How to do (hopefully) interesting research by Martin Vetterli, 17.9.15

1. Introduction

2. Why we do research?

3. The scientific method

4. Examples from the trenches

5. Experimental results

6. Mistakes to avoid

1. Open access, open data, reproducibility

2. Conclusions and outlook 1

Flamarion, 1890

Why I became a researcher

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Those from whom I learned....

• My advisor, Henri J. Nussbaumer• Co-workers• Former students• Current students

Acknowledgements

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1. Introduction

The most exciting phrase to hear in science, the one that heralds new discoveries, is not 'Eureka!' but 'That's funny...’

Isaac Asimov

Research is to see what everybody else has seen and think what nobody has thought.

Schopenhauer

What people think of as the moment of discovery is really the discovery of the question.

Jonas Salk

Koyasan (Japan) 20124

1. Introduction

Research versus search

Discovery versus invention

Creativity versus drudgery

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2. Why we do research?

It is like with artists, you do research if you cannot do anything else!

Remember, it is a 24/7 job….

If you wake up in the middle of the night and think about a problem, that is a good sign ;)

Even better, if you solve a problem while sleeping, then you are on the way to become a master!

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It is like with art, why should it be useful?

That is ‘’science is part of culture’’

The obsession with knowledge is a sign of civilization

Now, research is often useful• It has educational value• It is good training for other endeavors• Sometimes it does help cure cancer• Sometimes it creates Google

Etc!

Is research useful?

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What is research?

Science• See, find, understand something nobody has ever done before

Engineering• Build, invent, design something nobody has ever done before

In both cases• It is about ‘’discovery’’

Physics: Building models of the worldMathematics: Proving what we knowComputer Sciences: What can be computed and howElectrical engineering: Technological constraints, what can be built or not

Of course, Ernest Rutherford said:• “All science is either physics or stamp collecting”• “We’ve got no money, so we’ve got to think”

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Research can be dangerous to your health!

Various known effects

• Sleep deprivation• Nightmares• Anxiety• Helplessness • etc

But it can be marvellous!

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3. The Scientific Method

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Research is like playing Lego…

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Keep going, make sure it holds…

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Until there is diminishing returns!

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Sometimes there is a revival!

Don’t flog a dead horse… Sometimes there is a revolution!

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Cairns

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You see a goal, you see a path

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There is competition on the way

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There is an intermediate result

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If you are lost, sometimes there are sign posts

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There are many ways to skin a cat

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Team work is key!

• Find likeminded people

• Find complementary people

• There has to be a leader

• It is better to be one of 5 authors on a great paper than a signal author on a marginal one

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But also intellectual leadership...

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about concentration/obsession

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Keep notes!

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Creativity

Creativity is the power to connect the seemingly unconnectedWilliam Plomer

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Creativity

The ancient art of mathematics, Tao has discovered, does not reward speed so much as patience, cunning and, perhaps most surprising of all, the sort of gift for collaboration and improvisation that characterizes the best jazz musicians.

« The Singular Mind of Terry Tao », Gareth Cook, NYTimes, 24.7.2015

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Curiosity comes with a healthy dose of ignorance, with an open and often naïve mind, the sort open mind observed in children. It is said that a 12-year old Albert Einstein asked his mother what he would see if he travelled at the speed of light, holding a mirror in front of himThis is a very good question, driven by pure curiosity and childish ignorance.

The scientist is not a person who gives the right answers, he’s one who asks the right questions.

Claude Lévi-Strauss

The art of asking the right question

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There is a bag of tricks, but there is mostly hard work ;)

• The low hanging fruit• Listening to a children’s question• By brute force• By geometry• By analogy• By duality• Deterministic <-> Stochastic• Discrete <-> Continuous• By simplification• By generalization• By changing dimensions• By questioning common wisdom• By intuition• By paradox• By using a new tool• By teaching and setting a homework problem• By magic ;)

Below a few examples from my experience…

Methods?

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Methods versus application of the method

• A method is successful in domain A• Port it to domain B

Or: Take your tools and move to a new field

The low hanging fruit

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On the value of the LCAV ski day

• Thomas: ‘’Dad, what is the name of this mountain?’’• Serge and I: there must be an easy way to solve this!

Listening to a children’s question

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By brute force

There is an algorithm…

… let’s make a chip!

M.Vetterli, Analyse, synthèse et complexité de calcul de bancs de filtres numériques,EPFL, Thèse 617, 1986.

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Consistency

• Always use all the information you have at hand• It can help a lot, like linear -> quadratic decay

By geometry

N. T. Thao and M. Vetterli. Reduction of the MSE in R-times oversampled A/D conversion from O(1/R) to O(1/R^2), IEEE Transactions on Signal Processing, 1994

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Frame quantization and depth estimation in multi-camera systems

• It seems obvious!

By analogy

V. K. Goyal, M. Vetterli and N. T. Thao. Quantized overcomplete expansions in RN: Analysis, synthesis and algorithms, IEEE Transactions on IT, 1998. A.Ghasemi, A.Scholefield et al, On the Accuracy of

Point Localisation in a Camera-Arrayhttp://aghasemi.github.io/lincamarray.html

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By duality

ICASSP 1986: By duality…

Note: Adjoint operator is always a good object to look at

* I forgot to write the journal paper ;)

*

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Often problems are seen in either of the two views of the world

• Randomize algorithm• Pick a specific realization

Example• Quantization is often modeled as ‘’noise’’ • It is a deterministic phenomena• Substantial improvements

Remember:“Essentially, all models are wrong, but some are useful.”

G.E.P. Box

Deterministic <-> stochastic

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Often problems are seen/solved as either discrete or continuous time

• Discrete-time uncertainty: Continuous case is completely settled• Wavelets from filter banks• Curvelets <-> contourlets

Discrete <-> Continuous

M. Vetterli and C. Herley. Wavelets and Filter Banks: Theory and Design,in IEEE Transactions on Signal Processing, vol. 40, num. 9, p. 2207-2232, 1992

M. M. N. Do and M. Vetterli. The Contourlet Transform: An Efficient Directional Multiresolution Image Representation,in IEEE Transactions on IP, 2005

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If it looks to complicated, simplify

• Relay channel studies for 30 years, marginal gains• Intuition from Gupta-Kumar’s landmark paper on the capacity of

wireless networks

By simplification

M.Gastpar, M.Vetterli, On the capacity of wireless networks: The relay case, INFOCOM 2002.1994

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Frames of vectors -> frames of filters

• It seems obvious but it is hard work (in this case…)

By generalization

M. Vetterli, J. Kovacevic and V. K. Goyal, Foundations of Signal Processing,Cambridge University Press, 2014

Z. Cvetkovic and M. Vetterli. Oversampled Filter Banks, IEEE Transactions on Signal Processing, 1998.

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Go to smaller dimensions…• If you can’t solve it for 2 dimensions, you probably won’t for infinite

dimensions• There is always recursionGo to higher dimensions…• Result might just be waiting for you!

By changing dimensions

M.Vetterli, Analyse, synthèse et complexité de calcul de bancs de filtres numériques,EPFL, Thèse 617, 1986.

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Go to even higher dimensions…• If it worked once, it might work again• More seriously, it solved another problem, namely simple jont source

channel coding, something nobody wanted to touch because of the separation theorem ;)

By changing dimensions….

G.Karlsson, M.Vetterli,Three dimensional sub-band coding of video, ICASSP-88.41

Common approach: Separation theorem• Source coding and channel coding can be done separately without loss• Shannon’s gospel, design principle of communication systems!

New view: With finite delay or heterogeneous channels, not true• But messy, no nice Tr. on IT paper…• Addresses broadcast, multicast

By questioning common wisdom

S.McCanne, Van Jacobson, M.Vetterli, Receiver-driven layered multicast, ACM SIGCOMM, 1996

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There is always a trade-off, and rate-distortion theory is an obvious one

• Wavelet packets proposed by the wavelet community• No cost for complexity• Marginal gain an obvious tool

By intuition

K.Ramchandran, M.Vetterli, Best wavelet packet bases in a rate-distortion sense, IEEE Transactions on IP, 1993.

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Find a counter example, which becomes an example

• Shannon versus FRI

By paradox

M. Vetterli, P. Marziliano and T. Blu. Sampling Signals with Finite Rate of Innovation, IEEE Transactions on Signal Processing, 2002.

t

x(t)

Ttk

xk

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Rank property of EDM: There must be many applications!

• Calibration• Sensor network localization• Room reconstruction

By using a new tool

I. Dokmanic, R. Parhizkar, J. Ranieri and M. Vetterli,Euclidean Distance Matrices: Essential Theory, Algorithms and Applications,IEEE Signal Processing Magazine, Nov. 2015.

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Time-frequency duality

• Maximally compact sequences (rather than functions)

By teaching and setting an exam problem

R. Parhizkar, Y. Barbotin and M. Vetterli. Sequences with Minimal Time-Frequency Uncertainty, Applied and Computational Harmonic Analysis, 2015.

• Teaching is understanding in depth and finding new ideas!

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If you cannot find an answer to the problem…. Change the question!

• 1930: Transmit bits error free• Shannon 1948: Transmit bits with vanishingly small error probability• Totally changes the game!

If the answer is not coming, invent a new ‘’device’’• ‘’Computable numbers’’ -> Turing machine• If the Oracle can’t find it, you won’t

A few more tricks from the field

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4. Examples from the trenches: “Can one hear the shape of a room?”It sometimes takes a long time....

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Can one hear the shape of a room?I kept being obsessed with it....

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Can one hear the shape of a room?People tell me not to forget the question….

The question...

• Kac, 1966: “Can one hear the shape of a drum? ”

...and the answer

• Gordon, Webb & Wolpert, 1992: “One cannot hear the shape of a drum”

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Can one hear the shape of a room?Ivan’s work

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Can one hear the shape of a room?Who’s who?

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Can one hear the shape of a room?Sorting out the mess….

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Can one hear the shape of a room?And it actually works!

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5. Experimental results

Easy Hard Harder!

So what? Nice Whoaw!

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How to get ideas and results across (2)

Make it easy for the user… he/she will use your results!

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6. Mistakes to avoid

A good idea can still fail…

• It is too early• It is too innovative• It does not take the user into account• Etc

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6. Mistakes to avoidFrom a presentation to Nokia, May 2008

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6. Mistakes to avoidA few simple rules

• You have to be there first• You should not waste your results in conference papers• Get that journal paper out

And the usual suspects• Write clearly• “Illustrate” even more clearly (examples, figures, applications)

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7. Open access, open data, reproducibility

Well, there could be a whole talk about just this!

You know what I mean

But please, move to Python now!

We are mostly tool makers• Make sure the tools get used• Data, code, reproducibility, documentation

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8. Conclusion and OutlookA few random ideas

• The Mona Lisa smile

• Haptics and sampling

• Non-harmonic distortion due to quantization

• And the list goes on…

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8. Conclusion and Outlook

A few more points• A good idea is one that keeps coming back!• Respect authority while questioning it• Know but question common wisdom• Find your own voice (nobody else can)• Find what you like and are good at

And the usual suspects• Write clearly• “Illustrate” even more clearly (examples, figures, applications)

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On risk….

Risk

Reward

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Do’s and Don’t’sWrite• Write up your results, even if you don’t publish them

Writing helps understanding

Know and recognize when you are onto something• Mother lodeKnow and recognize when you are flogging a dead horse• Scorched earthKnow when you are stuck or wrong• Sometimes one is stuck in the wrong belief…

Full disclosure• There are big rugs, but nothing gets under it

First or not first• You are probably not the first one to think about what you did, nothing

wrong to give credit, share it

We are mostly tool makers• Make sure the tools get used• Data, code, reproducibility, documentation 64

• Know but question common wisdom

Explore the unexplored

“è maraviglioso sporgersi”

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• Otherwise, you might be doing the same over and over again…

Get out of your comfort zone…

• Leave the well trodden path. Or at least take it backwards• It is unlikely to find a gem where everybody has looked before …

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• Be humble (there is always Terry Tao ;)• Know your limits...• Go beyond your limits!• Be confident (there is always an unturned stone)• Be fearless!• Always ask the next question…• Be original• Be critical of your ego• Never give up (many ways to skin a cat;)• Make a good story (with a good title)• Recognize a good result when you have one,

and run with it!• Make everything as simple as possible…

but not simpler!

On limits…

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One for the road…

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References

1. J. Cleese http://tune.pk/video/3977274/john-cleese-how-to-inspire-creativity-within-yourselves

2. I. Asimovhttp://www.technologyreview.com/view/531911/isaac-asimov-asks-how-do-people-get-new-ideas/

3. G.Polya, How to Solve It: A New Aspect of Mathematical Method, Princeton, 1945, 2014

4. U.Alon, "How To Choose a Good Scientific Problem”, Molecular Cell , Volume 35 , Issue 6 , 726 - 728

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Additional material

The researcher hoping to break new ground in the theory of experimental design should involve himself in the design of actual experiments. G.E.P.Box

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