Because best way to understand is explaining.

Saturday, January 30, 2016

R Graph Objects: igraph vs. network

While working on adding new functions supporting Teradata Aster graph functions in my package toaster I had to pick from existing R objects. The choice was between network and graph objects from the network and igraph correspondingly - the two most prominent packages for creating and manipulating graphs and analyzing networks in R.

Interchangeability of network and graph objects


One can always use them interchangeably with little effort using package intergraph. Its sole purpose is providing "coercion routines for network data objects". Simply use its asNetwork and asIgraph functions to convert from one network representation to another:

library(igraph)
library(network)
library(intergraph)
 
# igraph 
pkg.igraph = graph_from_edgelist(edges.mat, directed = TRUE)
pkg.network.from.igraph = asNetwork(pkg.igraph)
all.equal(length(get.edgelist(pkg.igraph)), length(as.matrix(pkg.network.from.igraph, "edgelist")))
 
# network
pkg.network = network(edges.mat)
pkg.igraph.from.network = asIgraph(pkg.network)
all.equal(length(as.matrix(pkg.network, "edgelist")), length(get.edgelist(pkg.igraph.from.network)))
Created by Pretty R at inside-R.org

For more on using intergraph functions see tutorial.

Package dependencies with miniCRAN


To assess relative importance of packages network and igraph we will use package miniCRAN. Its access to CRAN packages' metadata including dependencies via "Depends", "Imports", "Suggests" provides necessary information about package relationships. Built-in makeDepGraph function recursively retrieves these dependencies and builds corresponding graph:

library(miniCRAN)
 
cranInfo = pkgAvail()
 
plot(makeDepGraph(c("network"), availPkgs = cranInfo))
plot(makeDepGraph(c("igraph"), availPkgs = cranInfo))
Created by Pretty R at inside-R.org

               
                   


Unfortunately, these dependency graphs show how network and igraph depend on other CRAN packages while the goal is to evaluate relationships the other way around: how much other CRAN packages depend on the two.

This will require some assembly as we construct a network of packages manually with edges being directed relationships (one of "Depends", "Imports", or "Suggests") as defined in DESCRIPTION for all packages. The following code builds this igraph object (we chose igraph for its functions utilized later):

cranInfoDF = as.data.frame(cranInfo, stringsAsFactors = FALSE)
 
edges = ddply(cranInfoDF, .(Package), function(x) {
  # split all implied (depends, imports, and suggests) packages and then concat into single array
  l = unlist(sapply(x[c('Depends','Imports','Suggests')], strsplit, split="(,|, |,\n|\n,| ,| , )"))
 
  # remove version info and empty fields that became NA
  l = gsub("^([^ \n(]+).*$", "\\1", l[!is.na(l)])
 
  # take care of empty arrays
  if (is.null(l) || length(l) == 0) 
    NULL
  else
    data.frame(Package = x['Package'], Implies = l, stringsAsFactors = FALSE)
} )
 
edges.mat = as.matrix(edges, ncol=2, dimnames=c('from','to'))
pkg.graph = graph_from_edgelist(edges.mat, directed = TRUE)
Created by Pretty R at inside-R.org

The resulting network pkg.graph contains all CRAN packages and their relationships. Let's extract and compare the neighborhoods for the two packages we are interested in:

# build subgraphs for each package
subgraphs = make_ego_graph(pkg.graph, order=1, nodes=c("igraph","network"), mode = "in")
g.igraph = subgraphs[[1]]
g.network = subgraphs[[2]]
 
# plotting subgraphs
V(g.igraph)$color = ifelse(V(g.igraph)$name == "igraph", "orange", "lightblue")
plot(g.igraph, main="Packages pointing to igraph")
V(g.network)$color = ifelse(V(g.network)$name == "network", "orange", "lightblue")
plot(g.network, main="Packages pointing to network")
Created by Pretty R at inside-R.org



The igraph neighborhood is much denser populated subgraph than the network neighborhood and hence its importance and acceptance must be higher.

Package Centrality Scores

Package igraph can produce various centrality measures on the nodes of a graph. In particular, pagerank centrality and eigenvector centrality scores are principal indicators of the importance of a node in given graph. We finish this exercise with validation using centrality scores for our initial conclusion that igraph package is more accepted and utilized across CRAN ecosystem than network package:

# PageRank
pkg.pagerank = page.rank(pkg.graph, directed = TRUE)
 
# Eigenvector Centrality
pkg.ev = evcent(pkg.graph, directed = TRUE)
 
toplot = rbind(data.frame(centrality="pagerank", type = c('igraph','network'), 
                          value = pkg.pagerank$vector[c('igraph','network')]),
               data.frame(centrality="eigenvector", type = c('igraph','network'), 
                          value = pkg.ev$vector[c('igraph','network')]))
 
library(ggplot2)
library(ggthemes)
ggplot(toplot) +
  geom_bar(aes(type, value, fill=type), stat="identity") +
  facet_wrap(~centrality, ncol = 2)
Created by Pretty R at inside-R.org



Conclusion

Both packages igraph and network are widely used across CRAN ecosystem. Due to its versatility and rich set of functions igraph leads in acceptance and importance. But as far as graph objects concern it is still a matter concrete requirements and even taste to prefer one's or another's object models to represent networks in R.

Tuesday, September 22, 2015

VW Big Data Play

Volkswagen made headlines lately for cheating U.S. EPA regulators. But let's pay some respect to their engineers.

Apparently, there is no button or switch that tells car it's being tested - indeed - that would be obvious flaw in the emission test protocol. So VW engineers designed and deployed sophisticated algorithm that detects car is undergoing emission testing and turns emission control on just in time to pass it with flying colors. Then, after the test is over, it recognizes normal driving conditions and switches car software back to run diesel engine in its normal mode (that creates smog at up to 40 times the legal limit).

Having such feature running flawlessly in real time conditions on hundred thousand cars all over the world deserves special recognition. In fact, it was pure accident that this "cheating device" was found (here is Bloomberg's story how). At least, let's congratulate VW data scientists and software engineers - but not their execs - with quite an accomplishment.

Friday, September 13, 2013

How to expand color palette with ggplot and RColorBrewer

Histograms are almost always a part of data analysis presentation. If it is made with R ggplot package then it may look like this:

data(mtcars)
 
ggplot(mtcars) +
  geom_histogram(aes(factor(cyl), fill=factor(cyl)))


The elegance of ggplot functions is in simple yet compact expression of visualization formula while hiding many options assumed by default. Hiding doesn't mean lacking as most options are just a step away. For example, color selection can change with one of scale functions such as scale_fill_brewer:

ggplot(mtcars) +
  geom_histogram(aes(factor(cyl), fill=factor(cyl))) +
  scale_fill_brewer()


In turn, scale_fill_brewer palette can be changed too:

ggplot(mtcars) +
  geom_histogram(aes(factor(cyl), fill=factor(cyl))) +
  scale_fill_brewer(palette="Set1")



Palettes used live in the package RColorBrewer - to see all available choices simply attach the package with library(RColorBrewer) and run display.brewer.all() to show this:
There are 3 types of palettes, sequential, diverging, and qualitative; each containing from 8 to 12 colors (see data frame brewer.pal.info and help ?RColorBrewer for details).

Curious reader may notice that if a histogram contains 13 or more bars (bins in case of continuous data) we may get in trouble with colors:

ggplot(mtcars) + 
  geom_histogram(aes(factor(hp), fill=factor(hp))) +
  scale_fill_brewer(palette="Set2")


Indeed length(unique(mtcars$hp)) finds 22 unique values for horse power in mtcars, while specified palette Set2 has 8 colors to choose from. Lack of colors in the palette triggers ggplot warnings like this (and invalidates plot as seen above):
1: In brewer.pal(n, pal) :
  n too large, allowed maximum for palette Set2 is 8
Returning the palette you asked for with that many colors
RColorBrewer gives us a way to produce larger palettes by interpolating existing ones with constructor function colorRampPalette. It generates functions that do actual job: they build palettes with arbitrary number of colors by interpolating existing palette. To interpolate palette Set1 to 22 colors (number of colors is stored in colourCount variable for examples to follow):

colourCount = length(unique(mtcars$hp))
getPalette = colorRampPalette(brewer.pal(9, "Set1"))
 
ggplot(mtcars) + 
  geom_histogram(aes(factor(hp)), fill=getPalette(colourCount)) + 
  theme(legend.position="right")


While we addressed color deficit other interesting things happened: even though all bars are back and are distinctly colored we lost color legend. I intentionally added theme(legend.position=...) to showcase this fact: despite explicit position request the legend is no more part of the plot.

The difference: fill parameter was moved outside of histogram aes function - this effectively removed fill information from aesthetics data set for ggplot. Hence, there is nothing to apply legend to.

To fix it place fill back into aes and use scale_fill_manual to define custom palette:

ggplot(mtcars) + 
  geom_histogram(aes(factor(hp), fill=factor(hp))) + 
  scale_fill_manual(values = getPalette(colourCount))


Another likely problem with large number of bars in histogram plots is placing of the legend. Adjust legend position and layout using theme and guides functions as follows :

ggplot(mtcars) + 
  geom_histogram(aes(factor(hp), fill=factor(hp))) + 
  scale_fill_manual(values = getPalette(colourCount)) +
  theme(legend.position="bottom") +
  guides(fill=guide_legend(nrow=2))


Finally, the same example using  in place palette constructor with different choice of library palette:

ggplot(mtcars) + 
  geom_histogram(aes(factor(hp), fill=factor(hp))) + 
  scale_fill_manual(values = colorRampPalette(brewer.pal(12, "Accent"))(colourCount)) +
  theme(legend.position="bottom") +
  guides(fill=guide_legend(nrow=2))
Created by Pretty R at inside-R.org


There are many more scale functions to choose from depending on aesthetics type (colour, fill), color types (gradient, hue, etc.), data values (discrete or continuous).

Wednesday, July 31, 2013

Quick R tip: ggplot in functions needs some extra care

When building visualizations with ggplot2 in R I decided to create specialized functions that encapsulate plotting logic for some of my creations. In this case instead of commonly used aes function I had to use its alternative -  aes_string - for aesthetic mapping from a string.

And now goes this handy tip:
while original aesthetic mapping function aes accepts x and y parameters by position:

p = ggplot(data, aes(x, y)) + ...

aes_string even though silently accepts them won't work like this:

my_plot_fun = function(data, xname, yname) {
  p = ggplot(data, aes_string(xname, yname)) + ...
}

It will run to compile plot object without problems but when plot p (returned from the function my_plot_fun) executed this rather cryptic error appears:

Error in as.environment(where) : 'where' is missing

What it means is that ggplot never got aesthetics defined right. This is due to aes_string function lacking the same position parameters as in its aes counterpart above. Instead, define both x and y parameters (and others if necessary) by name:

p = ggplot(data, aes_string(x=xname, y=yname)) + ...

Created by Pretty R at inside-R.org


UPDATE:


One more vote for using aes_string in place of aes comes from CRAN submission policy, i.e.:
In principle, packages must pass R CMD check without warnings or significant notes to be admitted to the main CRAN package area. If there are warnings or notes you cannot eliminate (for example because you believe them to be spurious) send an explanatory note as part of your covering email, or as a comment on the submission form. 
 (source: CRAN Repository Policy)
 What happens is that  R CMD check  reports notes like this for every aes call:

no visible binding for global variable [variable name]
It turns out that the most sensible solution is using aes_string instead.

Thursday, July 26, 2012

My New Calculator(s)

We all need a calculator from time to time. I used to reach to Start button, type Calc in the Run (or Search) box to get to Calculator app (Windows). Until recently that is. Now I simply start Octave and do my calculations there. Sometimes, I already have Python prompt and then I do my calculations there.

For example compute a variance for the sample of 10 coin flips: 4 Tails (0) and 6 Heads (1) (estimated mean p=0.6):
 octave-3.2.4.exe>(4*(0-0.6)**2 + 6*(1-0.6)**2)/(10-1)
 ans =  0.15360
This calculator really works for me. Sometimes I have a Python window and it works just as well:
>>> (4*(0-0.6)**2 + 6*(1-0.6)**2)/(10-1)
0.2666666666666667
Having said that Octave beats Python in easiness when calculating with vectors (or time series or sequences or anything that can be represented as a vector). Let's suppose we test if certain coin is not loaded (is fair) by flipping it 14 times. We would like to be 95% certain that coin is fair (i.e. p=0.5 which is equivalent to two-tailed test). Suppose that 14 flips resulted in only 3 heads. First, we build a critical interval - the number of tails that would result in rejecting coin fairness given number of heads:
critical_interval = binopdf(0:14,14,0.5) > 0.025 | binocdf(0:14,14,0.5)- binopdf(0:14,14,0.5) > 0.975
critical_interval is a Boolean vector where i-th element corresponds to (i-1) number of tails: if it's true then with 95% certainty it is a fair coin. This expression is a logical OR of 2 expressions: first for left tail and second for right tail. Octave seamlessly handles any vectors just as if it were a number: I can change this to 1000 flips with minimum keystrokes.

Thus, given number of tails 3 we get
octave-3.2.4.exe> critical_interval(3+1)
ans = 0
We use (3+1) as 1st element corresponds to 0 tails. Hence, we accept the fact that our coin is fair with 95% certainty because 3 heads do not belong to the critical interval. Similarly we have to reject this coin as loaded if number of tails happens to be 12:

octave-3.2.4.exe> critical_interval(12+1)
ans = 1

I leave Python example as an exercise to a reader but I am certain that result won't be close to Octave  in neither transparency nor conciseness. The Octave solution does leave me with the right to keep claiming this use similar to a calculator - not a programming.

Saturday, June 23, 2012

Intro to Octave for Coursera Students

Octave as a programming language has a lot to offer. To give you a taste this post attempts to showcase some of the cooler features of the language. But it also serves a purpose of introduction to Octave (or Matlab) for those who are taking or considering taking Coursera Machine Learning class by Professor Andrew Ng (great great idea). Not incidentally most of the examples were inspired by the homework assignments for the course.


Disclaimer: this post contains no concrete references, examples, excerpts or solutions for any of the Coursera courses, exercises, or homework assignments.


Matrix Basics

Suppose we have a 3 by 5 matrix A like this:
octave:> A = [1 2 3 4 5; 2 3 4 5 6; 3 4 5 6 7]

A =

   1 2 3 4 5
   2 3 4 5 6
   3 4 5 6 7

Then to extract a single element from A is just like in most other languages:
octave:> A(2,3)

ans = 4 
Just remember that following mathematical conventions Octave indexes start with 1.

Almost everything in Octave is array (vector or matrix or similar) and index is no exception. Let's take a range for example. Range is a row vector with evenly spaced elements, e.g.:

octave:> 1:5
ans =

   1   2   3   4   5

octave:> A(1:3,1:5)
ans =

   1   2   3   4   5
   2   3   4   5   6
   3   4   5   6   7
Operation A(1:3, 1:5) returns whole A again because it selects all of its rows and columns. Ranges can exist by themselves as vectors but there is special type which is available only in the context of matrix index:

octave:> A(2:end,3:end)
ans =

   4   5   6
   5   6   7
Ranges 2:end and 3:end are defined only within concrete matrix context as keyword end indicates last row or column position within matrix. You can even select elements for last 2 rows and columns like this:
octave:> A(end-1:end,end-1:end)
ans =

   5   6
   6   7

Logical Operations on Matrices

Logical arrays in Octave contain all logical elements and are usually results of relational operators with vectors and matrices like this:

octave:> A != 3
ans =

   1   1   0   1   1
   1   0   1   1   1
   0   1   1   1   1
One cool application of this is inverting identity matrix:
octave:> I = eye(3)
I =

Diagonal Matrix

   1   0   0
   0   1   0
   0   0   1

octave:> I == 0
ans =

   0   1   1
   1   0   1
   1   1   0

Euclidean Distance

Given two vectors (same size) find Euclidean distance between them.

a = [0 0 0];
b = [1 2 2];
distance = sqrt(sumsq(a-b));
If you find yourself writing in Octave more complex solutions for similar problems  with vectors  then stop and review your vectorization approach.

Vectorizing indexes

Suppose you have a collection of m vectors in n-dimensional space stored as m x n matrix X.  Suppose that the value of last (n-th) coordinate of these vectors is always 0 or 1. Then we want to produce 2 subsets of X - one subset of vectors with last coordinate equal to 0 and the other subset where vectors have last coordinate equal to 1:
n = size(X, 2);
X0 = X( find( X(:, n) == 0 ), :);
X1 = X( find( X(:, n) == 1 ), :);

Randomness

Random numbers appear in many problems. Basic approach is a matrix filled with random numbers from uniform distribution on the interval (0, 1):
octave:> rand(3,4)
ans =

   0.347937   0.317482   0.630678   0.245148
   0.917634   0.649125   0.634592   0.837635
   0.994745   0.092818   0.154936   0.966380
But Octave offers a few shortcuts. For one, such common distributions as normal, exponential, Poisson, and gamma each receive their own function randn, rande, randp, and randg.

Function randperm produces a row vector of randomly permuted integers from 1 to n:
octave:> randperm(5)
ans =

   3   1   4   5   2
If you are looking for an arbitrary vector with values between 0 and N of size n (n<=N) then randperm gets id done (in this case N = 100 and n = 10):
octave:> x = randperm(100)(1:10)
x =

   88    1   89   25   76   19   78   38   99   34

This combined with vector indexing accomplishes rather elaborate task in short one-liner: suppose we have m n-dimensional vectors stored as m x n matrix X and we need to pick k vectors (k < m) randomly. The following gets this done:

X(randperm(size(X, 1))(1:k), :);

Newer releases of Octave (I use 3.2.4) added functions randi and randperm(n, m) that offer even nice features.

Binary Singleton Expansion Function (bsxfun)

This function reminds me of Python map function, but having it in Octave is necessity (unlike in Python). When vectorizing in Octave we have a few options: 1) both parameters are of the same dimensions for element-wise application; 2) parameters are of compatible sizes for matrix operations like multiplication; 3) one parameter is a matrix and the other is a scalar.

And then we use bsxfun for vectorizing everything else, for example applying a vector to each row:

X = rand(5, 3);
mu = mean(X);
sigma = std(X);
X_norm = bsxfun(@minus, X, mu);
X_norm = bsxfun(@divide, X_norm, sigma);

The operations above resulted in normalizing all 5 vectors (rows) from XX_norm contains vectors with 0 means and standard deviations 1 for all 3 dimensions. In just 2 lines bsxfun applied mu (means) and sigma (standard deviations) to each row of X and X_norm.

Timing operations

Use functions tic and toc to measure execution time in Octave to tune performance when necessary:
octave:> tic; A * A'; toc
Elapsed time is 2.58e-008 seconds.

Monday, June 4, 2012

Gentle Intro to Octave or Matlab

I began using Octave for homework assignments from the online Machine Learning class. Having worked with languages like Python, Groovy and JavaScript I never expected a system designed for numerical computations to include such a complete and unique programming language. But it does and I can't resist sharing some examples.

There are two important things one should know about Octave (or Matlab as Octave is usually portable to Matlab):
  • Octave is a high level language just like Python or Groovy
  • Using Octave without matrices or vectors is like using Java without objects
Just these by themselves are worth a whole book on Octave but instead I go on with few cool  examples (leaving the book for later :-).

Matrices and Vectors

Creating vector or matrix in Octave is simple:
octave:> A = [1 2 3; 4 5 6; 7 8 9]
A =

   1   2   3
   4   5   6
   7   8   9
defines 3x3 matrix of integers.

Use special functions to define special matrices, e.g. identity:
octave:> I = eye(3)
I =

Diagonal Matrix

   1   0   0
   0   1   0
   0   0   1

all zeros:

octave:> allZeros = zeros(2,4)
allZeros =

   0   0   0   0
   0   0   0   0
vector (number of columns is 1) of all ones:

octave:> allOnes = ones(3,1)
allOnes =

   1
   1
   1
or matrix with random values:

octave:> X = rand(3, 5)
X =

   0.400801   0.091597   0.951333   0.063074   0.018309
   0.690633   0.194094   0.417911   0.658953   0.624323
   0.848887   0.696741   0.213559   0.363656   0.632738
And finally getting a vector of values from 1 to N (row vector):
octave:> 1:N
ans =

    1    2    3    4    5    6    7    8    9   10
 and column (vector above transposed):
octave:> (1:N)'
ans =

    1
    2
    3
    4
    5
    6
    7
    8
    9
   10

To stir things up a bit I make the following claim:
In Octave for any given problem there is higher than 50% chance that using matrices alone solves the problem with less code and more efficiently than when using loop and condition statements. 
Being a high level language Octave has control statements if, switch, loops for and while but using them in Octave is often your second choice. The reason are many matrix operators and functions Octave offers may accomplish a task without ever invoking a single control statement in a fraction of time.

Suppose you have a matrix X and you need to insert a column of 1s in front. Then I just concatenate a vector of 1s of proper size and X:

 X = [ ones(size(X, 1), 1),  X ];

What just happened: function size returned 1st dimension of array X (number of rows); then function ones generated a vector (2d dimension is 1) of 1s, and finally we concatenated column and X. But this is only beginning.

Matrix magic

This example illustrates why and how things may work out better without control statements in Octave. Suppose I have a row vector (we may call it also an array but ultimately it is a single row matrix) of numbers from 1 to 10:
octave:> y = randperm(10)
y =

    4    3    1    8    6   10    9    2    7    5

octave:> y = repmat(y, 1, 10);

Function randperm returned a row vector containing random permutation of numbers 1 through 10. Then I used function repmat to make vector y 10 times its original length by repeating it 10 times (which results in 1 by 100 matrix y).

Now, to the problem we will solve. Let's say each number from 1 to 10 corresponds to 10-dimensional vector of 0s and 1 with all of its elements set to 0 except the position of the number. Thus, 1 corresponds to vector (1 0 0 0 0 0 0 0 0 0), 2 corresponds to vector (0 1 0 0 0 0 0 0 0 0) and so on until 10 that corresponds to (0 0 0 0 0 0 0 0 0 1). Then given some vector y like above (where each element is a number from 1 to 10) we want to produce series of vectors that correspond to elements in y.

If you never worked with Octave before then solution may amaze you, if you did then this might be your normal routine:

A = eye(10)

A =

Diagonal Matrix

   1   0   0   0   0   0   0   0   0   0
   0   1   0   0   0   0   0   0   0   0
   0   0   1   0   0   0   0   0   0   0
   0   0   0   1   0   0   0   0   0   0
   0   0   0   0   1   0   0   0   0   0
   0   0   0   0   0   1   0   0   0   0
   0   0   0   0   0   0   1   0   0   0
   0   0   0   0   0   0   0   1   0   0
   0   0   0   0   0   0   0   0   1   0
   0   0   0   0   0   0   0   0   0   1

result = A(:, y);

What just happened: first we created an identity matrix A of size 10 - note that it consists of exactly 10 vectors we are mapping to and each is in right column position. Now, we just plug our original vector y into column index of matrix A. This will extract elements from A: all for rows and precisely right columns. Thus A(:, 2) gives us matrix which is 2nd column of A, A(:, 2:4) gives us matrix with columns of A from 2 to 4, same is accomplished with A(:, [2:4]), and A(:, [1 4 9]) selects 1st, 4th and 9th columns of A. Finally, we can plug an arbitrary vector in column index - in our case vector y just what we need and result becomes 10 by 100 matrix where each column corresponds to element of y.

As unconventional as it may sound I keep thinking of this solution in terms of ranges when indexing arrays. Indexing array could be via an integer, range, or array of numbers. The latter is just a vector and that is all to it.