In addition, it's multi spectral.

Identical in shape, size, spectral content.

We now talk about spectral clustering.

Realtime audio processor based on frequency spectral manipulation

For instance, you see the spectral line of the gold is the only spectral line in the spectrum of the Sun.

So it's, it's really a decomposition of factoring problem.

This is called affinity based clustering or spectral clustering.

Spectral partitioning, L1 minimization. This comes from the optimization community.

The fundamental idea of spectral clustering is to cluster by affinity.

So spectral clustering gets annotation of affinity to make clustering happen.

Mathematically, this is, again, equivalent to Fourier decomposition, but on a sphere.

So let me look at the simple example for spectral clustering that would also work for K means or EM, but they'll be useful to illustrate spectral clustering.

Let's see if we can tackle a more complicated partial fraction decomposition problem.

And it turns out once again that spectral sensitivity is very important here.

So in summary, spectral clustering builds an affinity matrix of the data points.

If we apply eigenvalue decomposition to this matrix over here, we get 2 eigenvalues.

One is the phong reflection model, which gives us a spectral highlight, shiny spot.

The trick that's being applied is to de rotate this image over here using eigenvalue decomposition.

And to understand the importance of spectral clustering, let me ask you a simple intuitive quiz.

So what kind of decomposition on numbers could be used to enable this kind of recursive approach.

Spectral stars that are like those that make elliptical convolved with say Gaussian distribution of Doppler shifts.

You learned about K means, you learned about expectation maximization, about dimensionality reduction and even spectral clustering.

These hyper spectral images are false colored so you can it's really good for determining vegetative use.

So the partial fraction decomposition of this right here is A, which we've solved for, which is 2.

And later we went to study the spectral stars to see is there anything strange with these objects.

The background radiation is simply too static to be able to be seen under the normal spectral analysis.

like for example the SVD function that stands for singular value decomposition but that turns out to be a

So perhaps this decomposition will have some use in enabling a recursive attack on how to multiply two integers.

It's then pumped with toxic formaldehyde to slow decomposition a practice which causes respiratory problems and cancer in funeral personnel.

And when the coupling time comes the pattern is frozen. If you now remember Fourier decomposition and in density field.

They want to actually signal their presence through these spectral lines, in the spectrum of a star, in different ways.

Let me illustrate this once again with the data set that has a different spectral clustering than a conventional clustering.

Let's see if we can learn a thing or two about partial fraction expansion, or sometimes it's called partial fraction decomposition.

The highest degree here is 1, the highest degree here is 2, so we're ready to commence our partial fraction decomposition.

This is the spectrum of the Sun 24,000 spectral lines, and about 15 percent of these lines is not yet identified.

There's one more case of partial fraction expansion or decomposition problems that you might see, so I thought I would cover it.

Their excrement is absolutely teeming with microbes, which continue the decomposition process, making all those once wasted nutrients available again as fertilizer.

Sometimes we have to deal with just one tiny, weak spectral line to measure the composition of that chemical element in the atmosphere.

I'm also making a decompiculture kit, a cocktail of capsules that contain Infinity Mushroom spores and other elements that speed decomposition and toxin remediation.

In our own reserch, we also have applied eigenvector decomposition to relatively challenging problems that don't look like a linear problem at the surface.

So the decomposition here is going to be A over x minus 1 plus B over x minus 2 plus C over x minus 2 squared.

The way we quantify this is through spherical harmonics, which is essentially in equivalent of Fourier decomposition on a sphere, schematically this is how it works.

Next example is analyzing the spectral emissions of stars and trying to find clusters of stars in dissimilar types that may be of interest to astronomers.

So the partial fraction decomposition of this, we're now done, is 7 over x minus 2 plus 3x plus 4, over x squared plus 2x plus 4.

Now I understand this doesn't have a unique answer, but in the best possible case where spectral clustering works well, how many large eigenvalues do you find?