<< Chapter < Page Chapter >> Page >
Summary of how we stretched matrix completion to discover its limits.

The stress test

The main focus of our project was not to simply implement matrix completion -- that has been done many times in the past and is proven to work. What we wanted to do was put the algorithm through a “stress test” to understand its limits.

To do this, we devised the following plan:

  1. Construct a low rank matrix
  2. Create a model of uniformity
  3. Vary the uniformity on unobserved indices in a matrix
  4. Complete the matrix
  5. Measure mean squared error between the original matrix and the completed matrix
  6. Plot mean squared error as a function of uniformity

Constructing a low rank matrix

In order to construct a low rank matrix, remove indices, and compare the results of matrix completion with the actual matrix, we first created two separate matrices of size m x r and r x n with random entries between 0 and 1, where r in the desired rank. We then multiplied those two matrices together, constructing one matrix of size m x n and rank r.

Modeling uniformity

Our second challenge was to generate a model of uniformity that provided a simple way to change how uniform the unobserved indices were. We decided to use a jointly Gaussian distribution, modifying the covariance to control uniformity. The idea is simple: low covariance results in a high concentration of indices removed from the center of the matrix, while high covariance results in an almost perfectly uniform distribution.

In the figure below, the matrix on the left shows a matrix with a very uniform distribution of unobserved entries, characterized by a jointly gaussian distribution with high covariance. The matrix on the right demonstrates a data set with a high degree of nonuniformity. The probability peaks at the center of the matrix, resulting in unobserved indices which are highly concentrated in the middle of the matrix.

A uniform and non uniform represented by a gaussian

Plotting mse and uniformity

After completing the matrix, we calculated the mean squared error between the original matrix and the prediction provided by matrix completion and stored it in an array, along with the corresponding uniformity percentage. We calculated the uniformity percentage by normalizing each covariance by the largest covariance used, providing a scale between 0 and 100%.

Questions & Answers

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
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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
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
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Mueller Reply
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!





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
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Breaking matrix completion: a stress test' conversation and receive update notifications?

Ask