Day 2 @ Strata 2012

The day went by very fast. However not a lot of interesting topics though. The keynote talks by Ben Goldacre and Avinash Kaushik were all right. Then the Netflix one was interesting, the speaker talked about what (quite a lot of) other things Netflix does beyond predicting ratings. The 'science of data visualization' was informative too.

One interesting observation I made today was that during the break hour, the man's room had lines, while the ladies' did not. That's totally different from other places I have been to, for example, the shopping mall. :P

Go Strata! Go DATA!

Today I finally walked in the Strata Conference for Data (and thank God that I live in California now.) I was quite excited about this, because there are tons going on in this conference. And people won't think you are a nerd, when you express your passion on ... DATA. Well, in my mind, the entire universe is a big dynamic information system. And what's floating inside the system? Of course, the data! And knowing more about data essentially helps people understand the system better, the universe better! It's so importance that it will become bigger and bigger part of your life. And maybe someday people will think data as vital as water and air :)

Anyway, today is the training day of Strata. I chose the 'Deep Data' track. The speakers were all fantastic! It's a great opportunity to see what others actually do with data and how they do it, instead of the tutorial sections where people just talk about the data. The talks I enjoyed the most are Claudia Perlich's 'From knowing what to understanding why' (she really has no holdout on the practical data mining tips. And I like the fact that she baked a lot of statistics knowledge into problem solving, which in my mind is missing on some of the data scientists. And I really like the assertive attitude when she said 'I will even look at the data, if somebody else pulled it'.), Ben Gimpert's 'The importance of importance: introduction to feature selection' (well, I always like these type of high level summary talks.), and, Matt Biddulph's 'Social network analysis isn't just for people' (the example that most impressed me is he used the fact that developers often listen to music while they write their code, so there is a connection between music and the programing language. Something that seems totally unrelated got brought into the wok and cooked together. Besides, he had some cool visualization using Gephi.)

At the end of day, there is an hour long debate between leading data scientist in the field (most of them came or come from Linkedin). The topic was 'Does domain expertise matters more than machine learning expertise?', meaning when you trying to assemble a team and make hire, do you have the machine learning guy or the domain expert? I personally vote against the statement, and I think the machine learning expertise matters more when I try to make the first hire. Think about it this way: when you have such an opening, you, the company should at least have idea about what you trying to solve (unless you are starting a machine learning consulting company, in which case the first hire better be machine learning people). So at that time, you already have some business domain experts inside your company. Then bringing in data miners will help you solve the problem that a domain expert couldn't solve. For example, your in-house domain expert could complain about data not very accessible, or too many predictors they don't know how and which one to look at. A machine learning person hopefully could provide advice on data storage, data processing, and modeling knowledge to help you sort out the data into some workable format, and systematically tell you that you are spending too much time on the features that do not make any difference and some other features should get more of your attention. To me, it's always an interactive feedback system between your data person and your domain expertise. And it's the way of thinking about business problems systematically in an approachable and organized fashion that values the most, not necessarily how many models or techniques that machine learning candidates knows.

Overall, Strata is a well-organized conference, that I want to attend every year!

Funnel plot, bar plot and R

I just finished my Omniture SiteCatalyst training in Mclean, VA a few days ago. It was ok (somehow boring), we only went through how to click buttons inside SiteCatalyst to generate reports, not necessarily how to implement it and let it track the information we want to track.

I got two impressions out of the class: one is Omniture is great and powerful web analytical tool; another is the funnel plots could be misleading from data visualization perspective. For example, regardless of why the second event 'Reg Form Viewed' has higher frequency than first event 'Web Landing Viewed', the funnel bar for second event is still narrower than the one for first event. Just because it's designed to be the second stage in the funnel report.


This is a typical example of visualization components do not match up the numbers. There could be other types of funnel plots that are misleading as well, as pointed out by Jon Peltier in his blog article. I totally agree with him on using the simple barplot to be an alternative for the funnel plots. And I also like his idea of adding another plot for visualizing some small yet important metric, like purchases as shown in his example.

Then I turned into R to see if I can do some quick poking around on how to display the misleading funnel I have here into something meaningful and hopefully beautiful. Since I always feel like I don't have a good grasp on how to do barplots in R, this is going to be a good exercise for me.

As always, figuring out the 3-letters parameters for base package plot function is painful. And I had to set up appropriate size of margins, so that my category names won't be cut off.

Then I drew the same plot using ggplot2. All the command names make sense. And the plot is built up layer by layer. However, I did not manage to get the x-axis to the top of the plot, which will involve creating new customized geom.


There are some nice R barchart tips on the web, for example on learning_r, stackoverflow, and gglot site. Anyway, this is what I used

##### barchart

dd = data.frame(cbind(234, 334, 82, 208, 68))
colnames(dd) = c('web_landing_viewed', 'reg_form_viewed', 'registration_complete', 'download_viewed', 'download_clicked')
dd_pct = round(unlist(c(1, dd[,2:5]/dd[,1:4]))*100, digits=0)

# plain barchart horizontal
#control outside margin so the text could be equeezed into the plot
par(omi=c(0.1,1.4,0.1,0.12))
#las directions of tick labels for x-y axis, range 0-3, so 4 combinations
mp<-barplot(as.matrix(rev(dd)), horiz=T, col='gray70', las=1, xaxt='n');
tot = paste(rev(dd_pct), '%');
# add percentage numbers
text(rev(dd)+17, mp, format(tot), xpd=T, col='blue', cex=.65)
# axis on top(side=3),'at' ticks location, las: parallel or pertanculiar to axis
axis(side=3,at=seq(from=0, to=30, by=5)*10, las=0)

# with ggplot2
dd2=data.frame(metric=c('web_landing_viewed', 'reg_form_viewed', 'registration_complete', 'download_viewed', 'download_clicked'), value=c(234, 334, 82, 208, 68))

ggplot(dd2, aes(metric, value)) + geom_bar(stat='identity', fill=I('grey50')) + coord_flip() + ylab('') + xlab('') + geom_errorbar(aes(ymin = value+10, ymax = value+10), size = 1) + geom_text(aes(y = value+20, label = paste(dd_pct, '%', sep=' ')), vjust = 0.5, size = 3.5)

Overlay two heatmaps in R

To-do: two heatmaps on two data sets with same dimension, overlay one over the other. For example, you have now heatmap 1 and 2 like these (generated in R, dataset is 4 by 2). How to overlay red one on top of the green one?


Well, I really hope this problem is as easy as overlay two pieces of paper. Unfortunately there are a few extra miles to go. The steps are clear though:

1. get the rgb number on the corresponding position for paint and background heatmap, regardless of the values in the dataset
2. merge two rgbs cell by cell
3. plot the result rgb color matrix.

Before that, understanding how R assign colors to data from a color list, is needed. I actually played with some toy datasets and color list. Then I found that R will arrange data from smallest to biggest, and then assign colors according to the rank, so that the smallest and biggest will get the beginning and end of the color list. Say you have color c1 to color c8, and your ranked data set is (1,2,3,4). R will assign color c8 to 4, color c1 to 1. Color b and c will get in this case get color c3 (ceiling ((2-1)/(4-1)*8) and color c6. Thus given the color list a heatmap uses and the dataset that's been plotted, one can calculate which color is used to plot which data point. Well, I wrote a R function to accomplish this

heatmap_col <- function(val_array, col_list) {

minv = min(val_array)
maxv = max(val_array)

out = val_array
for( i in 1:nrow(val_array))
for( j in 1:ncol(val_array))
# take max of 1 or the other value in case 0 is the ceiling result
out[i,j] = col_list[max(1, ceiling((val_array[i,j] - minv) / (maxv - minv) * length(col_list)))]

out
}

With this then, I can easily get the rgb used on each cell of the heatmap. However, the returns are simply rgb code, like '#FF000045'(red,green,blue,alpha). We need to know the exact numbers of red, green, blue and even alpha, which are critical for the blending. After some serious googling, I found this colorful presentation very helpful. It contains a hex constant table, which could be used to break down rgb color into 4 numbers between 0 and 1, corresponding to red, green, blue and alpha. R code is here

hex_constant = data.frame(hex=c(seq(from=0, to=9, by=1), toupper(letters[1:6])), decimal=seq(from=0, to=15, by=1), stringsAsFactors=F)


rgb2hex_number <- function(x, hex_constant){

num_collector = hex_constant$decimal[hex_constant$hex == toupper(substr(x, start=2, stop=2))]
for(i in 3:nchar(x))
num_collector = c(num_collector, hex_constant$decimal[hex_constant$hex == toupper(substr(x, start=i, stop=i)]))

R = (num_collector[1]*16+num_collector[2])/255
G = (num_collector[3]*16+num_collector[4])/255
B = (num_collector[5]*16+num_collector[6])/255

with_alpha = ifelse(nchar(x) > 7, TRUE, FALSE)

if(with_alpha) {
A = (num_collector[7]*16+num_collector[8])/255
return(c(R, G, B, A))
} else { # fill in alpha of 0
return(c(R, G, B, 0))
}
}

The next step is to merge two rgb numbers on the same position. Two stackoverflow posts (here and there) talked about how to do it in python. If one happens to look up in wikipedia, one has to be skeptical with it.
Wiki is wrong about the operation could be associative. It's actually not, meaning switching background and paint colors while blending can yield different color. A quick algebra is enough. The R code for this step is trivial.

mix_2rgb <- function(x, y){
# x is the paint color, y is the background color
# NOTICE: this operation is not associative. Switching x and y may yield different result.

# lookup table of hex and decimal
hex_constant=data.frame(hex=c(seq(from=0, to=9, by=1), toupper(letters[1:6])), decimal=seq(from=0, to=15, by=1), stringsAsFactors=F)

# belending two rgb colors evenly
x_out = rgb2hex_number(x, hex_constant)
y_out = rgb2hex_number(y, hex_constant)

# with alpha channel considered
ax = 1- (1 - x_out[4]) * (1 - y_out[4])

if( ax > 0 ) {

rx = x_out[1] * x_out[4] / ax + y_out[1] * y_out[4] * (1 - x_out[4]) / ax
gx = x_out[2] * x_out[4] / ax + y_out[2] * y_out[4] * (1 - x_out[4]) / ax
bx = x_out[3] * x_out[4] / ax + y_out[3] * y_out[4] * (1 - x_out[4]) / ax

return(rgb(rx, gx, bx, ax))

} else {

rx = (x_out[1] + y_out[1]) / 2
gx = (x_out[2] + y_out[2]) / 2
bx = (x_out[3] + y_out[3]) / 2

return(rgb(rx, gx, bx))
}
}

The last step is a little bit tricky. Since all I have for now is the colors I want to plot at each cell, but I don't have a data matrix to pass to "heatmap" function. So I have to do a hack using "rect" function. Anyway, This is the end result. Not bad, huh?

A Few Things Learned on Hadoop Streaming

In the past couple of days, I tried to run some map-reduce jobs on EMR through python streaming. The API I used is boto. It's really basic and not very documented. I was only able to find one example. One thing I learned the hard way is about the data coming out of hive. Surprising, no matter what input format (in terms of separators), the data out of hive is always 'ctrl-A' separated. Check this.

One-linear R: multiple ggplots on one page

First, par(mfrow=c(nrow,ncol)) does not go together with ggplot2 plots. Too bad, the simplest way I know of just wouldn't work.

There are two solutions I found out. The first is posted here. It's a smart function that performs par(mfrow) tasks. I just copied the code here

# Source: http://gettinggeneticsdone.blogspot.com/2010/03/arrange-multiple-ggplot2-plots-in-same.html

# Function used below in the function 'arrange'
vp.layout <- function(x, y) viewport(layout.pos.row=x, layout.pos.col=y)

# Function to plot multiple ggplots together
arrange <- function(..., nrow=NULL, ncol=NULL, as.table=FALSE) {
dots <- list(...)
n <- length(dots)
if(is.null(nrow) & is.null(ncol)) { nrow = floor(n/2) ; ncol = ceiling(n/nrow)}
if(is.null(nrow)) { nrow = ceiling(n/ncol)}
if(is.null(ncol)) { ncol = ceiling(n/nrow)}

## NOTE see n2mfrow in grDevices for possible alternative
grid.newpage()
pushViewport(viewport(layout=grid.layout(nrow,ncol) ) )
ii.p <- 1
for(ii.row in seq(1, nrow)){
ii.table.row <- ii.row
if(as.table) {ii.table.row <- nrow - ii.table.row + 1}

for(ii.col in seq(1, ncol)){
ii.table <- ii.p
if(ii.p > n) break
print(dots[[ii.table]], vp=vp.layout(ii.table.row, ii.col))
ii.p <- ii.p + 1
}}}

Another solution would be to use the 'grid.arrange' function in 'gridExtra' package. This function cooperates with not only plots, but also tables ('tableGrob'). So a plot can have both plots and text tables in it. And it has more controls over the title and sub titles. Very slick!

# Test
x <- qplot(mpg, wt, data=mtcars)
y <- qplot(1:10, letters[1:10])
arrange(x, y, nrow=1)
grid.arrange(x, y, ncol=1)

Use LDA Models on User Behaviors

LDA (Latent Dirichlet Allocation) model is a Bayesian statistical technique that is designed to find hidden (latent) groups of the data. For example, LDA helps to find topics (latent groups of individual words) among large document corpora. LDA is a probabilistic generative model, i.e., it assumes a generating mechanism underneath the observations and then use the observations to infer the parameters for the underlying mechanism.

When trying to find the topics among documents, LDA makes the following assumptions:

• ignoring the order of words, documents are simply bags of words and documents exhibits multiple topics.

• topics have distributions over words. So each word could appear in all the topics with different probabilities though. Say "transmission" will have a higher probability in the topic about auto repair, but lower probability in the topic about child education.

• each document is obtained by choosing some topics proportions, say {(topic A: .55), (topic B: .20), (topic C: 25)}.

• and for each word inside a document, choosing a topic from those proportions (say you randomly got number .6 (between 0 and 1 of course), the topic got chosen is B) then looking at the topic over words distribution and drawing a word from that topic (say word X).

Only the actual words are visible to us, so inference has to be made on per-word topic assignment, per-document topic proportion and per-corpus topic distribution. Dirichlet distributions are chosen to be the prior distributions for the latter two distributions. And various algorithms are used to make the inference, like Gibbs sampling (implemented in R package 'topicmodels').

LDA assumes a fixed number of topics existing in a document corpora and assigns soft membership of the topics to documents (i.e, a topic could be exhibited in multiple documents). Indeed, LDA is under a bigger umbrella called "mixed membership model framework" [refer to source [1] for more) .

The soft assignment and mixed membership nature of LDA models make it a reasonable candidate for user behavior analysis, particularly user behavior through a certain period of time. Say one has a log of user behavior at different stage of user life cycle (1st day, 2nd day, etc of a user's life). Then one can treat behavior as words, each day's users aggregated behavior log as document, and let LDA figure out the topics (group of behaviors that tend to appear together, 'co-appearance') and the proportions of the topics. And that will give some idea on how behavior of the group evolves over time. A R visualization could look like this (each tick on the y axis represents a topic).



However, I do find that sometime LDA tries too hard on discovering topics with niche words (after filtering out stop words and rare words). Depending on application, this could be a bless or a curse.

sources:
[1] http://www.cs.cmu.edu/~lafferty/pub/efl.pdf
[2] http://videolectures.net/mlss09uk_blei_tm/
[3] http://cran.r-project.org/web/packages/topicmodels/index.html
[4] http://www.cs.princeton.edu/~blei/