Musical sunbursts

We of­ten won­der what songs would look like. Here’s our take on what Bobby McFerrin’s Don’t Worry Be Happy looks like.

dont-worry-be-happy

This pic­ture is a spec­tro­gram of the song. It starts at the 12 o’clock po­s­i­tion, and moves clock­wise, end­ing at about 4:00 minutes. The in­tens­ity of col­our in­dic­ates the volume at dif­fer­ent fre­quen­cies – blue for high volume, red for me­di­um, yel­low for low and white for zero. The out­er ra­di­us rep­res­ents the lower fre­quen­cies and the in­ner ra­di­us the higher fre­quen­cies.

This sort of pic­ture al­most gives you a “fin­ger­print” of the song, and a feel for the kinds of ups-and-downs. For ex­ample, if you look at Bryan Adam’s Everything I Do, you can clearly see the light be­gin­ning, the some­what stronger middle; then a pause be­fore the 3:00 mark, strong again, and then fad­ing out.

Bryan Adams.Everything I Do (I Do It For You).mp3

For your amuse­ment, here are what a few more songs would look like – a mix of Bollywood, old and new.

songs

Visualising securities correlation

If you were won­der­ing how the se­cur­it­ies in the world move again­st each oth­er, the pic­ture be­low is the an­swer.

securities-correlation

This pic­ture shows the cor­rel­a­tion vari­ous cur­ren­cies, in­dices and com­mod­ity prices by link­ing to­geth­er three power­ful types of visu­al­isa­tions.

securities-correlation-example

The first is a col­oured cor­rel­a­tion mat­rix. In this pic­ture, we have three se­cur­it­ies: the British Pound (GBP), Gold Price (XAU) and the Dow Jones Index (^DJI). The price of GBP and Gold tend to move slightly to­geth­er, and have a cor­rel­a­tion of 0.36 (36%). So the cell that’s between GBP and XAU is marked with 36. Similarly, the cell that’s between XAU and ^DJI has a –64 be­cause Gold and the Dow Jones in­dex are slightly neg­at­ively cor­rel­ated.

The col­our cod­ing is based on the cor­rel­a­tion. Red is -1, Green is +1 and Yellow is 0.

securities-correlation-scatterplotThe second is a scat­ter­plot mat­rix. The cells that mir­ror the cor­rel­a­tions have a series of dots. Each dot rep­res­ents the price on a par­tic­u­lar day.

For ex­ample, com­pare Gold and the Dow Jones. It isn’t a straight-forward neg­at­ive cor­rel­a­tion. In fact, it al­most looks like there were two peri­ods: one in which gold was high when the Dow Jones was low, and vice ver­sa. But with­in those peri­ods, there ap­pears to have been a mild pos­it­ive cor­rel­a­tion.

securities-correlation-cluster

The third is the hier­arch­ic­al cluster. The se­cur­it­ies is grouped in­to sim­il­ar ones based on their cor­rel­a­tion. For ex­ample, GBP and Silver (XAG) and reas­on­ably close to each oth­er, and form one group. This group is most closely re­lated to the Euro (EUR), and the three of them are closest to the Australian Dollar.

Arranging the se­cur­it­ies by the hier­archy makes it easy to spot groups of se­cur­it­ies that tend to move to­geth­er.

For ex­ample, in the ori­gin­al visu­al­isa­tion, there ap­pear to be a set of lo­gic­al blocks

securities-correlation

At the centre, four se­cur­it­ies – the Pakistani Rupee (PKR), the Sensex (^BSES), the FTSE (^FTSE) and the S&P (^GSPC) – tend to move to­geth­er, with each oth­er; but move in the op­pos­ite dir­ec­tion to the next group of se­cur­it­ies – the Singapore Dollar (SGD), the Japanese Yen (JPY), Gold (XAU), the Swiss Franc (CHF) and the Chinese Yuan (CNY).

Similarly, the Swedish Krona, Canadian Dollar, Indian Rupee, Hong Kong Dollar and Mexican Peso form yet an­other group that moves to­geth­er, but in the op­pos­ite dir­ec­tion from the strong Asian cur­ren­cies in the block above.


We at Gramener have named this visu­al­isa­tion a cluster­plot. It’s a power­ful tech­nique when ap­plied to time series of mul­tiple (typ­ic­ally 5 – 50) vari­ables.

Here are some cases you might con­sider us­ing them:

  • Group your products based on con­sumer be­ha­vi­our. Which products tend to sell to­geth­er? Which ones can­ni­bal­ise the sale of the oth­er? Is there a way of ra­tion­al­ising the pro­duct base to re­duce com­plex­ity – without los­ing cus­tom­ers?
  • Group re­tail­ers based on sales. Which re­tail­ers tend to can­ni­bal­ise the sales across each oth­er? Which ones com­ple­ment each oth­er? Where would you need to ra­tion­al­ise to avoid du­plic­a­tion or over­lap?
  • Analyse pro­cess qual­ity drivers. For ex­ample, if tem­per­at­ure, pres­sure and sa­lin­ity af­fect your pro­duct qual­ity, what im­pact will in­creas­ing one para­met­er have on the oth­er?