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This section details our plans for expanding on the project and its results

Generalizing non uniformity

As stated earlier, we wanted our measure of nonuniformity to be simple and easy to control. For the purposes of this project, removing entries based on a jointly Gaussian Distribution met our requirements. However, this measure of nonuniformity is both unrealistic and overly simplistic for real world data sets. With this in mind, future work would involve finding ways to generalize our notion of nonuniformity so that our results are more accurate with regards to real world data sets.

Testing with real world data

One of the most obvious applications of matrix completion is image reconstruction. The figure below shows how matrix completion can be used to reconstruct a noisy image. The original image had a uniform distribution of removed indices, so matrix completion was able to successfully recreate the image.

Matrix completion used to denoise film

Our results suggest that the algorithm would similarly be able to complete the image if the removed indices had a certain degree of non uniformity. Further testing would involve looking for any kinds of exceptions to our results. Due to the visual nature of these matrices, it would be very easy to see when matrix completion succeeds or fails. We could then look for patterns to generalize the issues the algorithm takes with varying degrees of non uniformity in the missing indices.

Essentially, this is expanding the whole idea of our stress test to be more cognizant of real world issues of nonuniformity in data sets.

Alternative approaches

This whole project has been guided by the principal that the existing solution for matrix completion is as good as it will get. At our poster presentation, one of the judge’s proposed an interesting idea. Could we (or others with better qualifications) improve the solution? Is there a way to fix the algorithm so that it works for all levels of uniformity?

We don't know the answer to this question and probably don't have the analytical skills to begin looking for one. However, a simple but potentially effective solution quickly comes to mind. We could develop a preprocessing algorithm that makes the data uniform before running matrix completion. Such an algorithm would need to be fast and generalized to all sorts of data sets to truly be a viable solution.

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Breaking matrix completion: a stress test. OpenStax CNX. Dec 15, 2015 Download for free at http://legacy.cnx.org/content/col11934/1.1
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