Data Blast

Data, Telecom, Maths, Astronomy, Origami, and so on


Leave a comment

Dublin: Venture Capital Fundraising (by using Crunchbase)

Taking advantage of the Python and R scripts that I developed in a previous post, I wanted to learn about the state of the art of the companies in Dublin according to Crunchbase (APIv2). It’s true however that Crunchbase, and other similar websites, can give an incomplete vision about the companies in a specific city and on the other hand, this information, sometimes, is a bit biased, because they themselves manage, as it’s logical, what information want to show to potential investors and what not. In any case, it’s a good starting point to glimpse the technological potential of this city, where by the way, are many of the largest software companies worldwide. In this sense, I wanted to know some things related to “business ecosystem” of Dublin as the following ones: Which are the companies that have received more investments in the last years?, Who are the main investors?, Which is the order of magnitude of the investments?, Which are the most important business areas (“categories”) in the city?, etc.

An aspect to highlight in Crunchbase is that the companies indicate one or many categories (or fields) where their businesses are developed, so, there isn’t an unique “tag” that describes a company. However, some companies for example don’t choose the category “startup”, but in their descriptions they consider themselves as “startups”. On the other hand, doing a search for Dublin city, I gathered 1227 companies where only 186 included information about their investments, i.e. they mentioned investors and funding, although sometimes a “undisclosed amount” was considered as zero EUR. Furthermore, some companies like Mongodb-Inc, maybe must be considered as “outliers” or an unrepresentative company, because in this case, Mongodb’s Headquarter is in New York city, but its EMEA Headquarter is exactly in Dublin city. So, it’d be necessary to improve the search with filters more accurate to avoid this situation. Unfortunately, GPS coordinates are “missing in action” in the system and they must be generated directly using the addresses of the offices. I’ve a pending Python script via geopy to generate a new column with lat/long coordinates.

Anyway, the following figure shows a network graph with only 186 companies (“blue nodes”), 211 investors (“orange nodes”), and 534 links. Visually it may seem less links due to some investors are involved in several funding rounds with a same company, for example. Here ithere s a javascript chart.

dublin_graph1Perhaps, a Sankey diagram could be suitable to represent the connections between companies and investors because the width of the arrows is proportional to the investments which give us a clear idea about flow investment in Dublin. However, they are many companies and investors and the whole diagram is a bit confusing, so I only show a couple of companies/investors. By the way, this type of diagram is mainly used to visualize energy or material or cost transfers between processes. Here there is a javascript chart.

dublin_graph2Some Results:

a) Total Fundraised vs Year

graph3

b) Top 10 Companies

Company Total Fundraised
mongodb-inc EUR 214,922,988.84
green-apple-media EUR 122,760,000.00
mainstream-renewable-power EUR 120,000,000.00
gc-aesthetics EUR 83,700,000.00
intune-networks EUR 46,732,497.21
opsona EUR 40,277,993.28
sumup EUR 30,689,999.07
brandtone EUR 23,999,997.00
3v-transaction-services EUR 23,715,000.00

(*) Mongodb-Inc can be considered an “outlier”.

c) Top 10 Inversors

Investor Investment
marubeni-corporation EUR 100,000,000.00
robert-abus EUR 94,860,000.00
montreaux-equity-partners EUR 46,500,000.00
enterprise-ireland EUR 40,920,020.65
delta-partners EUR 35,554,481.07
sequoia-capital EUR 33,479,998.14
fountain-healthcare-partners EUR 33,271,332.38
robert-abus-2 EUR 27,900,000.00
intel-capital EUR 26,615,047.83

d) Main Categories

dublin_graph4  e) Degree and PageRank

By using Igraph for R, it’s possible to see the different connected components in the whole graph. This is an example:

dublin_graph5

 
Compamy Investor Type Investment Currency Year
sumup life-sreda venture 4030000 EUR 2014
sumup bbva-ventures venture 4030000 EUR 2014
sumup groupon venture 4030000 EUR 2014
sumup ta-venture undisclosed 0 EUR 2012
sumup bbva-ventures venture 0 EUR 2013
sumup groupon venture 0 EUR 2013
sumup klaus-hommels venture 4650000 EUR 2012
sumup tengelmann-ventures venture 4650000 EUR 2012
sumup shortcut-ventures-gmbh venture 4650000 EUR 2012
sumup brainstoventures venture 4650000 EUR 2012

Two charts that relate Funding with metrics like degree and pagerank.

degree_r

pagerank_r

Advertisements


Leave a comment

Next Stop Dublin: Public Libraries, Supermarkets and Voronoi Diagrams

I’ve been living in Dublin for only a couple of weeks and I’d like to write a post related to the city. In these few weeks I’ve visited some places that have surprised me pleasantly, as for example: The Trinity College Library with its “Book of Kells“, the huge Phoenix Park with its deers, and the Science Gallery and its interesting temporal exhibitions. In the surroundings of the city I visited the Celtic Boyne Valley (Trim castle included or “Braveheart” castle) and had the opportunity, for first time, to face the “Irish Bog” in the Seahan mountain near to Tallaght. So, I’d like to say simply I’m delighted with the city and its people. Moreover, it’s a very active city in IT issues with several meetups that worthwhile to consider such as: DublinR, Python Ireland, Hadoop User Group Ireland, DublinKind, and Big Data developers Dublin. A special mention is for Chapters Bookstore, a great find. collageDub Dublin Data As a newcomer to the city, I wanted to know where are located some key sites such as supermarkets or public libraries and therefore I got ready to build a map of locations with its respective Voronoi diagram in order to visualize the area of coverage or influence of each point. According to Wolfram MathWorld, a Voronoi diagram is “a partitioning of a plane with points into convex polygons such that each polygon contains exactly one generating point and every point in a given polygon is closer to its generating point than to any other. A Voronoi diagram is sometimes also known as a Dirichlet tessellation. The cells are called Dirichlet regions, Thiessen polytopes, or Voronoi polygons”. In order to find GPS coordinates in the case of the supermarkets I used a Python script to connect Yelp APIv2. I don’t know which is the problem with Yelp API, but I only could gather 1000 of 1153 points that Yelp search browser indicates and which 442 supermarkets are really in the Dublin city area. In the case of the public libraries I used “geopy” package, which geo-locates a query to an address and coordinates. In both cases, I must say there are some differences in the real position of some places, but as proof of concept, for me it’s OK. As Dublin City area I considered the five areas described in the city website:

  1. Central Area: This includes Broadstone, North Wall, East Wall, Drumcondra, Ballybough and the north city centre.
  2. North Central Area: This includes Kilbarrack, Raheny, Donaghmede, Coolock, Clontarf and Fairview.
  3. North West Area: This includes Cabra, Ashtown, Finglas, Ballymun, Santry, Whitehall, Glasnevin, the Phoenix Park and parts of Phibsborough.
  4. South Central Area: This includes Ballyfermot, Inchicore, Crumlin, Drimnagh, Walkinstown, The Liberties and the south west inner city.
  5. South East Area: This includes Rathmines, Rathgar, Terenure, Ringsend, Irishtown, Pearse Street and the south east inner city.

Additionally and as proof of concept again, by means of Dublinked (Open Data) and AIRO, I got two datasets with information about Primary and Post-Primary schools in Dublin city (census 2013-2014). My idea was for example to know how many students are studying in a particular area of the city or how many students are assigned, say, to a specific library (Voronoi polygon). In the case of Post-Primary schools dataset, school coordinates are in UTM coordinates, so it’s necessary to apply a transformation to GPS Coordinates (e.g. CRS(“+init=epsg:29902”) to CRS(“+init=epsg:4326”)). The datasets contain information (2013-2014) about school ethos or separation by gender but I was only interested in total values. In this Github, you can find kml and csv files. Some example:

library(deldir)
library(ggplot2)
library(ggmap)
library(sp)
library(rgdal)
library(maptools)

#Load data with GPS coordinates for Public Libraries in Dublin City 
df <- read.csv("t_lib.csv",header = TRUE, sep = ",",stringsAsFactors=FALSE)

# Voronoi data
vor <- deldir(df$long, df$lat)

# Creating Voronoi polygons
w = tile.list(vor)
polys = vector(mode='list', length=length(w))
for (i in seq(along=polys)) {
 pcrds = cbind(w[[i]]$x, w[[i]]$y)
 pcrds = rbind(pcrds, pcrds[1,])
 polys[[i]] = Polygons(list(Polygon(pcrds)), ID=as.character(i))
 }
SP = SpatialPolygons(polys)
voro = SpatialPolygonsDataFrame(SP, data=data.frame(x=df$long,y=df$lat, row.names=sapply(slot(SP, 'polygons'), function(x) slot(x, 'ID'))))

#Generating DataFrame with polygons
pvor1=data.frame()
for (i in seq_along(voro)){
pvor2=SP@polygons[[i]]@Polygons[[1]]@coords[,1:2]
pvor2=as.data.frame(pvor2)
pvor2$ID<-df$name[i]
pvor1<-rbind(pvor2,pvor1)
}

#Ploting: Points, Polygons and Segments
dub_map <- get_map(location = "Dublin", zoom = 11)
ggmap(dub_map) + geom_point(aes(x = long, y = lat), data = df, colour = "blue", size = 3)+
geom_polygon(aes(x=V1, y=V2,group=ID,fill=ID),data=pvor1, alpha=0.3)+
ggtitle("Voronoi Polygons for Public Libraries in Dublin City")+geom_segment(
 aes(x = x1, y = y1, xend = x2, yend = y2),
 size = 1,
 data = vor$dirsgs,
 linetype = 1,
 color= "#FFB958")

Voronoi_Dublin In this RPubs you can find the RMarkdown file. Other plots. PS: Donaghmede Library has zero students because this library is out of Dublin City area according to the boundary defined (North Central kml), so surrounding schools were filtered. plot1_1 plot1 plot2 plot3 plot_schools_dens Also it’s possible to generate kml files for points, polygons and segments and put into googlemap.

Comments:

I’d like to comment that “deldir” R package uses the Lee and Schachter’s algorithm for Delaunay Triangulation; however, it’d be interesting to apply an algorithm (e.g. modifying Fortune’s algorithm, etc) that allows generating, say, a weighted Voronoi diagram since in the reality each library has different resources and opening hours and so it’s possible to use other metrics, beyond Euclidean distance. In fact, an interesting next step would be to review “Power diagrams” which are a generalization of the Voronoi diagrams.

As last comment, I want to recommend the book “Longitude” written by Dava Sobel. I know it’s old (1995), but that is also one of the reasons why I wrote this post; it was a kind of inspiration. Well, in short, it’s a true story of a lone genius who solved the greatest scientific problem of his time: measuring the longitude in the sea. It’s a story with a clear scientific background where it’s possible to learn different concepts related to navigation and geography. Moreover, it’s a story of overcoming and how jealousy, egos and ignorance complicate the scientific progress.


Leave a comment

Discovering RHIPE with SDN-Mininet

Some days ago I attended a series of lectures organized by Telefonica Research (TID) where they explained several projects that have been developing in the last years in the field of Big Data. These projects or use cases mostly are related to the use of data gathered from their mobile phone communications, besides other sources such as credit card transactions and social networks (e.g. twitter and facebook). In general, the talks showed interesting information both at content and format level.  In addition, two key concepts, as it might be expected, were mentioned repeatedly during the explanation: “anonymity” and “aggregation”, conveying that personal data they collected are protected, in order to ensure the privacy of their users. Although I don’t want to doubt about this, we must recognize that this is a controversial issue both for Telcos and OTTs and whose discussion isn’t over; still a lot of water under the bridge must flow in order to clarify the suitable use of personal data. I mean It’s necessary the existence  of a strict legal framework that protects users worldwide, but that’s another topic for another post.

Well then, I understand and guess that in general the focus of these talks was simply to present compelling and novel visualizations, so audience can glimpse the power behind the data and the endless options that the use of Big Data technology can bring us in the future. Visualizations such as the movement of Russian tourists or cruise passengers through Barcelona, where they sleep, eat or buy luxury items, food, etc, (all geo-located) or also sentiment analysis by means of twitter of a determined event, etc. etc. Also to mention some research projects with social scope where TID is involved in several countries as could be the analysis of crowd movement after an earthquake or during a flood, i.e. migration events. On the other hand, they highlighted also something very important and revealing: analyze the behaviour of people by means of their movements through cellular radio system (and social networks) provides a more accurate and less biased notion of the users (potential clients) than an opinion survey. Anyway, it gets the feeling that Big Data is a world of possibilities and as Henry Ford said: “If I had asked people what they wanted, they would have said faster horses”. See Smart Steps project by TID.

However, it’s logical to think all this is the tip of the iceberg of an emerging business that could be very lucrative: “sales data”…well in fact, it already is the case. This reminds me a news of October 2012 where Von McConnell, director of technology at Sprint said, in relation to if Telcos became nothing more than a dumb pipe, “we could make a living just out of analytics”, this is, Telcos can survive on Big Data alone. Besides, I remember last year at Telecom Big Data conference (Barcelona), Telcos were aware that they are “sitting” on a goldmine of data and already are working on mechanisms to get useful business information, at all level, with a main goal: data monetization. However, here I would like to mention briefly an aspect that can modify this scenario: there exists a war Telco vs OTT players for dominance over the data, but it’s another story which we must be alert. Anyway, currently some relevant topics in a telco are: marketing analytics, M2M solutions, voice analytics, operational management (network and devices), advertising models, recommendation systems (cross/ up selling) etc. This give us an idea about the topics that Telcos are currently working. By the way, I recommend to check Okapi project by TID (Tools for large-scale Machine Learning and Graph Analytics).

Configuring RHIPE and SDN-Mininet

Well, actually this preamble was only a pretext to present a simple example where is possible to see an application of Big Data & analytics tools (e.g. Map/Reduce Hadoop and R) over data gathered from a network. It’s true however, these are well-known issues that I already had mentioned in previous posts, but my intention this time (as well as to repeat my speech) is to place Big Data in a context purely of network. Typically when we talk about Big Data or analytics in a Telco, some common examples appear such as customer churn analysis or pattern analysis over a cellular radio system.  SDN (and NFV) in this sense, by decoupling control and data plane, offers a clear opportunity to manage network communications in a centralized way, with which now it’s possible to have server a farm (Data Center) that can process several network metric in real time using Big Data analytics, i.e. now can be possible to do an advanced network tomography: huge network matrix, delay matrix, loss matrix, link state, alarms, etc

Anyway… currently however, I don’t have access to real traffic data of a Telco, which would be ideal, but as proof of concept, a simple network created with Mininet is enough from my point of view. So, I programmed a tree-based topology with Python, with an external POX controller and a series of Open Flow switches and hosts. In this tree-based topology is possible to configure the fanout (number of ports) and some characteristics for the links such as bandwidth and delay. It’s very easy to add packet loss rate or CPU load, but this time I only used the first two features. Moreover, it isn’t very complicated to programme a fat-tree or jellyfish topologies or inclusive random networks, if you prefer to work with more complex networks.

On the other hand, I used wireshark tool to gather network data. In any case, I only want to capture ICMP packets in order to calculate simply the latencies between nodes and then construct a “Delay Matrix”. Actually this is very simple, but now all analysis will be done with RHIPE package, in order to apply a Map/Reduce & HDFS scheme. According to Tessera project: “RHIPE is a R-Hadoop Integrated Programming Environment. RHIPE allows an analyst to run Hadoop MapReduce jobs wholly from within R. RHIPE is used by datadr when the back end for datadr is Hadoop. You can also perform D&R (Divide and Recombine) operations directly through RHIPE MapReduce jobs, as MapReduce is sufficient for D&R, although in this case you are programming at a lower level than for datadr.” So, basically RHIPE is a R library that acts as “wrapper” which allows interact directly with Hadoop.

For Hadoop environment, I used Vagrant Virtual Machine by Tessera Project that includes CDH4 and RStudio.  My R Code is in Rpubs and csv file (traffic_wireshark.csv) is in Github.

Configuring Mininet  (see Github for test_tree.py)

# Loading wireshark
sudo wireshark &
# Filter ICMP (hiding Open Flow messages)
icmp && !(of) && ip.addr == 10.0.0.0/24
#Loading POX controller
~/pox$ ./pox.py forwarding.l2_learning
#Loading tree-based topology
sudo python test_tree.py
SDN Topology

SDN Topology

Screenshot wireshark

Screenshot wireshark

Map-Reduce Scheme

Map-Reduce Scheme

Delay Matrix

Delay Matrix


Leave a comment

Venture Capital Fundraising, Crunchbase, and Barcelona ecosystem

Inspired by two readings apart in time, I decided to write this post. The first one, just a couple of days ago, when browsing I found a talk from Etsy, an e-commerce website, for “Business of APIs Conference 2012”. There, they talked about the need to think an API (Application Programming Interface) as a product and not simply as an interface to allow connections to a data repository. They also explained that in the development of a new product many people are involved from different disciplines or areas within the company as designers, project managers, marketers, etc. In contrast, the development of an API is more limited or restricted to the IT department, with the risk of losing focus on its usability and functionality, i.e. a vision too technical, maybe. With this I don’t mean that it always happens, surely many things have changed to date, but it’s clear that technical and commercial insights sometimes go in opposite directions and today an API is a great opportunity to make business, connect with customers more easily, and also to enhance the visibility of the business.

The second reading is older and goes back a few months ago; March to be exact., when I read an interesting blog post from Beautiful Data site in which the authors analyzed the Big Data investment in technology in 2014 using data gathered from CrunchBase portal. Now, I remember I liked how they presented this issue and how used CrunchBase API (RESTful interface) in order to find relationships between companies and investors related to Big Data. Although the use of APIs wasn’t alien to me then, because I already had done some developments using APIs from Facebook and Flickr for sentiment analysis, but its approach, at least for me, it was very interesting and with a great potential for evaluating and analyzing investments into a startup ecosystem. So, I remember I checked out CrunchBase API documentation (version 1) and then I applied a series of Python scripts getting some results comparing for instance, startup ecosystems at Barcelona, London, and Paris. Although in this point, I must say that API version 1 wasn’t very robust, moreover some fields were somewhat ambiguous and the requests rather limited.

Back to the present and considering both “revelations”, I tried to dust off my old code in order to publish some results in my blog, but unfortunately CrunchBase API had migrated to version 2 and I was forced to rebuild the scripts completely. Well, finally after some hours fighting with Python, R and MongoDB reached my goal. I used MongoBD because CrunchBase limits its usage to 2,500 calls per day and 50 calls per minute and I needed to save the requests in order to reduce the traffic. Moreover, MongoDB is a robust Non-SQL DB, very easy to configure and works fairly good with JSON-like documents. As tip, there is a package called Python Crunchbase 1.0.2 that “in theory” works well with version 2 but personally I haven’t tried (uploaded 17/09/14). In any case, most of scripts that I used are in this IPython Notebook.

Some details

According to Wikipedia, CrunchBase is “a database of companies and startups, which comprises around 500,000 data points profiling companies, people, funds, fundings and events. The company claims to have more than 50,000 active contributors. Members of the public, subject to registration, can make submissions to the database; however, all changes are subject to review by a moderator before being accepted. Data are constantly reviewed by editors to ensure they are up to date. CrunchBase says it has 2 million users accessing its database each month”.

Now, it’s important to remember that each CrunchBase member fills the information that wants or considers appropriate, so it isn’t unusual to find companies with a bit of relevant information. On the other hand, now version 2 includes IDs (uuids) for all objects, which it’s a new advantage compared with version 1, however, still there are some details to debug. Also, when you write a script must be careful to include exceptions handling because requests are very sensitive when a field is empty or doesn’t exist, maybe because it wasn’t filled properly or was removed intentionally for the system, etc. Also, depending on your app, perhaps you want to search companies for a specific city and in this case a first answer for this query could be too broad, i.e. it could include companies from other cities. For example, if the query is for Barcelona (uuid), between the companies gathered appears Veeva whose global headquarters is in USA but has an office in Barcelona that is its European headquarters. In this case it would be necessary to apply some filter to avoid confusions specially when you want to analyze strictly startups in a city. Even so, all this depends on how a company is defined itself…I mean its category.

In Barcelona for instance, if you sort by location (Barcelona, uuid: eead2c0cb178ad334e6d6c813c955e99) and category (“Startups”, uuid: 568e63721763cf41d3f05a985edc3220) just get 15 startups, when in reality there are many more on the list that could be considered startups currently. Anyway, data quality will depend on what a company wants to show: funding round, fundraise, if the funding is undisclosed, private equity, etc. and it’s for this reason that data gathered should be considered only as something illustrative.

Some results for Barcelona Ecosystem

A) The following figure shows a VC fundraising graph where is possible to see the relationships between companies (690 orange circles, 145 connected) and investors (188 blue circles). In this case, the representation is an undirected and unweighted graph where some links could be parallel links between two nodes, i.e. a multigraph but visually we see only one link, this is, because there are investors that participate in different funding rounds with the same company.

For an interactive visualization click here.

For interactive visualization click here

Also, as an remarkable detail, there are 42 connected components, i.e. 42 subgraphs, where in each one of them, any two nodes are connected to each other by paths but not with others nodes in the “supergraph”. This last point is key because there exists a big component comprised by 220 nodes, 98 companies and 122 investors forming a significant investment group for the city. Depending on which information you want to get, it’s possible to define this scheme as a weighted directed graph (see IPython notebook), for instance to apply pagerank algorithm or in/out degree centrality algorithm.

B) Total Fundraised vs Year

For interactive visualization click here.

For interactive visualization click here.

C) Top 10 Companies

Company Total Fundraised
privalia EUR 395,668,000.00
desigual EUR 285,000,000.00
scytl EUR 89,427,998.42
strands EUR 43,450,000.00
groupalia EUR 35,899,996.00
social-point EUR 34,845,998.42
arcplan-information-services-ag EUR 26,907,400.00
ntr-global EUR 26,860,000.00
gigle-semiconductor EUR 24,489,998.42

D) Top 10 Investors

investor money
eurazeo EUR 285,000,000.00
cabiedes-partners EUR 203,989,256.00
index-ventures EUR 66,547,928.00
general-atlantic EUR 66,547,928.00
vulcan-capital EUR 31,600,000.00
insight-venture-partners EUR 29,022,928.00
sofina EUR 25,000,000.00
highland-capital-partners EUR 24,371,500.00
nauta-capital EUR 23,557,527.14

E) Total Fundraised vs Pagerank

By Networkx, “PageRank computes a ranking of the nodes in the graph G based on the structure of the incoming links. It was originally designed as an algorithm to rank web pages”.

For interactive visualization click here.

For interactive visualization click here.

F) Total Funraised vs Degree Centrality (in-degree)

by Networkx, “the in-degree centrality for a node v is the fraction of nodes its incoming edges are connected to. The degree centrality values are normalized by dividing by the maximum possible degree in a simple graph n-1 where n is the number of nodes in G.”

For interactive visualization click here.

For interactive visualization click here.

G) Percentage Category

For interactive visualization click here.

For interactive visualization click here.

The increase in the value for both Pagerank and Degree Centrality indicate also an increase in the position within of the fundraising ecosystem, i.e. conditions more favourable to get funds. So, it isn’t necessary to reinvent the wheel to know that having a greater and better connection to big investors gives advantages to a company when it seeks more funding. As Arthur Conan Doyle wrote in The Great Keinplatz Experiment: “Knowledge begets knowledge, as money bears interest” and this makes even more sense when we think for instance in a startup that is well connected in the network and possibly can have access to better mentors, new opportunities of fundings, etc.,although also it’s true this isn’t guarantee of success because many other factors must be considered surely. On the other hand, from investor point of view, the position in the network of a startup could be a decision parameter to invest, maybe.

Anyway, with this post my intention was to dust off my code and also to share some thoughts about APIs…better APIs attract more developers and therefore it’s possible to develop better products and new businesses…visualizations, data analysis and so on. As tip, this website gathers links to 531 reference APIs. Finally given the data, many other conclusions can be said, such as fashion is the industry that has received more investments (total fundraised) followed by the e-commerce or that 2014 is being the year with biggest investment, etc etc.  but as I mentioned before, these data should be compared with other sources in order to validate certain trends. My example of Barcelona maybe wasn’t very representative, because in Spain, I think CrunchBase doesn’t have a critical mass, yet, but it’s a matter of changing city and making other analysis. Also, there are many other investor matchmaking websites. For example, Angellist is a case that could be interesting to analyze. Furthermore, there are companies like SiSense that develop analytics dashboard software with this type of data, or websites like Startup Genome, Foundum, etc.

In my github repository are the csv files, so anyone can try VC Fundraising graph with R.

library(RCurl)
library(d3Network)
library(igraph)
library(rCharts)

d1 <- read.csv("barcelona_link.csv",header = TRUE, sep = ",",stringsAsFactors=FALSE)
d2 <- read.csv("barcelona_role.csv",header = TRUE, sep = ",",stringsAsFactors=FALSE)
d1<-unique(d1)
d2<-unique(d2)
links<-data.frame(d1$company, d1$investor)
colnames(links)<-c('source','target')
nodes<-unique(data.frame(d2$name))
colnames(nodes)<-c('name')
m=match(links$source, nodes$name)
g <- graph.data.frame(links, directed=TRUE,nodes)
dat1<-(data.frame(get.edgelist(g, names=FALSE))-1)
links$source<-dat1$X1
links$target<-dat1$X2
nodes['group']<-1
nodes$group[m]<-2
d3ForceNetwork(Links = links, Nodes = nodes, Source = "source", Target = "target", NodeID = "name",Group = "group",width = 550, height = 400, opacity = 2, linkColour = "#000000", zoom = TRUE,file = "b_new.html")


Leave a comment

Remembrances, Exoplanets, and Data Mining in Astronomy

Just a couple of weeks ago I read an interesting article in Scientific American (Feb 26) about the Kepler mission and the search of the extrasolar planets or exoplanets. This report talked about the number of exoplanets validated to date by Kepler Telecope Team: 715 exoplanets; a revealing number since the mission was just launched in 2009 and in 2012 stopped taking data for technical glitches. It’s clear that all this is a promising fact because to date only a negligible zone of de Universe has been explored within a short time. There are many planets that remain undiscovered, although the most important thing is to find planets with habitability conditions. In this sense other approach that now comes to my mind is the Phoenix Project (SETI) devoted to extraterrestrial intelligence search based on the analysis of patterns in radio signals. In 2004 however, it was announced that after checking the 800 stars, the project had failed to find any evidence of extraterrestrial signals. In any case, all these attempts have huge value to improve our knowledge about the Universe.

Also, two weeks ago, in a boring Sunday, I bumped into a TV show called “How the Universe works: Planets from Hell” (S02E03, Discovery Max). It explained the features and conditions of the planets detected to date: most of them were gas giants and massive planets; i.e. new worlds with extreme environments in both senses: cold and heat, which make impossible life as we know it. However, an interesting concept called “Circumstellar habitable zone” (Goldlocks zone) was mentioned, which corresponds to a region around a star, neither too cold nor too hot, where are orbiting planets similar to the Earth. A shared particularity among them is that they can support liquid water, which is an essential ingredient necessary for life (as we know it). Continuing with this idea, other concept emerged: “Earth Similarity Index” (ESI), although it isn’t a measure of habitability, is at least a reference point because it measures how physically a planetary mass object is similar to the Earth. ESI is a formula that depends on the following planet parameters: radius, density, escape velocity and surface temperature. The output of the formula is a value on a scale from 0 to 1, with the Earth having a reference value of one.

Also, in the same TV-show, Michio Kaku, an outstanding theoretical physicist, I remember he said: “that science fiction writers of the 50s had fallen short in the description of these strange worlds and where clearly the reality has exceeded the fiction”. In this point, I would like to remind an amazing book “The Face of the Deep” (1943) written by Edmond Hamilton where “Captain Future” (my childhood hero, I admit it, specially his Japanese cartoon) along with a group of outlaws fall to a planet at the verge of extinction. Actually, this “planetoid” was in the Roche’s Limit, i.e. the closest that a moon (or a planetoid in this case, say) can come to other planet more massive without being broken up by the planet gravitational forces. It lies at about 2 ½ times the radius of the planet from the planet’s centre. Well, better to go to the source as a tribute:

 “He swept his hand in a grandiloquent gesture. “Out there beyond Pluto’s orbit is a whole universe for our refuge! Out there across the interstellar void are stars and worlds beyond number. You know that exploring expeditions have already visited the worlds of Alpha Centauri, and returned. They found those worlds wild and strange, but habitable.

The Martian’s voice deepened. “I propose that we steer for Alpha Centauri. It’s billions of miles away, I know. But we can use the auxiliary vibration-drive to pump this ship gradually up to a speed that will take it to that other star in several months.

Two months from now, this planetoid will be so near the System that its tidal strains will burst it asunder. Roche’s Limit, which determines the critical distance at which a celestial body nearing a larger body will burst into fragments, operates in the case of this world let as though the whole System were one great body it was approaching.

The fat Uranian’s moonlike yellow face twitched with fear, and his voice was husky. “It’s true that Roche’s Limit will operate for the whole System as though for one body, in affecting an unstable planetoid like this. If this planetoid gets much nearer than four billion miles, it will burst”.

My childhood memories and my old astronomical dictionary (by Ian Ridpath). Now, there exists a modern version called Oxford Dictionary of Astronomy (2012).

My childhood memories and my old astronomical dictionary (by Ian Ridpath). Now, there exists a modern version called Oxford Dictionary of Astronomy (2012).

Continuing with my memories, I must say Astronomy has been always a very interesting topic to me, even more during my engineering student days, where I was fortunate to work as a summer intern in Electronic Lab at two main observatories in Chile: ESO-La Silla Observatory in 1995 and Cerro Tololo Inter-American Observatory in 1996. On the other hand, I also worked in a university project for the development of an autoguider system for a telescope, i.e. an electronic system that helps to improve astrophotography sessions in order to get perfect round stars during long exposure time. For this, I still remember to work with different elements such as CCD image sensor TC-211 (165 x 192 pixels, today, it’s a joke), programming microprocessors via Assembler, a Peltier cell as a cooling system, and a servomotor controller for an equatorial mount, among other things.

Astro1

With all this, at that time, I felt like an amateur astronomer or at least an Astronomy enthusiast. However, looking back, now I have the feeling that an amateur astronomer in 1995 or 1996 was only able to take astronomical photos and maybe then to apply some filtering technique (e.g. Richardson-Lucy algorithm) to improve the image, or inclusive a person could make a homemade telescope with a robotic dome, etc. In this sense, I remember some amazing reports from Sky & Telescope magazine (I was subscribed five years, I recommend it) where people shared their experiences in astrophotography, gave tips about telescopes construction, and sometimes some “visionary” came into stage, teaching how to make a spectrograph with fiber optic, for example or another advanced technique. But beyond this, I don’t remember any remarkable report related to astronomical data analysis made by an amateur.

At that time, I know Internet didn’t have the development that currently has, also it’s true that available technical resources were scarce, and external information from astronomical organization was minimal or non-existent; I mean astronomical open data. Well, unfortunately after many years of being disconnected to Astronomy, I have newly discovered a “new world” thanks to many astronomical organizations have opened their databases enabled APIs, and where any person can download an astronomical file or, even, there are websites that include powerful analysis tools. Surely, someone can tell me, it isn’t novel and surely also he/she is absolutely right, but at least for me it’s a real discovery due to today I spend my time analyzing data, all this is really a gold mine and a great opportunity to continue with my hobby. By using tools like Python or R, it’s possible extract interesting information, for example, about exoplanets or another astronomical object of interest, and therefore, any person can contribute even more to enrich and expand the general knowledge in Astronomy. However, in spite of how challenging is to analyze data “from scratch and from my home”, to look at a starry night is an incomparable sensation to anything, especially in the Southern hemisphere (Atacama desert) with the Magellanic Clouds.

In Python there exist many packages and libraries associated to astronomical data analysis. AstroPython for example, is a great website where it’s possible to find different resources from emailing-lists or tutorials to Machine Learning and Data Mining tools like AstroML, whose authors also recently (January 2014) published an excellent book called “Statistics, Data Mining, and Machine Learning in Astronomy: A Practical Python Guide for the Analysis of Survey Data” (2014) by Zeljko Ivezic et al. Moreover in R there is a similar book called “Modern Statistical Methods for Astronomy: with R Applications “ (2012) by Eric D. Feigelson and G. Jogesh Babu. In general, many astronomical data are in FITS (Flexible Image Transport System) format and once you decode them, say, you can use any programming language (e.g. Python, C, Java, R, etc.) and any Machine Learning tool such as: Weka, Knime, RapidMiner, Orange or directly via Python (by using Scikit-Learn and Pandas) or R scripts (here, I also recommend RStudio).

Well, coming back to initial topic “explanets”, I would like to share some things that you can make with astronomical open data and Python, but previously I would like to comment some things about exoplanets.

A brief glance at Exoplanets

As mentioned before, Kepler Mission was launched in 2009 and from that moment till 2012 sent valuable information about possible exoplanets. Kepler satellite orbits the Sun (not Earth orbit) points its photometer to a field in the northern constellations of Cygnus, Lyra and Draco. In NASA Exoplanet Archive is possible to find much information about mission, technical characteristics, current statistics, and as well as access to interesting tools for data analysis.

I merely want to add that there are mainly two methods for detecting explanets: direct method and indirect method. The former is simply based on the direct observation of a planet i.e. direct imaging. It’s a complicated method because, as we know, a planet is an extremely faint light source compared to star and this light tends to be lost in the glare of the host star. In the case of indirect method, it consists in observing the effects that the planet produces (or exhibits) on the host star (see Table).

ExoMethod

As it can be seen in the following figures, Transit method based on light curves is currently the most common technique used in exoplanets detection. A light curve is simply an astronomical time series of brightness of a celestial object over time.Light curve analysis is an important tool in astrophysics used for estimation of stellar masses and distances to astronomical objects. Additional information in these links: Link1, Link2 and Link3.

Number of Exoplanet detected to date (Source NASA, more plots in this link)

Number of Exoplanet detected to date (Source NASA)

Mass of the detected planets with regard to Jupiter (Source NASA)

Mass of the detected planets with regard to Jupiter (Source NASA)

On MAST Kepler Public Light Curve website it’s possible to download light curves from Kepler Mission as tarfile or individually in FITS format for different quarters and type of cadence period. However, for easier access, I recommend to use Python packages such as Klpr and PyFITS . The following figure shows a simple example on how to get light curves for confirmed exoplanet Kepler-7b (KepID: 5780885, KOI Name: K00097.01, Q5, long cadence (lc) and normalized data). Also you can use NASA Exoplanet Archive tools to visualize the data. A light curve contains different data columns (see more detail here) but, in this example, I only used the following parameters:

  • TIME (64-bit floating point): The time at the mid-point of the cadence in BKJD. Kepler Barycentric Julian Day is Julian day minus 2454833.0 (UTC=January 1, 2009 12:00:00) and corrected to be the arrival times at the barycenter of the Solar System.
  • PDCSAP_FLUX (32-bit floating point): The flux contained in the optimal aperture in electrons per second after the PDC (Presearch Data Conditioning) module has applied its detrending algorithm to the PA (Photometric Analysis module) light curve. Actually, it’s a preprocessed and calibrated flux. Generating light curves from images isn’t trivial process. First it’s necessary calibrate the images because there are many systematic source of errors in the detector (e.g. bias and flat field). Next, it’s needed to select reference stars and correcting for image motion and then to apply some method like aperture photometry. It’s to be welcomed that in this case everything is OK.

LightCurve_K7b

Lightcurve_NASA_K7b

Now, given these light curves, you can to get interesting data about exoplanets just “from the plot” as proof of concept. However, I used only one curve in a specific quarter and cadence, but actually it’s necessary for more accuracy (and statistical rigor) to use many light curves in the measurement. Anyway, by using the same example, Kepler-7b light curve (Q5, lc), we can approximately estimate: Orbital Period (T), Total Transit Duration (T_t), Transit Flat (T_f, duration of the “flat” part of the transit), and Planet-Star radius ratio. The latter can be also calculated by using the phase plot, i.e. flux vs phase. In Python simply you can use “phase=(time % T)/T” and to create a new column in your DataFrame.

Period_Transit1

Phase

So, by applying some assumptions and simplifications from “A Unique Solution of Planet and Star Parameters from an Extrasolar Planet Transit Light Curve (2003) by S. Seager and G. Mallé́n-Ornelas, we can get additional parameters such as “a” (Orbit Semi-Major Axis) or Impact Parameter “b”. By means of using other formulas it’s possible to find stellar density, stellar mass-radius relation, etc.

ParameterK7b

ParameterNasa7b

Machine Learning for Exoplanets

As initial point, I would like to mention an interesting project called PlanetHunters, which is a citizen-driven initiative from ZooUniverse project launched in December 16, 2010 to detect exoplanet from light curves of stars recorded by Kepler Mission. It’s a tool that exploits the fact that humans are better at recognizing visual patterns than computers. Here, each user contributes with his/her own assessment indicating whether a light curve shows evidence of the presence of a planet orbiting the star.

Classifying a light curve isn’t an easy task. For example, a little planet could be undetectable because its effect in the dip of the light curve is imperceptible. Many times, variations in the intensity of a star are due to internal star processes (variable stars) or for the presence of an eclipsing binary system, i.e. a pair of stars that orbit each other. In this sense, it’s worth mentioning that a light curve associated to the transit of an exoplanet will be a light curve relatively constant, with certain regularity, and with small dips corresponding to the transit.

In fact, NASA defines three categories in Kepler Objects of Interest (KOI): confirmed, candidate and false positive. According to them, “a false positive has failed at least one of the tests described in Batalha et al. (2012). A planetary candidate has passed all prior tests conducted to identify false positives, although this does not a priori mean that all possible tests have been conducted. A future test may confirm this KOI as a false positive. False positives can occur when 1) the KOI is in reality an eclipsing binary star, 2) the Kepler light curve is contaminated by a background eclipsing binary, 3) stellar variability is confused for coherent planetary transits, or 4) instrumental artifacts are confused for coherent planetary transits.”

Taking as inspiration the paper called “Astronomical Implications of Machine Learning” (2013) by Arun Debray and Raymond Wu, I decided to try some ML supervised models to classify light curves and determine whether these correspond to exoplanets (confirmed) or non-exoplanets (false positive). As a footnote: All this is just a “proof of concept”. I don’t intend to write an academic paper and my interest is only at hobby level. Well, I selected 112 confirmed exoplanets and 112 false positives. I just considered the parameters PDCSAP_FLUX and Time from each light curve by using Q12-lc and normalized data. Here, a key point is to characterize a light curve in term of attributes (features) that allow its classification.

According to Matthew Graham in his talk “Characterizing Light Curves” (March 2012, Caltech), “light curves can show tremendous variation in their temporal coverage, sampling rates, errors and missing values, etc., which makes comparisons between them difficult and training classifiers even harder. A common approach to tackling this is to characterize a set of light curves via a set of common features and then use this alternate homogeneous representation as the basis for further analysis or training. Many different types of features are used in the literature to capture information contained in the light curve: moments, flux and shape ratios, variability indices, periodicity measures, model representations”.

In my case, I simply used the following attributes: basic dispersion measures (e.g. percentile 25/50/75 and standard deviation), shape ratio (e.g. fraction of curve below median), periodicity measures (e.g. amplitudes, frequencies-harmonics, and amplitude ratios between harmonics by means of the periodogram based on Lomb-Scargle algorithm), and distance from a baseline light curve (false positive) by using Dynamic Time Warping (DTW) algorithm.

For getting periodogram, I used the pYSOVAR module and the Scipy Signal Processing module. According to Peter Plavchan, “A periodogram calculates the significance of different frequencies in time series data to identify any intrinsic periodic signals. A periodogram is similar to the Fourier Transform, but is optimized for unevenly time-sampled data, and for different shapes in periodic signals. Unevenly sampled data is particularly common in Astronomy, where your target might rise and set over several nights, or you have to stop observing with your spacecraft to download the data”. Moreover, for DTW, I used the mlpy module. Alternatively, it’s also possible to use R scripts over Python by using the Rpy2 module. Regarding to this topic, in the paper called “Pattern Recognition in Time Series” (2012), Jessica Lin et al. mention: “the classical Euclidian distance is very brittle because its use requires that input sequences be of the same length, and it’s sensitive to distortions, e.g. shifting, along the time axis and such a problem can generally be handled by elastic distance measures as DTW. DTW algorithm searches for the best alignment between two time series, attempting to minimize the distance between them”. For this reason, distance DTW could be a interesting metric to characterize a light curve. Finally, two examples for periodogram and DTW.

DTW

periodogram

After generating a DataFrame and creating a csv file (or .tab), I used Orange tool to apply different classification techniques over the dataset. At this point, as I said above, there are many tools that you can use. Also, I tested available classifiers on the dataset by using 10-folds cross-validation scheme. Previously, it’s possible to see some relationships between attributes such as: sd (standard deviation), sr (shape ratio), f1 (maximum frequency in periodogram) Amax (maximum amplitude periodogram), and dist1 (DTW distance). Shape ratio, as we see, is an attribute that can give advantage in the task of classification because it would allow a clearer separation of classes.

R_lc

As first approach, I used 5 basic methods: Classification Tree, Random Forest, k-NN, Naïve Bayes and SVM. The results are presented in the following tables and plots (ROC curve). There are a large variety of measures that can used to evaluate classifiers. However, some measures used in a particular research project may not be appropriate to the particular problem domain. Choosing the best model is almost an art because it‘s necessary to consider the effect of different features and operating condition of the algorithms such as type of data (e.g. categorical, discrete, continuous), number of samples for class (e.g. large or little difference between classes which can impact in the classification bias), performance (e.g. execution time), complexity (to avoid overfitting), accuracy, etc. Well, in order to simplify the selection and taking into account for example CA and AuC, Classification Tree, Random Forest and k-NN (k=3) are the best options. Also, applying performance formulas over Confusion Matrix it’s possible to reach this obvious conclusion. Moreover, according to literature an AuC value between 0.8 and 0.9 is considered “good” so that three methods are in the range. By the way, for more detail how Orange calculates some index, I recommend to read this link. As final comment, it’s true, however, that a more detailed study is needed (e.g. statistical test, new advanced models, etc.), but my intention was only to show that with a few scripts could be possible to do amateur Astronomy of “certain” quality.

Table

ROC2

ROC1