I feel all fuzzy inside...

Just kidding.

I've not been around much recently as I've been working hard at my MSc project.  For part of this I've had to implement something called a "Fuzzy Transform", this was initially presented by Irina Perfilieva and has been developed by the Institute for Research and Applications of Fuzzy Modeling (IRAFM) at the University of Ostrava in Ostrava in the Czech Republic.

The way in which I'm presently using the Fuzzy Transform is one that provides a numerical analysis method that is a cross between fuzzy logic and a filtering function (a filtering function is used to remove noise [unwanted information] from a signal; such functions are in use everywhere in our modern world, from cellphones to missile guidance systems).  It's a numerical method, because it doesn't try to "guess" what gave rise to the original data (methods that try to work out what gave rise to the data in the first place are "estimators" and tend to use "mathematical models" to represent whatever is generating the data from a given input); if you wanted to you could feed in a totally random stream of numbers and a numerical method would have a good go at approximating the numbers "with arbitrary accuracy" (this means "as well as you make it", see below).

One of the things that the fuzzy transform provides as well as the filtering capability of the filtering function is an ability called "Universal Approximation", this means that provided any series of data a correctly set-up fuzzy transform can be used to approximate the data.  Universal Approximators are useful since they allow you to do all kinds of fun stuff, such as pattern matching (for example, character recognition and face recognition), data compression and forecasting... but more on this later.

So, let's take a varying series of data:

This isn't of anything very exciting other than something that provides a nice wiggly line (if you're really interested it's y=sin(x.π)+x with added zero mean, normally distributed noise with variance 0.01).  So what happens if we use the fuzzy transform?  We get a plot a little like this:

The blue line in the above plot is the result of the Fuzzy Transform, this was obtained by dividing the original wiggly line into 10 horizontally measured sections, or partitions, taking the Fuzzy Transform of the data and then inverting (reversing) the transform; and you can see that it kind of matches the original wavy line, but as well as removing all the noise, the F-Transform has also removed a lot of the shape of the original line (we've lost information).  Using 20 partitions gives this:

Which uses the same colours for the noisy data and the approximation as previously and is a better fit, but still leaves a few gaps.  While using 30 partitions gives this:

Which again uses the same colours for the noisy data and the approximation as previously and almost exactly matches the original function, which I've plotted below (in green) along with the 30-partition approximation to allow an easy comparison:

So what does this mean?  It means that the Fuzzy Transform can approximate the data "with arbitrary accuracy", which we can now see is a way of saying that it can match the data we feed into it (the red line) as closely as we want it to.  Why might we not want to try to get an exact match?  Well, firstly, the more accurate we make the approximation, the more calculations are required and so it takes longer to get the approximation, and, secondly, if we make the approximation too accurate then it will also start to approximate the noise (the Fuzzy Transform doesn't know where the data has come from, so it can't tell what is "noise" and what is "signal").  This means that we need to find a balance between ease of calculation, and being a good enough approximation, while still "filtering out" the noise.

In the example above, doubling our "effort" by going from 10 to 20 partitions gives quite a large benefit, but putting in another half as much effort again to get from 20 to 30 partitions doesn't give a very big improvement (so if the end use could tolerate the inaccuracy of the 20 partition transform then we'd use that rather than "wasting effort").

Finally, I suppose you want to know how can this be used?  Well IRAFM and others have shown how the Fuzzy Transform can be used to detect patterns and relationships that underlie quite complex data.  For example, in one paper published in 2008 [subscription required] the Fuzzy Transform was used to provide a model of the GDP of the Czech Republic based on a set of other data, such as unemployment, the rate of inflation, etc.  The Fuzzy Transform has also been used to automatically combine multiple images to provide an image that is of better quality overall than the constituent images [PDF].  Pretty impressive, eh?

If you want to learn more about the Fuzzy Transform, or the other things that IRAFM are involved in researching and developing then they have an extensive list of publications that are publicly available in PDF format.

This may be a bit technical, so please ask questions, I'll do my best to explain, or point you to somewhere you can find more information!

From Evernote:

Breakfast time

Using Evernote again to blog from my HTC, so please excuse any dodgy formatting or misplaced images!

If you're ever in Leamington Spa before midday then you should seriously consider a visit to Alfonso's Place, on Station Approach. They do the best fried breakfasts in Leamington, and in fact one if the best I've had anywhere. I tend to go for the Breakfast Supreme:

Which is awesome, and looks a bit like this:

Obviously, it's not something that one should eat everyday, but it's a great occasional treat! If you're in the area you should definitely try it. After 11 at the weekends it can get very busy, so if you arrive later on in the breakfast shift then you may need to wait a while.

Alfonso's also doubles as a Portuguese restaurant in the evenings, so if you fancy some salt cod or bitoque and it's later in the day then give it a go then too.

  

From Evernote:

This is new...

Ok, I'm trying an experiment. I've just started seriously using Evernote to work on my MSc thesis.

It's great! Combined with Swype on both my Android devices I can easily jot notes, take screenshots and link in references as I go along. I'm wondering why I never used it before. It's going to change my life.

Here is a photo of my desktop client showing how I've used Evernote to pick up relevant parts of my reading list.

From the photo you can see I've tagged the note with relevant keywords, and inserted images where I want to quote equations.

What else?  Oh yes, I wrote this entirely in Evernote as a note and then sent it to Blogger by email through the "share" feature :-)

Oh and did I mention the search feature?  Evernote has implemented OCR (character recognition) so that your searches will also give results for words that are in images.  How cool is that!?

DELIVERing the future

Crumbs - it's a while since I've been here, in my defence it's been a very busy time.  Work has been off the scale, and studying as well has loaded me up to the point where pretty much all I do is eat, work, sleep and study since July!  Only another 9 months of this to go though...


Anyway, what's been going on?  Well at work we have secured a part in an EU seventh framework programme - with the acronym "DELIVER" (do you see what I did in the title now?).  The EU webpage for this is here: http://www.green-cars-initiative.eu/public/projects/deliver


In case the link moves or changes this says:

Design of Electric Light Vans for Environment-Impact Reduction

The DELIVER project concept aims to explore urban light duty vehicle concepts intended for larger scale production by executing a broad scope conceptual design study which will start by establishing initial design specifications and continue right through to the detailed realistic performance assessment of one prototyped vehicle concept.

DELIVER is pre-competitive, focusing on the rules of the design of ELDVs to be launched by 2020, and providing a platform for integrated design brought together into one holistic design by a team of experienced design engineers and design researchers of various backgrounds.

The project will build upon the progress made and foreseen in subsystems and main components that are to be integrated into the ELDV through networking with complementary R&D projects, as well as with the support of a multi stakeholder Advisory Board consisting of high level representatives of Europe's cities, large urban delivery fleet owners and others.

If you want to find out more about the project participants and the EU Green Cars initiative then there is a project portfolio document (PDF) available from the EU website here: http://www.green-cars-initiative.eu/public/documents/GreenCarsInitiative-Broschure_09-2011_WEB.pdf/view


As a small UK company it's a measure of how well the UK electric vehicle industry is regarded for us to be involved in an international concept vehicle project with both VW and Fiat - and we have some other similar projects in the application process, so I hope to be able to talk about these more in the future.

Something I wrote a while ago about the USA...

The following is something that I wrote a while ago as a Facebook "note", I thought I'd copy it here for you to read...


                                               
Wednesday, 21 July 2010 at 04:19 UTC


I've just had the most amazing drive in the most dire car along the most boring roads that I've ever encountered. Journey: Eastern Indiana to North-Western Indiana; Car: Chevrolet HHR; Time: 8pm to 11pm

I set off about 30 minutes before sunset, and as I got onto US-33 the sun hit the horizon, and the verges and the air above them started to glitter. The glittering was thousands of fireflies along the roadside reacting to my approach. As the sun dipped lower the fireflies became more obvious, until it seemed that I was driving along a tunnel of lights similar to a 70s sci-fi effect. Then Venus started shining in the sky above the sun.

And as the sun disappeared I was driving into a huge orange sunset with Venus overhead and surrounded by fireflies. Absolutely magical, and I've just done it no justice at all with these few brief words. But that is the story of my last evening in the USA.

Ohai2u!

Hello there!


So here we are... I have no idea where this is going to go, or how it will get there, but it should be interesting to find out.


I suppose the first thing I should tell you is a few things about me, for those too lazy to read my account; I live in Warwick in the UK and I am in the middle of a few things, I'll probably write about them now and then:

1. A part-time MSc in Control Engineering.  This came about after an argument with a (now ex) girlfriend where we split up for a while, I decided that I would need something to do, and decided, for want of a better expression, to "improve myself" in a way that might make me more useful at work (q.v.).  At the time of writing I have about 9 months left to go (which will be taken up with my project, this will involve some Matlab and the report for which will have to be written in LaTeX).
2. Teaching myself to play the guitar (this has been going on for about 6 years), one day I expect I'll get around to paying someone for a lesson.
3. Relearning to play the cornet (I first learnt at school, a few years ago now).
4. Running a photography business.
5. Sitting on the board of a high technology company that is in the field of electric vehicle design and engineering.  Primarily I'm responsible for all electrical and electronic systems activities, but I also have some input into other areas, such as customer service and information systems.

Something I'm planning to add to the above is that I want to work through, "The Elements of Computing Systems: Building a Modern Computer from First Principles" by Noam Nisan and Shimon Schocken, which is freely available at: http://www1.idc.ac.il/tecs/ so feel free to join in if you'd like to.