I needed to generate a uniform random distribution of points inside a circle and, later, a sphere. This is part of a bigger project, but the code to do this is kind of interesting. There were no solutions available for IgorPro, but stackexchange had plenty of examples in python and mathematica. There are many ways to do this. The most popular seems to be to generate a uniform random set of points in a square or cube and then discard those that are greater than the radius away from the origin. I didn’t like this idea, because I needed to extend it to spheroids eventually, and as I saw it the computation time saved was minimal.

Here is the version for points in a circle (radius = 1, centred on the origin).

This gives a nice set of points, 1000 shown here.

And here is the version inside a sphere. This code has variable radius for the sphere.

The three waves (xw,yw,zw) can be concatenated and displayed in a Gizmo. The code just plots out the three views.

My code uses var + enoise(var) to get a random variable from 0,var. This is because enoise goes from -var to +var. There is an interesting discussion about whether this is a truly flat PDF here.

This is part of a bigger project where I’ve had invaluable help from Tom Honnor from Statistics.

This post is part of a series on esoterica in computer programming.

An occasional series in esoteric programming issues.

As part of a larger analysis project I needed to implement a short program to determine the closest distance of two line segments in 3D space. This will be used to sort out which segments to compare… like I say, part of a bigger project. The best method to do this is to find the closest distance one segment is to the other when the other one is represented as an infinite line. You can then check if that point is beyond the segment if it is you use the limits of the segment to calculate the distance. There’s a discussion on stackoverflow here. The solutions point to one in C++ and one in MATLAB. The C++ version is easiest to port to Igor due to the similarity of languages, but the explanation of the MATLAB code was more approachable. So I ported that to Igor to figure out how it works.

The MATLAB version is:

>> P = [-0.43256      -1.6656      0.12533]
P =
-0.4326   -1.6656    0.1253
>> Q = [0.28768      -1.1465       1.1909]
Q =
0.2877   -1.1465    1.1909
>> R = [1.1892    -0.037633      0.32729]
R =
1.1892   -0.0376    0.3273
>> S = [0.17464     -0.18671      0.72579]
S =
0.1746   -0.1867    0.7258
>> N = null(P-Q)
N =
-0.3743   -0.7683
0.9078   -0.1893
-0.1893    0.6115
>> r = (R-P)*N
r =
0.8327   -1.4306
>> s = (S-P)*N
s =
1.0016   -0.3792
>> n = (s - r)*[0 -1;1 0];
>> n = n/norm(n);
>> n
n =
0.9873   -0.1587
>> d = dot(n,r)
d =
1.0491
>> d = dot(n,s)
d =
1.0491
>> v = dot(s-r,d*n-r)/dot(s-r,s-r)
v =
1.2024
>> u = (Q-P)'(S - (S*N)*N') - P)' u = 0.9590 >> P + u*(Q-P) ans = 0.2582 -1.1678 1.1473 >> norm(P + u*(Q-P) - S) ans = 1.0710  and in IgorPro: Function MakeVectors() Make/O/D/N=(1,3) matP={{-0.43256},{-1.6656},{0.12533}} Make/O/D/N=(1,3) matQ={{0.28768},{-1.1465},{1.1909}} Make/O/D/N=(1,3) matR={{1.1892},{-0.037633},{0.32729}} Make/O/D/N=(1,3) matS={{0.17464},{-0.18671},{0.72579}} End Function MakeVectors() Make/O/D/N=(1,3) matP={{-0.43256},{-1.6656},{0.12533}} Make/O/D/N=(1,3) matQ={{0.28768},{-1.1465},{1.1909}} Make/O/D/N=(1,3) matR={{1.1892},{-0.037633},{0.32729}} Make/O/D/N=(1,3) matS={{0.17464},{-0.18671},{0.72579}} End Function DoCalcs() WAVE matP,matQ,matR,matS MatrixOp/O tempMat = matP - matQ MatrixSVD tempMat Make/O/D/N=(3,2) matN Wave M_VT matN = M_VT[p][q+1] MatrixOp/O tempMat2 = (matR - matP) MatrixMultiply tempMat2, matN Wave M_product Duplicate/O M_product, mat_r MatrixOp/O tempMat2 = (matS - matP) MatrixMultiply tempMat2, matN Duplicate/O M_product, mat_s Make/O/D/N=(2,2) MatUnit matUnit = {{0,1},{-1,0}} MatrixOp/O tempMat2 = (mat_s - mat_r) MatrixMultiply tempMat2,MatUnit Duplicate/O M_Product, Mat_n Variable nn nn = norm(mat_n) MatrixOP/O new_n = mat_n / nn //new_n is now a vector with unit length Variable dd dd = MatrixDot(new_n,mat_r) //print dd //dd = MatrixDot(new_n,mat_s) //print dd dd = abs(dd) // now find v // v = dot(s-r,d*n-r)/dot(s-r,s-r) variable vv MatrixOp/O mat_s_r = mat_s - mat_r MatrixOp/O tempmat2 = dd * mat_n - mat_r vv = MatrixDot(mat_s_r,tempmat2) / MatrixDot(mat_s_r,mat_s_r) //print vv //because vv &amp;gt; 1 then closest post is s (because rs(1) = s) and therefore closest point on RS to infinite line PQ is S //what about the point on PQ is this also outside the segment? // u = (Q-P)'\((S - (S*N)*N') - P)' variable uu MatrixOp/O matQ_P = matQ - matP MatrixTranspose matQ_P //MatrixOP/O tempMat2 = ((matS - (matS * matN) * MatrixTranspose(MatN)) - MatrixTranspose(matP)) Duplicate/O MatN, matNprime MatrixTranspose matNprime MatrixMultiply matS, matN Duplicate/O M_Product, matSN MatrixMultiply M_Product, matNprime MatrixOP/O tempMat2 = ((matS - M_product) - matP) MatrixTranspose tempMat2 MatrixLLS matQ_P tempMat2 Wave M_B uu = M_B[0] // find point on PQ that is closest to RS // P + u*(Q-P) MatrixOp/O matQ_P = matQ - matP MatrixOp/O matPoint = MatP + (uu * MatQ_P) MatrixOP/O distpoint = matPoint - matS Variable dist dist = norm(distpoint) Print dist End  The sticking points were finding the Igor equivalents of • null() • norm() • dot() • \ otherwise known as mldivide Which are: • MatrixSVD (answer is in the final two columns of wave M_VT) • norm() • MatrixDot() • MatrixLLS MatrixLLS wouldn’t accept a mix of single-precision and double-precision waves, so this needed to be factored into the code. As you can see, the Igor code is much longer. Overall, I think MATLAB handles Matrix Math better than Igor. It is certainly easier to write. I suspect that there are a series of Igor operations that can do what I am trying to do here, but this was an exercise in direct porting. More work is needed to condense this down and also deal with every possible case. Then it needs to be incorporated into the bigger program. SIMPLE! Anyway, hope this helps somebody. The post title is taken from the band Adventures In Stereo. ## The Great Curve: Citation distributions This post follows on from a previous post on citation distributions and the wrongness of Impact Factor. Stephen Curry had previously made the call that journals should “show us the data” that underlie the much-maligned Journal Impact Factor (JIF). However, this call made me wonder what “showing us the data” would look like and how journals might do it. What citation distribution should we look at? The JIF looks at citations in a year to articles published in the preceding 2 years. This captures a period in a paper’s life, but it misses “slow burner” papers and also underestimates the impact of papers that just keep generating citations long after publication. I wrote a quick bit of code that would look at a decade’s worth of papers at one journal to see what happened to them as yearly cohorts over that decade. I picked EMBO J to look at since they have actually published their own citation distribution, and also they appear willing to engage with more transparency around scientific publication. Note that, when they published their distribution, it considered citations to papers via a JIF-style window over 5 years. I pulled 4082 papers with a publication date of 2004-2014 from Web of Science (the search was limited to Articles) along with data on citations that occurred per year. I generated histograms to look at distribution of citations for each year. Papers published in 2004 are in the top row, papers from 2014 are in the bottom row. The first histogram shows citations in the same year as publication, in the next column, the following year and so-on. Number of papers is on y and on x the number of citations. Sorry for the lack of labelling! My excuse is that my code made a plot with “subwindows”, which I’m not too familiar with. What is interesting is that the distribution changes over time: • In the year of publication, most papers are not cited at all, which is expected since there is a lag to publication of papers which can cite the work and also some papers do not come out until later in the year, meaning the likelihood of a citing paper coming out decreases as the year progresses. • The following year most papers are picking up citations: the distribution moves rightwards. • Over the next few years the distribution relaxes back leftwards as the citations die away. • The distributions are always skewed. Few papers get loads of citations, most get very few. Although I truncated the x-axis at 40 citations, there are a handful of papers that are picking up >40 cites per year up to 10 years after publication – clearly these are very useful papers! To summarise these distributions I generated the median (and the mean – I know, I know) number of citations for each publication year-citation year combination and made plots. The mean is shown on the left and median on the right. The layout is the same as in the multi-histogram plot above. Follow along a row and you can again see how the cohort of papers attracts citations, peaks and then dies away. You can also see that some years were better than others in terms of citations, 2004 and 2005 were good years, 2007 was not so good. It is very difficult, if not impossible, to judge how 2013 and 2014 papers will fare into the future. What was the point of all this? Well, I think showing the citation data that underlie the JIF is a good start. However, citation data are more nuanced than the JIF allows for. So being able to choose how we look at the citations is important to understand how a journal performs. Having some kind of widget that allows one to select the year(s) of papers to look at and the year(s) that the citations came from would be perfect, but this is beyond me. Otherwise, journals would probably elect to show us a distribution for a golden year (like 2004 in this case), or pick a window for comparison that looked highly favourable. Finally, I think journals are unlikely to provide this kind of analysis. They should, if only because it is a chance for a journal to show how it publishes many papers that are really useful to the community. Anyway, maybe they don’t have to… What this quick analysis shows is that it can be (fairly) easily harvested and displayed. We could crowdsource this analysis using standardised code. Below is the code that I used – it’s a bit rough and would need some work before it could be used generally. It also uses a 2D filtering method that was posted on IgorExchange by John Weeks. The post title is taken from “The Great Curve” by Talking Heads from their classic LP Remain in Light. ## At a Crawl: Analysis of Cell Migration in IgorPro In the lab we have been doing quite a bit of analysis of cell migration in 2D. Typically RPE1 cells migrating on fibronectin-coated glass. There are quite a few tools out there to track cell movements and to analyse their migration. Naturally, none of these did quite what we wanted and none fitted nicely into our analysis workflow. This meant writing something from scratch in IgorPro. You can access the code from my GitHub pages. We’ve previously published a paper doing these kinds of analysis, but this code is all-new, faster and more efficient The CellMigration repo contains an ipf that has three functions which will import tracks into Igor and analyse them. We use manual tracking in ImageJ/FIJI to obtain the co-ordinates for analysis, this is the only non-Igor part. I figured it was not worth porting this part too. Instructions are given in the repo and are hopefully self-explanatory. Here’s a screenshot of a typical experiment. Acknowledgements: Colour palette is taken from the SRON stylesheet. The excellent igorutils (by yamad) gave me the idea for a structure and jtigor helped me with referencing StrConstants. The post title is taken from the track “At a Crawl” by The Melvins from their Ozma LP ## Wrong Number: A closer look at Impact Factors This is a long post about Journal Impact Factors. Thanks to Stephen Curry for encouraging me to post this. tl;dr • the JIF is based on highly skewed data • it is difficult to reproduce the JIFs from Thomson-Reuters • JIF is a very poor indicator of the number of citations a random paper in the journal received • reporting a JIF to 3 d.p. is ridiculous, it would be better to round to the nearest 5 or 10. I really liked this recent tweet from Stat Fact It’s a great illustration of why reporting means for skewed distributions is a bad idea. And this brings us quickly to Thomson-Reuters’ Journal Impact Factor (JIF). I can actually remember the first time I realised that the JIF was a spurious metric. This was in 2003, after reading a letter to Nature from David Colquhoun who plotted out the distribution of citations to a sample of papers in Nature. Up until that point, I hadn’t appreciated how skewed these data are. We put it up on the lab wall. Now, the JIF for a given year is calculated as follows: A JIF for 2013 is worked out by counting the total number of 2013 cites to articles in that journal that were published in 2011 and 2012. This number is divided by the number of “citable items” in that journal in 2011 and 2012. There are numerous problems with this calculation that I don’t have time to go into here. If we just set these aside for the moment, the JIF is still used widely today and not for the purpose it was originally intended. Eugene Garfield, created the metric to provide librarians with a simple way to prioritise subscriptions to Journals that carried the most-cited scientific papers. The JIF is used (wrongly) in some institutions in the criteria for hiring, promotion and firing. This is because of the common misconception that the JIF is a proxy for the quality of a paper in that journal. Use of metrics in this manner is opposed by the SF-DORA and I would encourage anyone that hasn’t already done so, to pledge their support for this excellent initiative. Why not report the median rather than the mean? With the citation distribution in mind, why do Thomson-Reuters calculate the mean rather than the median for the JIF? It makes no sense at all. If you didn’t quite understand why from the @statfact tweet above, then look at this: The Acta Crystallographica Section A effect. The plot shows that this journal had a JIF of 2.051 in 2008 which jumped to 49.926 in 2009 due to a single highly-cited paper. Did every other paper in this journal suddenly get amazingly awesome and highly-cited for this period? Of course not. The median is insensitive to outliers like this. The answer to why Thomson-Reuters don’t do this is probably for ease of computation. The JIF (mean) requires only three numbers for each journal, whereas calculating the median would require citation information for each paper under consideration for each journal. But it’s not that difficult (see below). There’s also a mismatch in the items that bring in citations to the numerator and those that count as “citeable items” in the denominator. This opacity is one of the major criticisms of the Impact Factor and this presents a problem for them to calculate the median. Let’s crunch some citation numbers I had a closer look at citation data for a small number of journals in my field. DC’s citation distribution plot was great (in fact, superior to JIF data) but it didn’t capture the distribution that underlies the JIF. I crunched the IF2012 numbers (released in June 2013) sometime in December 2013. This is shown below. My intention was to redo this analysis more fully in June 2014 when the IF2013 was released, but I was busy, had lost interest and the company said that they would be more open with the data (although I’ve not seen any evidence for this). I wrote about partial impact factors instead, which took over my blog. Anyway, the analysis shown here is likely to be similar for any year and the points made below are likely to hold. I mainly looked at Nature, Nature Cell Biology, Journal of Cell Biology, EMBO Journal and J Cell Science. Using citations in 2012 articles to papers published in 2010 and 2011, i.e. the same criteria as for IF2012. The first thing that happens when you attempt this analysis is that you realise how unreproducible the Thomson-Reuters JIFs are. This has been commented on in the past (e.g. here), yet I had the same data as the company uses to calculate JIFs and it was difficult to see how they had arrived at their numbers. After some wrangling I managed to get a set of papers for each journal that gave close to the same JIF. From this we can look at the citation distribution within the dataset for each journal. Below is a gallery of these distributions. You can see that the data are highly skewed. For example, JCB has kurtosis of 13.5 and a skewness of 3. For all of these journals ~2/3 of papers had fewer than the mean number of citations. With this kind of skew, it makes more sense to report the median (as described above). Note that Cell is included here but was not used in the main analysis. So how do these distributions look when compared? I plotted each journal compared to JCB. They are normalised to account for the differing number of papers in each dataset. As you can see they are largely overlapping. If the distributions overlap so much, how certain can we be that a paper in a journal with a high JIF will have more citations than a paper in a journal with a lower JIF? In other words, how good is the JIF (mean or median) at predicting how many citations a paper published in a certain journal is likely to have? To look at this, I ran a Monte Carlo analysis comparing a random paper from one journal with a random one from JCB and looked at the difference in number of citations. Papers in EMBO J are indistinguishable from JCB. Papers in JCS have very slightly fewer citations than JCB. Most NCB papers have a similar number of cites to papers in JCB, but there is a tail of papers with higher cites, a similar but more amplified picture for Nature. Thomson-Reuters quotes the JIF to 3 d.p. and most journals use this to promote their impact factor (see below). The precision of 3 d.p. is ridiculous when two journals with IFs of 10.822 and 9.822 are indistinguishable when it comes to the number of citations to randomly sampled papers in that journal. So how big do differences in JIF have to be in order to be able to tell a “Journal X paper” from a “Journal Y paper” (in terms of citations)? To look at this I ran some comparisons between the journals in order to get some idea of “significant differences”. I made virtual issues of each journal with differing numbers of papers (5,10,20,30) and compared the citations in each via Wilcoxon rank text and then plotted out the frequency of p-values for 100 of these tests. Please leave a comment if you have a better idea to look at this. I liked this method over the head-to-head comparison for two papers as it allows these papers the benefit of the (potential) reflected glory of other papers in the journal. In other words, it is closer to what the JIF is about. OK, so this shows that sufficient sample size is required to detect differences, no surprise there. But at N=20 and N=30 the result seems pretty clear. A virtual issue of Nature trumps a virtual issue of JCB, and JCB beats JCS. But again, there is no difference between JCB and EMBO J. Finally, only ~30% of the time would a virtual issue of NCB trump JCB for citations! NCB and JCB had a difference in JIF of almost 10 (20.761 vs 10.822). So not only is quoting the JIF to 3 d.p. ridiculous, it looks like rounding the JIF to the nearest 5 (or 10) might be better! This analysis supports the idea that there are different tiers of journal (in Cell Biology at least). But the JIF is the bluntest of tools to separate these journals. A more rigorous analysis is needed to demonstrate this more clearly but it is not feasible to do this while having a dataset which agrees with that of Thomson-Reuters (without purchasing the data from the company). If you are still not convinced about how shortcomings of the JIF, here is a final example. The IF2013 for Nature increased from 38.597 to 42.351. Let’s have a look at the citation distributions that underlie this rise of 3.8! As you can see below they are virtually identical. Remember that there’s a big promotion that the journal uses to pull in new subscribers, seems a bit hollow somehow doesn’t it? Disclaimer: I think this promotion is a bit tacky, but it’s actually a really good deal… the News stuff at the front and the Jobs section at the back alone are worth ~£40. Show us the data! Recently, Stephen Curry has called for Journals to report the citation distribution data rather than parroting their Impact Factor (to 3 d.p.). I agree with this. The question is though – what to report? • The IF window is far too narrow (2 years + 1 year of citations) so a broader window would be more useful. • A comparison dataset from another journal is needed in order to calibrate ourselves. • Citations are problematic – not least because they are laggy. A journal could change dramatically and any citation metric would not catch up for ~2 years. • Related to this some topics are hot and others not. I guess we’re most interested in how a paper in Journal X compares to others of its kind. • Any information reported needs to be freely available for re-analysis and not in the hands of a company. Google Scholar is a potential solution but it needs to be more open with its data. They already have a journal ranking which provides a valuable and interesting alternative view to the JIF. One solution would be to show per article citation profiles comparing these for similar papers. How do papers on a certain topic in Journal X compare to not only those in Journal Y but to the whole field? In my opinion, this metric would be most useful when assessing scholarly output. Summary Thanks for reading to the end (or at least scrolling all the way down). The take home points are: • the JIF is based on highly skewed data. • the median rather than the mean is better for summarising such distributions. • JIF is a very poor indicator of the number of citations a random paper in the journal received! • reporting a JIF to 3 d.p. is ridiculous, it would be better to round to the nearest 5 or 10. • an open resource for comparing citation data per journal would be highly valuable. The post title is taken from “Wrong Number” by The Cure. I’m not sure which album it’s from, I only own a Greatest Hits compilation. ## Waiting to happen II: Publication lag times Following on from the last post about publication lag times at cell biology journals, I went ahead and crunched the numbers for all journals in PubMed for one year (2013). Before we dive into the numbers, a couple of points about this kind of information. 1. Some journals “reset the clock” on the received date with manuscripts that are resubmitted. This makes comparisons difficult. 2. The length of publication lag is not necessarily a reflection of the way the journal operates. As this comment points out, manuscripts are out of the journals hands (with the reviewers) for a substantial fraction of the time. 3. The dataset is incomplete because the deposition of this information is not mandatory. About 1/3 of papers have the date information deposited (see below). 4. Publication lag times go hand-in-hand with peer review. Moving to preprints and post-publication review would eradicate these delays. Thanks for all the feedback on my last post, particularly those that highlighted the points above. To see how all this was done, check out the Methods bit below, where you can download the full summary. I ended up with a list of publication lag times for 428500 papers published in 2013 (see left). To make a bit more sense of this, I split them by journal and then found the publication lag time stats for each. This had to be done per journal since PLoS ONE alone makes up 45560 of the records. To try and visualise what these publication lag times look like for all journals, I made a histogram of the Median lag times for all journals using a 10 d bin width. It takes on average ~100 d to go from Received to Accepted and a further ~120 d to go from Accepted to Published. The whole process on average takes 239 days. To get a feel for the variability in these numbers I plotted out the ranked Median times for each journal and overlaid Q25 and Q75 (dots). The IQR for some of the slower journals was >150 d. So the papers that they publish can have very different fates. Is the publication lag time longer at higher tier journals? To look at this, I used the Rec-Acc time and the 2013 Journal Impact Factor which, although widely derided and flawed, does correlate loosely with journal prestige. I have fewer journals in this dataset, because the lookup of JIFs didn’t find every journal in my starting set, either because the journal doesn’t have one or there were minor differences in the PubMed name and the Thomson-Reuters name. The median of the median Rec-Acc times for each bin is shown. So on average, journals with a JIF <1 will take 1 month longer to accept your paper than journal with an IF ranging from 1-10. After this it rises again, to ~2 months longer at journals with an IF over 10. Why? Perhaps at the lower end, the trouble is finding reviewers; whereas at the higher end, multiple rounds of review might become a problem. The executive summary is below. These are the times (in days) for delays at all journals in PubMed for 2013. Interval Median Q25 Q75 Received-to-Accepted 97 69 136 Accepted-to-Published 122 84 186 Received-to-Published 239 178 319 For comparison: 1. Median time from ovulation to birth of a human being is 268 days. 2. Mark Beaumont cycled around the world (29,446 km) in 194 days. 3. Ellen MacArthur circumnavigated the globe single-handed in 72 days. On the whole it seems that publishing in Cell Biology is quite slow compared to the whole of PubMed. Why this is the case is a tricky question. Is it because cell biologists submit papers too early and they need more revision? Are they more dogged in sending back rejected manuscripts? Is it because as a community we review too harshly and/or ask too much of the authors? Do Editors allow too many rounds of revision or not give clear guidance to expedite the time from Received-to-Accepted? It’s probably a combination of all of these factors and we’re all to blame. Finally, this amusing tweet to show the transparency of EMBO J publication timelines raises the question: would these authors have been better off just sending the paper somewhere else? Methods: I searched PubMed using journal article[pt] AND ("2013/01/01"[PDAT] : "2013/12/31"[PDAT]) this gave a huge xml file (~16 GB) which nokogiri balked at. So I divided the query up into subranges of those dates (1.4 GB) and ran the script on all xml files. This gave 1425643 records. I removed records that did not have a received date or those with greater than 12 in the month field (leaving 428513 records). 13 of these records did not have a journal name. This gave 428500 records from 3301 journals. Again, I filtered out negative values (papers accepted before they were received) and a couple of outliers (e.g. 6000 days!). With a bit of code it was quite straightforward to extract simple statistics for each of the journals. You can download the data here to look up the information for a journal of your choice (wordpress only allows xls, not txt/csv). The fields show the journal name and the number of valid articles. Then for Acc-Pub, Rec-Acc and Rec-Pub, the number, Median, lower quartile, upper quartile times in days are given. I set a limit of 5 or more articles for calculation of the stats. Blank entries are where there was no valid data. Note that there are some differences with the table in my last post. This is because for that analysis I used a bigger date range and then filtered the year based on the published field. Here my search started out by specifying PDAT, which is slightly different. The data are OK, but the publication date needs to be taken with a pinch of salt. For many records it was missing a month or day, so the date used for some records is approximate. In retrospect using the Entrez date or one of the other required fields would have probably be better. I liked the idea of the publication date as this is when the paper finally appears in print which still represents a significant delay at some journals. The Recieved-to-Accepted dates are valid though. ## Waiting to Happen: Publication lag times in Cell Biology Journals My interest in publication lag times continues. Previous posts have looked at how long it takes my lab to publish our work, how often trainees publish and I also looked at very long lag times at Oncogene. I recently read a blog post on automated calculation of publication lag times for Bioinformatics journals. I thought it would be great to do this for Cell Biology journals too. Hopefully people will find it useful and can use this list when thinking about where to send their paper. What is publication lag time? If you are reading this, you probably know how science publication works. Feel free to skip. Otherwise, it goes something like this. After writing up your work for publication, you submit it to a journal. Assuming that this journal will eventually publish the paper (there is usually a period of submitting, getting rejected, resubmitting to a different journal etc.), they receive the paper on a certain date. They send it out to review, they collate the reviews and send back a decision, you (almost always) revise your paper further and then send it back. This can happen several times. At some point it gets accepted on a certain date. The journal then prepares the paper for publication in a scheduled issue on a specific date (they can also immediately post papers online without formatting). All of these steps add significant delays. It typically takes 9 months to publish a paper in the biomedical sciences. In 2015 this sounds very silly, when world-wide dissemination of information is as simple as a few clicks on a trackpad. The bigger problem is that we rely on papers as a currency to get jobs or funding and so these delays can be more than just a frustration, they can affect your ability to actually do more science. The good news is that it is very straightforward to parse the received, accepted and published dates from PubMed. So we can easily calculate the publication lags for cell biology journals. If you don’t work in cell biology, just follow the instructions below to make your own list. The bad news is that the deposition of the date information in PubMed depends on the journal. The extra bad news is that three of the major cell biology journals do not deposit their data: J Cell Biol, Mol Biol Cell and J Cell Sci. My original plan was to compare these three journals with Traffic, Nat Cell Biol and Dev Cell. Instead, I extended the list to include other journals which take non-cell biology papers (and deposit their data). A summary of the last ten years Three sets of box plots here show the publication lags for eight journals that take cell biology papers. The journals are Cell, Cell Stem Cell, Current Biology, Developmental Cell, EMBO Journal, Nature Cell Biology, Nature Methods and Traffic (see note at the end about eLife). They are shown in alphabetical order. The box plots show the median and the IQR, whiskers show the 10th and 90th percentiles. The three plots show the time from Received-to-Published (Rec-Pub), and then a breakdown of this time into Received-to-Accepted (Rec-Acc) and Accepted-to-Published (Rec-Pub). The colours are just to make it easier to tell the journals apart and don’t have any significance. You can see from these plots that the journals differ widely in the time it takes to publish a paper there. Current Biology is very fast, whereas Cell Stem Cell is relatively slow. The time it takes the journals to move them from acceptance to publication is pretty constant. Apart from Traffic where it takes an average of ~3 months to get something in to print. Remember that the paper is often online for this period so this is not necessarily a bad thing. I was not surprised that Current Biology was the fastest. At this journal, a presubmission inquiry is required and the referees are often lined up in advance. The staff are keen to publish rapidly, hence the name, Current Biology. I was amazed at Nature Cell Biology having such a short time from Received-to-Acceptance. The delay in Review-to-Acceptance comes from multiple rounds of revision and from doing extra experimental work. Anecdotally, it seems that the review at Nature Cell Biol should be just as lengthy as at Dev Cell or EMBO J. I wonder if the received date is accurate… it is possible to massage this date by first rejecting the paper, but allowing a resubmission. Then using the resubmission date as the received date [Edit: see below]. One way to legitimately limit this delay is to only allow a certain time for revisions and only allow one round of corrections. This is what happens at J Cell Biol, unfortunately we don’t have this data to see how effective this is. How has the lag time changed over the last ten years? Have the slow journals always been slow? When did they become slow? Again three plots are shown (side-by-side) depicting the Rec-Pub and then the Rec-Acc and Acc-Pub time. Now the intensity of red or blue shows the data for each year (2014 is the most intense colour). Again you can see that the dataset is not complete with missing date information for Traffic for many years, for example. Interestingly, the publication lag has been pretty constant for some journals but not others. Cell Stem Cell and Dev Cell (but not the mothership – Cell) have seen increases as have Nature Cell Biology and Nature Methods. On the whole Acc-Pub times are stable, except for Nature Methods which is the only journal in the list to see an increase over the time period. This just leaves us with the task of drawing up a ranked list of the fastest to the slowest journal. Then we can see which of these journals is likely to delay dissemination of our work the most. The Median times (in days) for 2013 are below. The journals are ranked in order of fastest to slowest for Received-to-Publication. I had to use 2013 because EMBO J is missing data for 2014. Journal Rec-Pub Rec-Acc Acc-Pub Curr Biol 159 99.5 56 Nat Methods 192 125 68 Cell 195 169 35 EMBO J 203 142 61 Nature Cell Biol 237 180 59 Traffic 244 161 86 Dev Cell 247 204 43 Cell Stem Cell 284 205 66 You’ll see that only Cell Stem Cell is over the threshold where it would be faster to conceive and give birth to a human being than to publish a paper there (on average). If the additional time wasted in submitting your manuscript to other journals is factored in, it is likely that most papers are at least on a par with the median gestation time. If you are wondering why eLife is missing… as a new journal it didn’t have ten years worth of data to analyse. It did have a reasonably complete set for 2013 (but Rec-Acc only). The median time was 89 days, beating Current Biology by 10.5 days. Methods Please check out Neil Saunders’ post on how to do this. I did a PubMed search for (journal1[ta] OR journal2[ta] OR ...) AND journal article[pt] to make sure I didn’t get any reviews or letters etc. I limited the search from 2003 onwards to make sure I had 10 years of data for the journals that deposited it. I downloaded the file as xml and I used Ruby/Nokogiri to parse the file to csv. Installing Nokogiri is reasonably straightforward, but the documentation is pretty impenetrable. The ruby script I used was from Neil’s post (step 3) with a few lines added:  #!/usr/bin/ruby require 'nokogiri' f = File.open(ARGV.first) doc = Nokogiri::XML(f) f.close doc.xpath("//PubmedArticle").each do |a| r = ["", "", "", "", "", "", "", "", "", "", ""] r[0] = a.xpath("MedlineCitation/Article/Journal/ISOAbbreviation").text r[1] = a.xpath("MedlineCitation/PMID").text r[2] = a.xpath("PubmedData/History/PubMedPubDate[@PubStatus='received']/Year").text r[3] = a.xpath("PubmedData/History/PubMedPubDate[@PubStatus='received']/Month").text r[4] = a.xpath("PubmedData/History/PubMedPubDate[@PubStatus='received']/Day").text r[5] = a.xpath("PubmedData/History/PubMedPubDate[@PubStatus='accepted']/Year").text r[6] = a.xpath("PubmedData/History/PubMedPubDate[@PubStatus='accepted']/Month").text r[7] = a.xpath("PubmedData/History/PubMedPubDate[@PubStatus='accepted']/Day").text r[8] = a.xpath("MedlineCitation/Article/Journal/JournalIssue/Pubdate/Year").text r[9] = a.xpath("MedlineCitation/Article/Journal/JournalIssue/Pubdate/Month").text r[10] = a.xpath("MedlineCitation/Article/Journal/JournalIssue/Pubdate/Day").text puts r.join(",") end  and then executed as described. The csv could then be imported into IgorPro and processed. Neil’s post describes a workflow for R, or you could use Excel or whatever at this point. As he notes, quite a few records are missing the date information and some of it is wrong, i.e. published before it was accepted. These need to be cleaned up. The other problem is that the month is sometimes an integer and sometimes a three-letter code. He uses lubridate in R to get around this, a loop-replace in Igor is easy to construct and even Excel can handle this with an IF statement, e.g. IF(LEN(G2)=3,MONTH(1&LEFT(G2,3)),G2) if the month is in G2. Good luck! Edit 9/3/15 @ 17:17 several people (including Deborah Sweet and Bernd Pulverer from Cell Press/Cell Stem Cell and EMBO, respectively) have confirmed via Twitter that some journals use the date of resubmission as the submitted date. Cell Stem Cell and EMBO journals use the real dates. There is no way to tell whether a journal does this or not (from the deposited data). Stuart Cantrill from Nature Chemistry pointed out that his journal do declare that they sometimes reset the clock. I’m not sure about other journals. My own feeling is that – for full transparency – journals should 1) record the actual dates of submission, acceptance and publication, 2) deposit them in PubMed and add them to the paper. As pointed out by Jim Woodgett, scientists want the actual dates on their paper, partly because they are the real dates, but also to claim priority in certain cases. There is a conflict here, because journals might appear inefficient if they have long publication lag times. I think this should be an incentive for Editors to simplify revisions by giving clear guidance and limiting successive revision cycles. (This Edit was corrected 10/3/15 @ 11:04). The post title is taken from “Waiting to Happen” by Super Furry Animals from the “Something 4 The Weekend” single. ## Division Day: using PCA in cell biology In this post I’ll describe a computational method for splitting two sides of a cell biological structure. It’s a simple method that relies on principal component analysis, otherwise known as PCA. Like all things mathematical there are some great resources on the web, if you want to understand this operation in more detail (for example, this great post by Lior Pachter). PCA can applied to many biological problems, you’ve probably seen it used to find patterns in large data sets, e.g. from proteomic studies. It can also be useful for analysing microscopy data. Since our analysis using this method is unlikely to make it into print any time soon, I thought I’d put it up on Quantixed. During mitosis, a cell forms a mitotic spindle to share copied chromosomes equally to the two new cells. Our lab is working on how this process works and how it goes wrong in cancer. The chromosomes attach to the spindle via kinetochores and during prometaphase they are moved to the middle of the cell. Here, the chromosomes are organised into a disc-like structure called the metaphase plate. The disc is thin in the direction of the spindle axis, but much larger in width and height. To examine the spatial distribution of kinetochores on the plate we wanted a way to approximately separate kinetochores on one side if the plate from the other. Kinetochores can be easily detected in 3D confocal images of mitotic cells by particle analysis. Kinetochores are easily stained and appear as bright spots that a computer can pick out (we use Imaris for this). The cartesian coordinates of each detected kinetochore were saved as csv and fed into IgorPro. A procedure could then be run which works in three steps. The code is shown at the bottom, it is wrapped in further code that deals with multiple datasets from many cells/experiments etc. The three steps are: 1. PCA 2. Point-to-plane 3. Analysis on each subset I’ll describe each step and how it works. 1. Principal component analysis This is used to find the 3rd eigenvector, which can be used to define a plane passing through the centre of the plate. This plane is used for division. Now, because the metaphase plate is a disc it has three dimensions, the third of which – “thickness” – is the smallest. PCA will find the principal component, i.e. the direction in which there is most variance. Orthogonal to that is the second biggest variance and orthogonal to that direction is the smallest. These directions are called eigenvectors and their magnitude is the eigenvalue. As there are three dimensions to the data we can get all three eigenvectors out and the 3rd eigenvector corresponds to thickness of the metaphase plate. Metaphase plates in cells grown on coverslips are orientated similarly, but the cells themselves are at random orientations. PCA takes no notice of this and can simply reveal the direction of the smallest dimension of a 3D structure. The movie shows this in action for a simulated data set. The black spots are arranged in a disk shape about the origin. They are rotated about x by 45° (the blue spots). We then run PCA and show the eigenvectors as unit vectors (red lines). The 3rd eigenvector is normal to the plane of division, i.e. the 1st and 2nd eigenvectors lie on the plane of division. Also, the centroid needs to be defined. This is simply the cartesian coordinates for the average of each dimension. It is sometimes referred to as the mean vector. In the example this was the origin, in reality this will depend on the position and the overall height of the cell. A much longer method to get the eigenvectors is to define the variance-covariance matrix (sometimes called the dispersion matrix) for each dimension, for all kinetochores and then do an eigenvector decomposition on the matrix. PCA is one command, whereas the matrix calculation would be an extra loop followed by an additional command. 2. Point-to-plane The distance of each kinetochore to the plane that we defined is calculated. If it is a positive value then the kinetochore lies on the same side as the normal vector (defined above). If it is negative then it is on the other side. The maths behind how to do this are in section 10.3.1 of Geometric Tools for Computer Graphics by Schneider & Eberly (starting on p. 374). Google it, there is a PDF version on the web. I’ll save you some time, you just need one equation that defines a plane, \(ax+by+cz+d=0

Where the unit normal vector is [a b c] and a point on the plane is [x y z]. We’ll use the coordinates of the centroid as a point on the plane to find d. Now that we know this, we can use a similar equation to find the distance of any point to the plane,

$$ax_{i}+by_{i}+cz_{i}+d$$

Results for each kinetochore are used to sort each side of the plane into separate waves for further calculation. In the movie below, the red dots and blue dots show the positions of the kinetochores on either side of the division plane. It’s a bit of an optical illusion, but the cube is turning in a right hand fashion.

3. Analysis on each subset

Now that the data have been sorted, separate calculations can be carried out on each. In the example, we were interested in how the kinetochores were organised spatially and so we looked at the distance to nearest neighbour. This is done by finding the Euclidean distance from each kinetochore to every other kinetochore and putting the lowest value for each kinetochore into a new wave. However, this calculation can be anything you want. If there are further waves that specify other properties of the kinetochores, e.g. brightness, then these can be similarly processed here.

Other notes

The code in its present form (not very streamlined) was fast and could be run on every cell from a number of experiments, reading out positional data for 10,000 kinetochores in ~2 s. For QC it is possible to display the two separated coordinated sets to check that the division worked fine (see above). The power of this method is that it doesn’t rely on imaging spindle poles or anything else to work out the orientation of the metaphase plate. It works well for metaphase cells, but cells with any misaligned chromosomes ruin the calculation. It is possible to remove these and still fit the plane, but for our analysis we focused on cells at metaphase with a defined plate.

What else can it be used for?

Other structures in the cell can be segregated in a similar way. For example, the Golgi apparatus has a trans and a cis side, which could be similarly divided (although using the 2nd eigenvector as normal to the plane, rather than the 3rd).

Acknowledgements: I’d like to thank A.G. at WaveMetrics Inc. for encouraging me to try PCA rather than my dispersion matrix approach.

If you want to use it, the code is available here (it seems I can only upload PDF at wordpress.com). I used pygments for annotation.

The post title comes from “Division Day” a great single by Elliott Smith.

## Tips from the blog III – violin plots

Having recently got my head around violin plots, I thought I would explain what they are and why you might want to use them.

There are several options when it comes to plotting summary data. I list them here in order of granularity, before describing violin plots and how to plot them in some detail.

Bar chart

This is the mainstay of most papers in my field. Typically, a bar representing the mean value that’s been measured is shown with an error bar which shows either the standard error of the mean, the standard deviation, or more rarely a confidence interval. The two data series plotted in all cases is the waiting time for Old Faithful eruptions (waiting), a classic dataset from R. I have added some noise to waiting (waiting_mod) for comparison. I think it’s fair to say that most people feel that the bar chart has probably had its day and that we should be presenting our data in more informative ways*.

Pros: compact, easy to tell differences between groups

Cons: hides the underlying distribution, obscures the n number

Box plot

The box plot – like many things in statistics – was introduced by Tukey. It’s sometimes known as a Tukey plot, or a box-and-whiskers plot. The idea was to give an impression of the underlying distribution without showing a histogram (see below). Histograms are great, but when you need to compare many distributions they do not overlay well and take up a lot of space to show them side-by-side. In the simplest form, the “box” is the interquartile range (IQR, 25th and 75th percentiles) with a line to show the median. The whiskers show the 10th and 90th percentiles. There are many variations on this theme: outliers can be shown or not, the whiskers may show the limits of the dataset (or something else), the boxes can be notched or their width may represent the sample size…

Pros: compact, easy to tell differences between groups, shows normality/skewness

Cons: hides multimodal data, sometimes obscures the n number, many variations

Histogram

A histogram is a method of showing the distribution of a dataset and was introduced by Pearson. The number of observations within a bin are counted and plotted. The ‘bars’ sit next to each other, because the variable being measured is continuous. The variable being measured is on the x-axis, rather than the category (as in the other plots).

Often the area of all the bars is normalised to 1 in order to assess the distributions without being confused by differences in sample size. As you can see here, “waiting” is bimodal. This was hidden in the bar chart and in the bot plot.

Related to histograms are other display types such as stemplots or stem-and-leaf plots.

Pros: shows multimodal data, shows normality/skewness clearly

Cons: not compact, difficult to overlay, bin size and position can be misleading

Scatter dot plot

It’s often said that if there are less than 10 data points, then best practice is to simply show the points. Typically the plot is shown together with a bar to show the mean (or median) and maybe with error bars showing s.e.m., s.d., IQR. There are a couple of methods of plotting the points, because they need to be scattered in x value in order to be visualised. Adding random noise is one approach, but this looks a bit messy (top). A symmetrical scatter can be introduced by binning (middle) and a further iteration is to bin the y values rather than showing their true location (bottom). There’s a further iteration which constrains the category width and overlays multiple points, but again the density becomes difficult to see.

These plots still look quite fussy, the binned version is the clearest but then we are losing the exact locations of the points, which seems counterintuitive. Another alternative to scattering the dots is to show a rug plot (see below) where there is no scatter.

Pros: shows all the observations

Cons: can be difficult to assess the distribution

Violin plot

This type of plot was introduced in the software package NCSS in 1997 and described in this paper: Hintze & Nelson (1998) The American Statistician 52(2):181-4 [PDF]. As the title says, violin plots are a synergism between box plot and density trace. A thin box plot is shown together with a symmetrical kernel density estimate (KDE, see explanation below). The point is to be able to quickly assess the distribution. You can see that the bimodality of waiting in the plot, but there’s no complication of lots of points just a smooth curve to see the data.

Pros: shows multimodal data, shows normality/skewness unambiguously

Cons: hides n, not familiar to many readers.

* Why is the bar chart so bad and why should I show my data another way?

The best demonstration of why the bar chart is bad is Anscombe’s Quartet (the figure to the right is taken from the Wikipedia page). These four datasets are completely different, yet they all have the same summary statistics. The point is, you would never know unless you plotted the data. A bar chart would look identical for all four datasets.

Making Violin Plots in IgorPro

I wanted to make Violin Plots in IgorPro, since we use Igor for absolutely everything in the lab. I wrote some code to do this and I might make some improvements to it in the future – if I find the time! This was an interesting exercise, because it meant forcing myself to understand how smoothing is done. What follows below is an aide memoire, but you may find it useful.

What is a kernel density estimate?

A KDE is a non-parametric method to estimate a probability density function of a variable. A histogram can be thought of as a simplistic non-parametric density estimate. Here, a rectangle is used to represent each observation and it gets bigger the more observations are made.

What’s wrong with using a histogram as a KDE?

The following examples are taken from here (which in turn are taken from the book by Bowman and Azzalini described below). A histogram is simplistic. We lose the location of each datapoint because of binning. Histograms are not smooth and the estimate is very sensitive to the size of the bins and also the starting location of the first bin. The histograms to the right show the same data points (in the rug plot).

Using the same bin size, they result in very different distributions depending on where the first bin starts. My first instinct to generate a KDE was to simply smooth a histogram, but this is actually quite inaccurate as it comes from a lossy source. Instead we need to generate a real KDE.

How do I make a KDE?

To do this we place a kernel (a Gaussian is commonly used) at each data point. The rationale behind this is that each observation can be thought of as being representative of a greater number of observations. It sounds a bit bizarre to assume normality to estimate a density non-parametrically, but it works. We can sum all of the kernels to give a smoothed distribution: the KDE. Easy? Well, yes as long as you know how wide to make the kernels. To do this we need to find the bandwidth, h (also called the smoothing parameter).

It turns out that this is not completely straightforward. The answer is summarised in this book: Bowman & Azzalini (1997) Applied Smoothing Techniques for Data Analysis. In the original paper on violin plots, they actually do not have a good solution for selecting h for drawing the violins, and they suggest trying several different values for h. They recommend starting at ~15% of the data range as a good starting point. Obviously if you are writing some code, the process of selecting h needs to be automatic.

Optimising h is necessary because if h is too large, the estimate with be oversmoothed and features will be lost. If is too small, then it will be undersmoothed and bumpy. The examples to the right (again, taken from Bowman & Azzalini, via this page) show examples of undersmoothed, oversmoothed and optimal smoothing.

An optimal solution to find h is

$$h = \left(\frac{4}{3n}\right)^{\frac{1}{5}}\sigma$$

This is termed Silverman’s rule-of-thumb. If smoothing is needed in more than one dimension, the multidimensional version is

$$h = \left\{\frac{4}{\left(p+2\right)n}\right\}^{\frac{1}{\left(p+4\right)}}\sigma$$

You might need multidimensional smoothing to contextualise more than one parameter being measured. The waiting data used above describes the time to wait until the next eruption from Old Faithful. The duration of the eruption is measured, and also the wait to the next eruption can be extracted, giving three parameters. These can give a 3D density estimate as shown here in the example.

The Bowman & Azzalini recommend that, if the distribution is long-tailed, using the median absolute deviation estimator is robust for $$\sigma$$.

$$\tilde\sigma=median\left\{|y_i-\tilde\mu|\right\}/0.6745$$

where $$\tilde\mu$$ is the median of the sample. All of this is something you don’t need to worry about if you use R to plot violins, the implementation in there is rock solid having been written in S plus and then ported to R years ago. You can even pick how the h selection is done from sm.density, or even modify the optimal h directly using hmult.

To get this working in IgorPro, I used some code for 1D KDE that was already on IgorExchange. It needed a bit of modification because it used FastGaussTransform to sum the kernels as a shortcut. It’s a very fast method, but initially gave an estimate that seemed to be undersmoothed. I spent a while altering the formula for h, hence the detail above. To cut a long story short, FastGaussTransform uses Taylor expansion of the Gauss transform and it just needed more terms to do this accurately. This is set with the /TET flag. Note also, that in Igor the width of a Gauss is sigma*2^1/2.

OK, so how do I make a Violin for plotting?

I used the draw tools to do this and placed the violins behind an existing box plot. This is necessary to be able to colour the violins (apparently transparency is coming to Igor in IP7). The other half of the violin needs to be calculated and then joined by the DrawPoly command. If the violins are trimmed, i.e. cut at the limits of the dataset, then this required an extra point to be added. Without trimming, this step is not required. The only other issue is how wide the violins are plotted. In R, the violins are all normalised so that information about n is lost. In the current implementation, box width is 0.1 and the violins are normalised to the area under the curve*(0.1/2). So, again information on n is lost.

Future improvements

Ideas for developments of the Violin Plot method in IgorPro

• incorporate it into the ipf for making boxplots so that it is integrated as an option to ‘calculate percentiles’
• find a better solution for setting the width of the violin
• add other bandwidth options, as in R
• add more options for colouring the violins

What do you think? Did I miss something? Let me know in the comments.

References

Bowman, A.W. & Azzalini, A. (1997) Applied Smoothing Techniques for Data Analysis : The Kernel Approach with S-Plus Illustrations: The Kernel Approach with S-Plus Illustrations. Oxford University Press.

Hintze, J.L. & Nelson, R.D. (1998) Violin plots: A Box Plot-Density Trace Synergism. The American Statistician, 52:181-4.

## My Favorite Things

I realised recently that I’ve maintained a consistent iTunes library for ~10 years. For most of that time I’ve been listening exclusively to iTunes, rather than to music in other formats. So the library is a useful source of information about my tastes in music. It should be possible to look at who are my favourite artists, what bands need more investigation, or just to generate some interesting statistics based on my favourite music.

Play count is the central statistic here as it tells me how often I’ve listened to a certain track. It’s the equivalent of a +1/upvote/fave/like or maybe even a citation. Play count increases by one if you listen to a track all the way to the end. So if a track starts and you don’t want to hear it and you skip on to the next song, there’s no +1. There’s a caveat here in that the time a track has been in the library, influences the play count to a certain extent – but that’s for another post*. The second indicator for liking a track or artist is the fact that it’s in the library. This may sound obvious, but what I mean is that artists with lots of tracks in the library are more likely to be favourite artists compared to a band with just one or two tracks in there. A caveat here is that some artists do not have long careers for a variety of reasons, which can limit the number of tracks actually available to load into the library. Check the methods at the foot of the post if you want to do the same.

What’s the most popular year? Firstly, I looked at the most popular year in the library. This question was the focus of an earlier post that found that 1971 was the best year in music. The play distribution per year can be plotted together with a summary of how many tracks and how many plays in total from each year are in the library. There’s a bias towards 90s music, which probably reflects my age, but could also be caused by my habit of collecting CD singles which peaked as a format in this decade. The average number of plays is actually pretty constant for all years (median of ~4), the mean is perhaps slightly higher for late-2000s music.

Favourite styles of music: I also looked at Genre. Which styles of music are my favourite? I plotted the total number of tracks versus the total number of plays for each Genre in the library. Size of the marker reflects the median number of plays per track for that genre. Most Genres obey a rule where total plays is a function of total tracks, but there are exceptions. Crossover, Hip-hop/Rap and Power-pop are highlighted as those with an above average number of plays. I’m not lacking in Power-pop with a few thousand tracks, but I should probably get my hands on more Crossover or Hip-Hop/Rap.

Using citation statistics to find my favourite artists: Next, I looked at who my favourite artists are. It could be argued that I should know who my favourite artists are! But tastes can change over a 10 year period and I was interested in an unbiased view of my favourite artists rather than who I think they are. A plot of Total Tracks vs Mean plays per track is reasonably informative. The artists with the highest plays per track are those with only one track in the library, e.g. Harvey Danger with Flagpole Sitta. So this statistic is pretty unreliable. Equally, I’ve got lots of tracks by Manic Street Preachers but evidently I don’t play them that often. I realised that the problem of identifying favourite artists based on these two pieces of information (plays and number of tracks) is pretty similar to assessing scientists using citation metrics (citations and number of papers). Hirsch proposed the h-index to meld these two bits of information into a single metric, the h-index. It’s easily computed and I already had an Igor procedure to calculate it en masse, so I ran it on the library information.

Before doing this, I consolidated multiple versions of the same track into one. I knew that I had several versions of the same track, especially as I have multiple versions of some albums (e.g. Pet Sounds = 3 copies = mono + stereo + a capella), the top offending track was “Baby’s Coming Back” by Jellyfish, 11 copies! Anyway, these were consolidated before running the h-index calculation.

The top artist was Elliott Smith with an h-index of 32. This means he has 32 tracks that have been listened to at least 32 times each. I was amazed that Muse had the second highest h-index (I don’t consider myself a huge fan of their music) until I remembered a period where their albums were on an iPod Nano used during exercise. Amusingly (and narcissistically) my own music – the artist names are redacted – scored quite highly with two out of three bands in the top 100, which are shown here. These artists with high h-indeces are the most consistently played in the library and probably constitute my favourite artists, but is the ranking correct?

The procedure also calculates the g-index for every artist. The g-index is similar to the h-index but takes into account very highly played tracks (very highly cited papers) over the h threshold. For example, The Smiths h=26. This could be 26 tracks that have been listened to exactly 26 times or they could have been listened to 90 times each. The h-index cannot reveal this, but the g-index gets to this by assessing average plays for the ranked tracks. The Smiths g=35. To find the artists that are most-played-of-the-consistently-most-played, I subtracted h from g and plotted the Top 50. This ranked list I think most closely represents my favourite artists, according to my listening habits over the last ten years.

Track length: Finally, I looked at the track length. I have a range of track lengths in the library, from “You Suffer” by Napalm Death (iTunes has this at 4 s, but Wikipedia says it is 1.36 s), through to epic tracks like “Blue Room” by The Orb. Most tracks are in the 3-4 min range. Plays per track indicates that this track length is optimal with most of the highly played tracks being within this window. The super-long tracks are rarely listened to, probably because of their length. Short tracks also have higher than average plays, probably because they are less likely to be skipped, due to their length.

These were the first things that sprang to mind for iTunes analysis. As I said at the top, there’s lots of information in the library to dig through, but I think this is enough for one post. And not a pie-chart in sight!

Methods: the library is in xml format and can be read/parsed this way. More easily, you can just select the whole library and copy-paste it into TextEdit and then load this into a data analysis package. In this case, IgorPro (as always). Make sure that the interesting fields are shown in the full library view (Music>Songs). To do everything in this post you need artist, track, album, genre, length, year and play count. At the time of writing, I had 21326 tracks in the library. For the “H-index” analysis, I consolidated multiple versions of the same track, giving 18684 tracks. This is possible by concatenating artist and the first ten characters of the track title (separated by a unique character) and adding the play counts for these concatenated versions. The artist could then be deconvolved (using the unique character) and used for the H-calculation. It’s not very elegant, but seemed to work well. The H-index and G-index calculations were automated (previously sort-of-described here), as was most of the plot generation. The inspiration for the colour coding is from the 2013 Feltron Report.

* there’s an interesting post here about modelling the ideal playlist. I worked through the ideas in that post but found that it doesn’t scale well to large libraries, especially if they’ve been going for a long time, i.e. mine.

The post title is taken from John Coltrane’s cover version of My Favorite Things from the album of the same name. Excuse the US English spelling.