Automated Data Interpretation

  • The goal is to construct a map from a large dataset to particular questions of interest.

Feature Selection is the middle-man between a dataset and these questions.

What might some distinctive features be for the following data?

  1. A mystery audio clip

  2. A set of handwritten characters

Sometimes features are not necessary - they just become a side problem. For many other applications, it is beneficial to use intuition to identify distinctive features. Often, however, the features must be sought out and identified learned from the data itself.

These efforts/algorithms can be supervised or unsupervised, and machine learning describes the automating the tasks of data analysis, feature selection and classification. (clickbait)

Let's consider some linearly separable data

In [51]:
from numpy import *
%pylab inline

d = 2 #2 dimensions
n = 500 #data points
x = random.rand(d,n) #randomly place points in 2D
#print(x)
subplot(111,aspect=1)
plot(x[0],x[1],'o')

Populating the interactive namespace from numpy and matplotlib
Out[51]:
[<matplotlib.lines.Line2D at 0x1139cddd8>]

lets draw a line and split the points into 2 groups, above vs below the line

In [55]:
# lets use the line y = 1/3 + 2/3 x, or 0=-1-2x+3y

y = sign(dot(array([-2,+3.]),x) - 1)
#print(y)
xp = x.T[y>0].T 
xm = x.T[y<0].T 
subplot(111,aspect=1)
plot(xp[0],xp[1],'ro')
plot(xm[0],xm[1],'bo');

let's open up a little space between the classes

In [56]:
# let's open up a little space between the classes
halfgap = 0.05
x[-1,][y>0] += halfgap
x[-1,][y<0] -= halfgap
In [57]:
xp = x.T[y>0].T 
xm = x.T[y<0].T 
subplot(111,aspect=1)
plot(xp[0],xp[1],'ro')
plot(xm[0],xm[1],'bo');

Now forget that we already know a separating W !!!

Our task is to use learn separating hyperplane: W

Our approach is the

Perceptron learning algorithm (PLA)

See this blog here