I have a dataset with different quality data. There are A-grade, B-grade, C-grade and D-grade data, being the A-grade the best ones and the D-grade the ones with more scatter and uncertainty.
The data comes from a quasi periodic signal and, taking into consideration all the data, it covers just one cycle. If we only take into account the best data (A and B graded, in green and yellow) we don't cover the whole cycle but we are sure that we are only using the best data points.
After computing a periodogram to determine the period of the signal for both, the whole sample and only the A and B graded, I ended up with the following results: 5893 days and 4733 days respectively.
Using those values I fit the data to a sine and I plot them in the following plot:
Plot with the data
In the attached file the green points are the best ones and the red ones are the worst.
As you can see, the data only cover one cycle, and the red points (the worst ones) are crucial to cover that cycle, but they are not as good in quality. So I would like to know if the curve fit is better with those points or not.
I was trying to use the R² parameter but I have read that it only works properly for lineal functions...
How can I quantify which of those fits is better?
Thank you
Related
I want to perform an interpolation (IDW or other) of points taking into account only discrete parts of the territory, such as different types of use or coverage, leaving others uncalculated?
Trying to do with QGIS or Python. The results I am not sure if the process followed is ok.
I have samples of points distributed throughout the territory with a series of indicators related to pollutants in soil. As it is not an interpolation of a phenomenon that is homogeneously distributed throughout the territory (such as temperature, for example), I am not sure which would be the best method to use.
First question:
With IDW and weight = 1 I obtain in some cases higher values than the points. Why it could be?
Natural soils raster:
When I perform the interpolation I obtain a continuous raster and then extract its values to the soil raster.
Continuos raster:
Extract values with raster calculator:
I want the interpolation to be distributed only in the areas where natural soil appears, for which I have a discrete raster (with gaps). Once I do the interpolation I extract the data from the continuous raster (interpolated) to the discrete raster (natural soils).
Second question:
Is it possible to do it taking in account only the pixels in the soils raster? Using QGIS and GDAL I am not sure how to do it.
I would prefer an opposite process, i.e. that the interpolation by distances is done only for the areas with natural soils (discrete raster). And not having to calculate areas where it is not necessary to have that information. Also, there may be areas that are close but have no continuity because they are in separate, non-contacting soil patches (regionalise the soil patches?). Any input is welcome.
I am currently learning how to use OPTICS in sklearn. I am inputting a numpy array of (205,22). I am able to get plots out of it, but I do not understand how I am getting a 2d plot out of multiple dimensions and how I am supposed to read it. I more or less understand the reachability plot, but the rest of it makes no sense to me. Can someone please explain what is happening. Is the function just simplifying the data to two dimensions somehow? Thank you
From the sklearn user guide:
The reachability distances generated by OPTICS allow for variable density extraction of clusters within a single data set. As shown in the above plot, combining reachability distances and data set ordering_ produces a reachability plot, where point density is represented on the Y-axis, and points are ordered such that nearby points are adjacent. ‘Cutting’ the reachability plot at a single value produces DBSCAN like results; all points above the ‘cut’ are classified as noise, and each time that there is a break when reading from left to right signifies a new cluster.
the other three plots are a visual representation of the actual clusters found by three different algorithms.
as you can see in the OPTICS Clustering plot there are two high density clusters (blue and cyan) the gray crosses acording to the reachability plot are classify as noise because of the low xi value
in the DBSCAN clustering with eps = 0.5 everithing is considered noise since the epsilon value is to low and the algorithm can not found any density points.
Now it is obvious that in the third plot the algorithm found just a single cluster because of the adjustment of the epsilon value and everything above the 2.0 line is considered noise.
please refer to the user guide:
I have a series of many thousands of (1D) spectra corresponding to different repetitions of an experiment. For each repetition, the same data has been recorded by two different instruments - so I have two very similar spectra, each consisting of a few hundred individual peaks/events. The instruments have different resolutions, precisions and likely detection efficiencies so the each pair of spectra are non-identical but similar - looking at them closely by eye one can confidently match many peaks in each spectra. I want to be able to automatically and reliably match the two spectra for each pair of spectra, i.e confidently say which peak corresponds to which. This will likely involve 'throwing away' some data which can't be confidently matched (e.g only one of the two instruments detect an event).
I've attached an image of what the data look like over an entire spectra and zoomed into a relatively sparse region. The red spectra has essentially already been peak found, such that it is 0 everywhere apart from where a real event is. I have used scipy.signal.find_peaks() on the blue trace, and plotted the found peaks, which seems to work well.
Now I just need to find a reliable method to match peaks between the spectra. I have tried matching peaks by just pairing the peaks which are closest to each other - however this runs into significant issues due to some peaks not being present in both spectra. I could add constraints about how close peaks must be to be matched but I think there are probably better ways out there. There are also issues arising from the red trace being a lower resolution than the blue. I expect there are pattern finding algorithms/python packages out there that would be best suited for this - but this is far from my area of expertise so I don't really know where to start. Thanks in advance.
Zoom in of relatively spare region of example pair of spectra :
An entire example pair of spectra, showing some very dense regions :
Example code to generate to plot the spectra:
from scipy.signal import find_peaks
for i in range(0, 10):
spectra1 = spectra1_list[i]
spectra2 = spectra2_list[i]
fig, ax1 = plt.subplots(1, 1,figsize=(12, 8))
peaks, properties = scipy.signal.find_peaks(shot_ADC, height=(6,None), threshold=(None,None), distance=2, prominence = (5, None))
plt.plot(spectra1)
plt.plot(spectra2_axis, spectra2, color='red')
plt.plot(peaks, spectra1[peaks], "x")
plt.show()
Deep learning perspective: you could train a pair of neural networks using cycle loss - mapping from signal A to signal B, and back again should bring you to the initial point on your signal.
Good start would be to read about CycleGAN which uses this to change style of images.
Admittedly this would be a bit of a research project and might take some time until it will work robustly.
I have two sets of points, one from an analysis and another that I will use for the results of post-processing on the analysis data.
The analysis data, in black, is scattered.
The points used for results are red.
Here are the two sets on the same plot:
The problem I have is this: I will be interpolating onto the red points, but as you can see there are red points which fall inside areas of the black data set that are in voids. Interpolation causes there to be non-zero values at those points but it is essential that these values be zero in the final data set.
I have been thinking of several strategies for getting those values to zero. Here are several in no particular order:
Find a convex hull whose vertices only contain black data points and which contains only red data points inside the convex set. Also, the area of this hull should be maximized while still meeting the two criteria.
This has proven to be fairly difficult to implement, mostly due to having to select which black data points should be excluded from the iterative search for a convex hull.
Add an extra dimension to the data sets with a single value, like 1 or 0, so both can be part of the same data set yet still distinguishable. Use a kNN (nearest neighbor) algorithm to choose only red points in the voids. The basic idea is that red points in voids will have nearest n(6?) nearest neighbors which are in their own set. Red data points that are separated by a void boundary only will have a different amount, and lastly, the red points at least one step removed from a boundary will have a almost all black data set neighbors. The existing algorithms I have seen for this approach return indices or array masks, both of which will be a good solution. I have not yet tried implementing this yet.
Manually extract boundary points from the SolidWorks model that was used to create the black data set. No on so many levels. This would have to be done manually, z-level by z-level, and the pictures I have shown only represent a small portion of the actual, full set.
Manually create masks by making several refinements to a subset of red data points that I visually confirm to be of interest. Also, no. Not unless I have run out of options.
If this is a problem with a clear solution, then I am not seeing it. I'm hoping that proposed solution 2 will be the one, because that actually looks like it would be the most fun to implement and see in action. Either way, like the title says, I'm still looking for direction on strategies to solve this problem. About the only thing I'm sure of is that Python is the right tool.
EDIT:
The analysis data contains x, y, z, and 3 electric field component values, Ex, Ey, and Ez. The voids in the black data set are inside of metal and hence have no change in electric potential, or put another way, the electric field values are all exactly zero.
This image shows a single z-layer using linear interpolation of the Ex component with scipy's griddata. The black oval is a rough indicator of the void boundary for that central racetrack shaped void. You can see that there is red and blue (for + and - E field in the x direction) inside the oval. It should be zero (lt. green in this plot). The finished data is going to be used to track a beam of charged particles and so if a path of one of the particles actually crossed into the void the software that does the tracking can only tell if the electric potential remains constant, i.e. it knows that the path goes through solid metal and it discards that path.
If electric field exists in the void the particle tracking software doesn't know that some structure is there and bad things happen.
You might be able to solve this with the big-data technique called "Support Vector Machine". Assign the 0 and 1 classifications as you mentioned, and then run this through the libsvm algorithm. You should be able to use this model to classify and identify the points you need to zero out, and do so programmatically.
I realize that there is a learning curve for SVM and the libsvm implementation. If this is outside your effort budget, my apologies.
My software should judge spectrum bands, and given the location of the bands, find the peak point and width of the bands.
I learned to take the projection of the image and to find width of each peak.
But I need a better way to find the projection.
The method I used reduces a 1600-pixel wide image (eg 1600X40) to a 1600-long sequence. Ideally I would want to reduce the image to a 10000-long sequence using the same image.
I want a longer sequence as 1600 points provide too low resolution. A single point causes a large difference (there is a 4% difference if a band is judged from 18 to 19) to the measure.
How do I get a longer projection from the same image?
Code I used: https://stackoverflow.com/a/9771560/604511
import Image
from scipy import *
from scipy.optimize import leastsq
# Load the picture with PIL, process if needed
pic = asarray(Image.open("band2.png"))
# Average the pixel values along vertical axis
pic_avg = pic.mean(axis=2)
projection = pic_avg.sum(axis=0)
# Set the min value to zero for a nice fit
projection /= projection.mean()
projection -= projection.min()
What you want to do is called interpolation. Scipy has an interpolate module, with a whole bunch of different functions for differing situations, take a look here, or specifically for images here.
Here is a recently asked question that has some example code, and a graph that shows what happens.
But it is really important to realise that interpolating will not make your data more accurate, so it will not help you in this situation.
If you want more accurate results, you need more accurate data. There is no other way. You need to start with a higher resolution image. (If you resample, or interpolate, you results will acually be less accurate!)
Update - as the question has changed
#Hooked has made a nice point. Another way to think about it is that instead of immediately averaging (which does throw away the variance in the data), you can produce 40 graphs (like your lower one in your posted image) from each horizontal row in your spectrum image, all these graphs are going to be pretty similar but with some variations in peak position, height and width. You should calculate the position, height, and width of each of these peaks in each of these 40 images, then combine this data (matching peaks across the 40 graphs), and use the appropriate variance as an error estimate (for peak position, height, and width), by using the central limit theorem. That way you can get the most out of your data. However, I believe this is assuming some independence between each of the rows in the spectrogram, which may or may not be the case?
I'd like to offer some more detail to #fraxel's answer (to long for a comment). He's right that you can't get any more information than what you put in, but I think it needs some elaboration...
You are projecting your data from 1600x40 -> 1600 which seems like you are throwing some data away. While technically correct, the whole point of a projection is to bring higher dimensional data to a lower dimension. This only makes sense if...
Your data can be adequately represented in the lower dimension. Correct me if I'm wrong, but it looks like your data is indeed one-dimensional, the vertical axis is a measure of the variability of that particular point on the x-axis (wavelength?).
Given that the projection makes sense, how can we best summarize the data for each particular wavelength point? In my previous answer, you can see I took the average for each point. In the absence of other information about the particular properties of the system, this is a reasonable first-order approximation.
You can keep more of the information if you like. Below I've plotted the variance along the y-axis. This tells me that your measurements have more variability when the signal is higher, and low variability when the signal is lower (which seems useful!):
What you need to do then, is decide what you are going to do with those extra 40 pixels of data before the projection. They mean something physically, and your job as a researcher is to interpret and project that data in a meaningful way!
The code to produce the image is below, the spec. data was taken from the screencap of your original post:
import Image
from scipy import *
from scipy.optimize import leastsq
# Load the picture with PIL, process if needed
pic = asarray(Image.open("spec2.png"))
# Average the pixel values along vertical axis
pic_avg = pic.mean(axis=2)
projection = pic_avg.sum(axis=0)
# Compute the variance
variance = pic_avg.var(axis=0)
from pylab import *
scale = 1/40.
X_val = range(projection.shape[0])
errorbar(X_val,projection*scale,yerr=variance*scale)
imshow(pic,origin='lower',alpha=.8)
axis('tight')
show()