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Review 5

Clustering

Distance Calculation Tricks

In the following code i.fun is some two argument function that returns the distance between two rows i,j. The code illustrates an important trick for reasoning over distance calculations.

  • Explain that trick
  • Why, when doing recursive random projections might that trick be useful?
  • Why, when doing a cross-validation experiment, might that trick be useful?
def dist(i,one,two):
    k1,k2 = i.key(one), i.key(two)
    if k1 > k2: 
       k1,k2   = k2,k1
    k = (k1,k2)
    if not k in i.cache:
        i.cache[k] = i.fun(one,two)
   return i.cache[k]

Pivots for Random Projections

There are at least two ways to do random projections:

  1. Gaussian matrix multiplication
  2. Random pivots

Explain:

  • "Random pivots are preferred when handling symbolic and missing values."
  • "Random pivots can scale to larger data sets than Gaussian matrix multiplication."

Draw an football-shaped cloud of points on a two-dimensional grid (and that grid have two axes (x,y), each of which run 0..1).

  • Using that cloud, explain the Fastmap algorithm for finding two distant points

Draw a second football-shaped cloud of points on a two-dimensional grid that illustrates "the problem of outliers". Make sure you write text to explain that problems.

LSR

(This section might require some self study. See here.)

Draw two squares.

  • In square one, draw some dots showing a very very strong negative correlation between x and y
  • In square one, draw some dots showing a weak positive correlation between x and y
  • In square three, draw some dots showing zero correlation between x and y

LSR

  • What is "LSR" short for?
  • What is the output format of the model found by LSR?
  • How could that model be used for classification?

Draw some dots that run from bottom left to top right on a two-dimensional grid (and that grid have two axes (x,y), each of which run 0..1).

  • On that plot, show a line that might be added by LSR
  • On that plot, show a line that probably would not be added by LSR