WD-20151006

1. Afternoon

• worked with Jon to port his old tahirTrackViewer.cpp into new cvg2, and works.
• be aware of the origin convention when using Calibration related functions

2. Morning

• Trajectories with 3D coords done, sent to Luis
• Silly mistake of config file of calibration, waisted 2 hours in total…

3. Worth-noting points this week

1. SDS tracker

2. ported MTT stuff into cvg2

Basically it’s a point tracker

3. Hungarian Algorithm

• Also called Munkres’ Assignment Algorithm
• It appears to be two different solutions…
  
  • Assignment Problem and Hungarian Algorithm
  • Munkres’ Assignment Algorithm

 4. JPDAF

 5. New ColorMap in Matplotlib

A Better Default Colormap for Matplotlib
How We Designed Matplotlib’s New Default Colormap (and You Can Too)
Perceptual Color Maps in matplotlib for Oceanography

6. Theono 

Still don not quite get the idea of all algorithms are defined symbolically, therefore It’s more like writing out math than writing code

All the examples (entry level of course) I’ve come across so far,

• Theano at a Glance
• Theano Tutorial
• Baby Steps - Algebra
  They are use the same letter/word for ‘symbol’ and variable, like

>>> import theano.tensor as T
>>> from theano import function
>>> x = T.dscalar('x')
>>> y = T.dscalar('y')
>>> z = x + y
>>> f = function([x, y], z)

or,

# The theano.tensor submodule has various primitive symbolic variable types.
# Here, we're defining a scalar (0-d) variable.
# The argument gives the variable its name.
foo = T.scalar('foo')
# Now, we can define another variable bar which is just foo squared.
bar = foo**2
# It will also be a theano variable.
print type(bar)
print bar.type
# Using theano's pp (pretty print) function, we see that 
# bar is defined symbolically as the square of foo
print theano.pp(bar)

4. Highlights from last week

1. presentation on GMM

2. scikit-learn

Gaussian mixture models

Density Estimation for a mixture of Gaussians

Gaussian Mixture Model Ellipsoids

Gaussian Mixture Model Selection

GMM classification

1D Gaussian Mixture Example

How to draw PDF

x = np.linspace(-6, 6, 1000)
logprob, responsibilities = M_best.eval(x)
pdf = np.exp(logprob)
pdf_individual = responsibilities * pdf[:, np.newaxis]

GMM and score_samples(X) back to probabilities

The probability density can be greater than 1. The only normalization criterion is that it integrates to 1.

Take a simple 1D example of where the probability is zero except in the range (0, 0.1). Then the probability density must have an average value of 10 in that region for the normalization criterion to be met!

data = []
for _ in range(100) :
    data.append( [np.random.rand(), np.random.rand(), np.random.rand()] )
model = GMM(n_components=1).fit(data)
logprob, _ = model.score_samples(data)
print (np.max(np.exp(logprob)))
# 2.57627579814

grid = np.linspace(-0.5, 1.5, 100)
x, y, z = np.meshgrid(grid, grid, grid)
X = np.vstack([x.ravel(), y.ravel(), z.ravel()]).T
logprob, _ = model.score_samples(X)
print (np.max(np.exp(logprob)))
# 2.65717824707

print(np.exp(logprob).sum() * (grid[1] - grid[0]) ** 3)
# 0.998503826652

3. matplotlib

Pyplot tutorial

• Working with multiple figures and axes

import matplotlib.pyplot as plt
plt.figure(1)     # the first figure
plt.subplot(211)  #the first subplot in the first figure
plt.plot([1,2,3])
plt.subplot(212) #the second subplot in the first figure
plt.plot([4,5,6])

plt.figure(2)      # a second figure
plt.plot([4,5,6])  # creates a subplot(111) by default

plt.figure(1)   #figure 1 current; 
                #subplot(212) still current
plt.subplot(211) # make subplot(211) in figure1 current
plt.title('Easy as 1,2,3')   # subplot 211 title