lvl+1)
             else -- no cut found, mark everything "lo" to "hi" as "bin"
               breaks[bin] = breaks[bin] or -10^32
             if ranges[hi].hi > breaks[bin] then
                   breaks[bin] = ranges[hi].hi  
               end 
             end
             return bin end

Main program

 
  combine(1,#ranges, 
           memo(1,#ranges,{}),
           1,0)  
  return labels(breaks) end

Legal

LURE, Copyright (c) 2017, Tim Menzies All rights reserved, BSD 3-Clause License

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

  • Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
  • Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
  • Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.