Day 22

Tuesday, April 26, 2017

Pandas, conclusion

Questions we asked about movies

https://docs.google.com/document/d/1ROIGH32bXHTVWBWF2v17ur4t7D32LA4tfhDTQZ8y6U8

(change first X to Z)

Each group choose one, develop code to answer it, present to class.

Enter useful things you learn in this google doc:

https://docs.google.com/document/d/11UvTNvxmPpHuL1jubcK-owFrIGybk_rJSBE-rrAQJdo

(Change first x to a z)

Deep learning, Tensorflow

A brute force approach to machine learning. Let's revisit our handwritten character recognition, and abandon the pre-processing step of feature extraction.

Your images are here

A simple linear model

How about computing the average of all the "8"s, of all the "4"s, etc.? Let's see what we get.

If we form the dot product of the average of the "4"s with a single image, we might expect that dot product to be large if the image is a 4 and smaller if it isn't a 4. Let's take a look.

from glob import glob
from PIL import Image
from numpy import *
import matplotlib.pyplot as pl
import os
imagefolder = 'day22images/'
if not os.path.exists(imagefolder): os.makedirs(imagefolder)

allpngs = glob('pngs/*.png')
#pngs[:10]
def getsig(png): return png[-6:-4]
sigs = list(set([getsig(png) for png in allpngs]))
sigs
sampleimg = Image.open(allpngs[0])
print( array(sampleimg).shape )
h,w,nc = array(sampleimg).shape

ad = {}

for sig in sigs:
         pngs = [png for png in allpngs if getsig(png)==sig]
         print(sig,len(pngs))
         avg = zeros((h,w),dtype=float)

         for png in pngs:
             a = 255-array(Image.open(png))[:,:,0]  # select just the red channel (and invert)
             avg += a
         avg -= avg.mean()
         pl.imsave(imagefolder+'average_'+sig+'.png',avg,vmin=avg.min(),vmax=avg.max(),cmap='seismic')
         ad[sig] = avg

ad['_0'].max()
seismic.png
(125, 100, 4)
_0 230
_7 230
09 219
_1 230
_9 230
_o 230
_r 231
_2 230
_m 230
_8 230
20887.536079999998

The shifted averages of each character class:

average_09.png average__0.png average__1.png average__2.png average__7.png average__8.png average__9.png average__m.png average__o.png average__r.png

Using these shifted averages for character recognition

We could try recognition of the character represented in a given image by forming the "dot products" of that image with each of the above shifted averages and saying the one that gives the largest value is our character prediction.

20170425_1.png
for sig in sigs:
         pngs = [png for png in allpngs if getsig(png)==sig]
         #print(sig,len(pngs))
         preds = []
         for png in pngs:
             a = 255-array(Image.open(png))[:,:,0]  # select just the red channel (and invert)
             dps = []
             for sig2 in sigs:
                 dps.append((a*ad[sig2]).sum())
             pred = argmax(dps)
             preds.append(pred)
         ncorrect = sum([sigs[pred]==sig for pred in preds])
         print('{:2} {:4d} of {:3d}, {:2.1f}% correct'.format(sig,ncorrect,len(pngs), ncorrect/len(pngs)*100))
_0  127 of 230, 55.2% correct
_7   75 of 230, 32.6% correct
09  182 of 219, 83.1% correct
_1  175 of 230, 76.1% correct
_9  172 of 230, 74.8% correct
_o  181 of 230, 78.7% correct
_r  109 of 231, 47.2% correct
_2   81 of 230, 35.2% correct
_m  224 of 230, 97.4% correct
_8  225 of 230, 97.8% correct

Not bad, but can we do better? If we call the shifted average images "weights", can we find modified weights that will give us better accuracy in recognition? How? Perhaps we could define a scalar measure of success and then try to maximize it by following the gradient of that measure with respect to the 10x125x100 = 125000 variables under our control (the pixel values of the set of all the weights images).

20170425_2.png

We can implement this "gradient ascent" in Tensorflow.

Tensor flow

Download the Jupyter notebook supplied with this excellent video tutorial by Magnus Erik Hvass Pedersen.

Quiz: "hvass01" As we watch and discuss the video, each student should ask at least one question via the quiz form.