I'm trying to understand what makes a valid covariance matrix valid. Wikipedia tells me all covariance matrices are positive semidefinite (and, in fact, they're positive definite unless one signal is an exact linear combination of others). I don't have a very good idea of what this means in...
I've looked more closely at my problem and have determined three further constraints:A\geq0\\B\geq0\\C\sin(2x)\geq0Imposing these constraints seems to provide a unique solution in my computer simulations... but I'm not really certain why. Can anyone offer any insight?
Okay that's really clever... it's taken me a while to figure out how that works.
So, if I have 0 \leq x < 2\pi, I think taking the arcsin would give:\alpha+2x=\frac{3\pi}{2}Then, given how we've defined \alpha, I feel like we can say:\tan\alpha = \frac{(B-A)}{2C}Putting those things together, I...
I have a function:
f(x) = Asin2(x) + Bcos2(x) + Csin(2x)
and I want to find the minimum turning point(s). To start with, I calculated:
f'(x) = (A - B)sin(2x) + 2Ccos(2x)
Therefore, turning points occur when f'(x)=0, or:
tan(2x) = 2C / (B - A)
To find the minima, I then want to...
As I tried to explain, I consider proper segmentation of the points to be a difficult problem in its own right. Once the clusters are differentiated, locating their respective centres is straightforward, so segmenting would certainly be one route to a solution. On the other hand, it is...
I can tolerate a fair amount of latency, but the data will ultimately have to be streaming through at full rate. Plus, the more resources I can save on this task, the more I'll have left over to do everything else.
I'm looking at an embedded application, so something more like a dirt-cheap microcontroller than a big sophisticated Pentium processor.
Thanks - these notes look pretty good. I haven't found anything on Gaussian fitting yet, but I'll keep ploughing through.
Unfortunately, I cannot. Ideally, I would like to be able to handle heavily overlapping clusters. It's funny that it's so easy to locate the cluster centres by eye, but identifying a really elegant algorithm for doing it is not straightforward.
I would need to replace this "45 degrees" with an angle that separates the two clusters (we don't know this angle in advance, so would need to estimate it from the data). The mean angle across all the data points may seem like an obvious choice, but there is no guarantee that both clusters will...
Would you be able to recommend a nice simple one? I did a bit of googling and k-means clustering shows up a lot... but it would appear to be an iterative method, which makes me reluctant to use it.
I suppose a good initial step would be to compute the angle of all the data points with respect...
Yes, to clarify: the circle is definitely centred on (0,0).
As mfb suggests, I have a feeling this would require too much computation. Computational simplicity is a critical requirement.
If I understand correctly, this would give me only one point (located somewhere between the two points I am...
I have some noisy data (x-y coordinates) containing two distinct clusters of data. Each cluster is centred at an unknown point on the unit circle. How can I estimate these two points (green points in the diagram)?
We can assume the noise is Gaussian and noise power is equal in x and y...