Archive for January 28, 2012

The H-index is Redundant…

Posted in Bad Statistics, Science Politics with tags , , , , , on January 28, 2012 by telescoper

An interesting paper appeared on the arXiv last week by astrophysicist Henk Spruit on the subject of bibliometric indicators, and specifically the Hirsch index (or H-index) which has been the subject of a number of previous blog posts on here. The author’s surname is pronounced “sprout”, by the way.

The H-index is defined to be the largest number H such that the author has written at least H papers having H citations. It can easily be calculated by looking up all papers by a given author on a database such as NASA/ADS, sorting them by (decreasing) number of citations, and working down the list to the point where the number of citations of a paper falls below the number representing position in the list. Normalized quantities – obtained by dividing the number of citations a paper receives by the number of authors of that paper for each paper – can be used to form an alternative measure.

Here is the abstract of the paper:

Here are a couple of graphs which back up the claim of a near-perfect correlation between H-index and total citations:

The figure shows both total citations (right) and normalized citations (left); the latter, in my view, a much more sensible measure of individual contributions. The basic problem of course is that people don’t get citations, papers do. Apportioning appropriate credit for a multi-author paper is therefore extremely difficult. Does each author of a 100-author paper that gets 100 citations really deserve the same credit as a single author of a paper that also gets 100 citations? Clearly not, yet that’s what happens if you count total citations.

The correlation between H index and the square root of total citation numbers has been remarked upon before, but it is good to see it confirmed for the particular field of astrophysics.

Although I’m a bit unclear as to how the “sample” was selected I think this paper is a valuable contribution to the discussion, and I hope it helps counter the growing, and in my opinion already excessive, reliance on the H-index by grants panels and the like. Trying to condense all the available information about an applicant into a single number is clearly a futile task, and this paper shows that using H-index and total numbers doesn’t add anything as they are both measuring exactly the same thing.

A very interesting question emerges from this, however, which is why the relationship between total citation numbers and h-index has the form it does: the latter is always roughly half of the square-root of the former. This suggests to me that there might be some sort of scaling law describing onto which the distribution of cites-per-paper can be mapped for any individual. It would be interesting to construct a mathematical model of citation behaviour that could reproduce this apparently universal property….

Gershwin, Adams & Rachmaninov

Posted in Music with tags , , , , , , , , on January 28, 2012 by telescoper

Yesterday (Friday) being the last day of (relative) freedom before teaching resumes on Monday I took the opportunity to go to a concert by the Orchestra of Welsh National Opera at the splendid St David’s Hall in Cardiff. I had been looking forward to it for some time, as the programme featured two favourite pieces of mine, George Gershwin’s Rhapsody in Blue and John Adams’ The Chairman Dances (A Foxtrot for Orchestra), plus one longer piece that I’ve never heard live before, Symphony No. 2 (in E minor) by Sergei Rachmaninov.

There was a good crowd in St David’s last night, not surprisingly given the popularity of the pieces being performed. Conductor for the evening was Frédéric Chaslin, who led the orchestra from the piano during the opening number, Rhapsody in Blue. This is a very famous piece, and is played so often that it is in danger of becoming a bit of a cliché, especially when classical orchestras try too hard to sound like jazz musician; the piece was originally written for Paul Whiteman’s Orchestra. A case in point is the opening clarinet solo, which is often played like a ham-fisted parody. Not last night, though. Principal clarinettist of WNO Leslie Craven gave a very characterful rendition of the notoriously tricky opening, which seemed to inspire the orchestra into an excellent all-round performance. I particularly enjoyed seeing the cello section slapping the strings of their instruments much as a jazz-era double-bass player would.

Chaslin gave an idiosyncratic account of the piano part, to the extent that in the final solo passage before the finale he departed from the script entirely and interpolated an improvised section all of his own. Not everyone in the audience approved – there were a few tuts behind me – but it’s a piece undoubtedly inspired by jazz, so I don’t see anything wrong with doing this. I thought his ad-libbing was charming, and very witty. What I wasn’t so happy about were the changes in tempo, which were too exaggerated. I suppose conducting from the piano means you can do whatever you want, but I think he took the rubato too far. Some sections rely on strict rhythm for their sense of urgency, and I felt he got bogged down a bit in places. Still, on balance, it was very refreshing to hear an orchestra trying to do something different. Nothing hackneyed about last night’s performance, that’s for sure.

Next one up was The Chairman Dances by John Adams. This isn’t actually in the opera Nixon in China, which is what a lot of people seem to think. It was composed at the same time, but cut out and developed as a standalone concert piece. I posted a recording of this yesterday, so won’t say too much today, except that I thoroughly enjoyed my first live experience of this work. So did the orchestra by the look of it! It’s a hugely entertaining piece and had many in the audience tapping their feet along with it. As a matter of fact, I wouldn’t have minded getting up and dancing along myself..

Special mention has to go the percussion section of the orchestra for doing such an excellent job. The four xylophones were  a delight to listen to, and the drums, temple blocks, triangles and assorted ironmongery coped brilliantly with the intricate polyrhythms.

Then it was the interval, and a glass of wine before returing to savour the main piece of the evening, Rachmaninov’s Second Symphony. It’s a remarkable work because it’s not only a “proper” symphony in its construction and development but also the best part of an hour of one glorious melody after another. Rachmaninov’s music is not really very much like Mozart, but they certainly had a similar ear for the Big Tune! I particularly loved the third movement (Adagio), but I thought it was a magnificent performance throughout, not least because you could see how much both conductor and orchestra were enjoying themselves.

The end of the concert was met with rapturous applause from the (normally rather reticent) St Davids audience. Now I have to find the best recording I can of Rachmaninov’s Second Symphony so I can enjoy it again. Any suggestions?