i did a course on hamming and correcting code two years ago, and I had to go back on it recently for another course. I must admit I forget some part of it, I know the meaning of the terms and how to do the operations separately, but I can't figure how to visualize the linear code for these questions if someone could help me.
Questions
Related
I'm working on a simple project in which I'm trying to describe the relationship between two positively correlated variables and determine if that relationship is changing over time, and if so, to what degree. I feel like this is something people probably do pretty often, but maybe I'm just not using the correct terminology because google isn't helping me very much.
I've plotted the variables on a scatter plot and know how to determine the correlation coefficient and plot a linear regression. I thought this may be a good first step because the linear regression tells me what I can expect y to be for a given x value. This means I can quantify how "far away" each data point is from the regression line (I think this is called the squared error?). Now I'd like to see what the error looks like for each data point over time. For example, if I have 100 data points and the most recent 20 are much farther away from where the regression line/function says it should be, maybe I could say that the relationship between the variables is showing signs of changing? Does that make any sense at all or am I way off base?
I have a suspicion that there is a much simpler way to do this and/or that I'm going about it in the wrong way. I'd appreciate any guidance you can offer!
I can suggest two strands of literature that study changing relationships over time. Typing these names into google should provide you with a large number of references so I'll stick to more concise descriptions.
(1) Structural break modelling. As the name suggest, this assumes that there has been a sudden change in parameters (e.g. a correlation coefficient). This is applicable if there has been a policy change, change in measurement device, etc. The estimation approach is indeed very close to the procedure you suggest. Namely, you would estimate the squared error (or some other measure of fit) on the full sample and the two sub-samples (before and after break). If the gains in fit are large when dividing the sample, then you would favour the model with the break and use different coefficients before and after the structural change.
(2) Time-varying coefficient models. This approach is more subtle as coefficients will now evolve more slowly over time. These changes can originate from the time evolution of some observed variables or they can be modeled through some unobserved latent process. In the latter case the estimation typically involves the use of state-space models (and thus the Kalman filter or some more advanced filtering techniques).
I hope this helps!
I'm trying to find powerlines in LIDAR points clouds with skimage.measures ransac() function. This is my very first time meddling with these modules in python so bear with me.
So far all I knew how to do reliably was filtering low or 'ground' points from the cloud to reduce the number of points to deal with.
def filter_Z(las, threshold):
filtered = laspy.create(point_format = las.header.point_format, file_version = las.header.version)
filtered.points = las.points[las.Z > las.Z.min() + threshold]
print(f'original size: {len(las.points)}')
print(f'filtered size: {len(filtered.points)}')
filtered.write('filtered_points2.las')
return filtered
The threshold is something I put in by hand since in the las files I worked with are some nasty outliers that prevent me from dynamically calculating it.
The filtered point cloud, or one of them atleast looks like this:
Note the evil red outliers on top, maybe they're birds or something. Along with them are trees and roofs of buildings. If anyone wants to take a look at the .las files, let me know. I can't put a wetransfer link in the body of the question.
A top down view:
I've looked into it as much as I could, and found the skimage.measure module and the ransac function that comes with it. I played around a bit to get a feel for it and currently I'm stumped on how to continue.
def ransac_linefit_sklearn(points):
model_robust, inliers = ransac(points, LineModelND, min_samples=2, residual_threshold=1000, max_trials=1000)
return model_robust, inliers
The result is quite predictable (I ran ransac on a 2D view of the cloud just to make it a bit easier on the pc)
Using this doesn't really yield any good results in examples like the one I posted. The vegetation clusters have too many points and the line is fitted through it because it has the highest point density.
I tried DBSCAN() to cluster up the points but it didn't work. I also attempted OPTICS() but as I write it still hasn't finished running.
From what I've read on various articles, the best course of action would be to cluster up the points and perform RANSAC on each individual cluster to find lines, but I'm not really sure on how to do that or what clustering method to use in situations like these.
One thing I'm also curious about doing is just filtering out the big blobs of trees that mess with model fititng.
Inadequacy of RANSAC
RANSAC works best whenever your data fits a mono-modal distribution around your model. In the case of this point cloud, it works best whenever there is only one line with outliers, but there are at least 5 lines when viewed birds-eye. Check out this older SO post that discusses your problem. Francesco's response suggests an iterative RANSAC based approach.
Octrees and SVD
Colleagues worked on a similar problem in my previous job. I am not fluent in the approach, but I know enough to provide some hints.
Their approach resembled Francesco's suggestion. They partitioned the point-cloud into octrees and calculated the singular value decomposition (SVD) within each partition. The three resulting singular values will correspond to the geometric distribution of the data.
If the first singular value is significantly greater than the other two, then the points are line-like.
If the first and second singular values are significantly greater than the other, then the points are plane-like
If all three values are of similar magnitude, then the data is just a "glob" of points.
They used these rules iteratively to rule out which points were most likely NOT part of the lines.
Literature
If you want to look into published methods, maybe this paper is a good starting point. Power lines are modeled as hyperbolic functions.
I've read this article and try to use it with my project whitch is a point to several polygons shortest distance.
https://medium.com/analytics-vidhya/calculating-distances-from-points-to-polygon-borders-in-python-a-paris-example-3b597e1ea291
enter image description here
but it says"In order to keep our algorithm lean, let’s not account for these specific cases and always calculate the distance to the middle point of our lines. Especially in accurately defined polygons (on a small space), the differences are negligible."
So now it won't work if I want to know the shortest distance,and it'll sometimes got the wrong vertex(I'll figure out later) is there any solutions to know the polygon and the points shortest distance?
btw I'm not in English so sorry for the grammer...
Background
I'm learning about text mining by building my own text mining toolkit from scratch - the best way to learn!
SVD
The Singular Value Decomposition is often cited as a good way to:
Visualise high dimensional data (word-document matrix) in 2d/3d
Extract key topics by reducing dimensions
I've spent about a month learning about the SVD .. I must admit much of the online tutorials, papers, university lecture slides, .. and even proper printed textbooks are not that easy to digest.
Here's my understanding so far: SVD demystified (blog)
I think I have understood the following:
Any (real) matrix can be decomposed uniquely into 3 multiplied
matrices using SVD, A=U⋅S⋅V^T
S is a diagonal matrix of singular values, in descending order of magnitude
U and V^T are matrices of orthonormal vectors
I understand that we can reduce the dimensions by filtering out less significant information by zero-ing the smaller elements of S, and reconstructing the original data. If I wanted to reduce dimensions to 2, I'd only keep the 2 top-left-most elements of the diagonal S to form a new matrix S'
My Problem
To see the documents projected onto the reduced dimension space, I've seen people use S'⋅V^T. Why? What's the interpretation of S'⋅V^T?
Similarly, to see the topics, I've seen people use U⋅S'. Why? What's the interpretation of this?
My limited school maths tells me I should look at these as transformations (rotation, scale) ... but that doesn't help clarify it either.
** Update **
I've added an update to my blog explanation at SVD demystified (blog) which reflects the rationale from one of the textbooks I looked at to explain why S'.V^T is a document view, and why U.S' is a word view. Still not really convinced ...
I'd like to know what method is best suited for predicting event occurrences.
For example, given a set of data from 5 years of malaria infection occurrences and several other factors that affect the occurrences, I'd like to predict the next five years for malaria infection occurrences.
What I thought of doing was to derive a kind of occurrence factor using fuzzy logic rules, and then average the occurrences with the occurrence factor to get the first predicted occurrence, and then average all again with the predicted occurrence and keep on iterating for all five years, but I decided to seek for help online.
There are many ways to do forecasting, each has its own advantages and disadvantages. The science of determining the accuracy of a forecast often consists of trying to minimize error. All forecasting comes down to using the past as a predictor of the future, adjusting it by some amount. E.g. tomorrow the temperature will be the same as today, plus or minus some amount. How you decide the +/- is what varies.
Here are a range of techniques you might want to review:
Moving Averages (simple, single, double)
Exponential Smoothing
Decomposition(Trend + Seasonality + Cyclicals + Irregualrities)
Linear Regression
Multiple Regression
Box-Jenkis (a.k.a. ARIMA,
Auto-Regressive Integrated Moving
Average)
Sorry, for the vague answer but forecasting is complex stuff.
What you describe about feeding your predictions back into the model to produce future predictions is standard stuff. I don't know if "fuzzy logic" gets you anything in particular. As any forecasting instructor will tell you, sometimes you just squint and look at the data. Context is everything.
I would use a logit or probit model to predict occurrence given a set of exogenous circumstances. Not sure why you want to iterate. That would basically be equivalent to including a lag in the regression formula. You could do it, and as long as the coefficient was <1, you wouldn't have the explosion problem.
If you want to introduce an element of endogeneity to the independent variables, you could use a VAR.
I think with your idea as stated, you'll have asymptotic behavior as time goes by. Either your data will converge to 0, or it will explode. That said, you'd probably have to give some data and/or describe its properties before anyone can help you. This is basically a simulation, and the factors are everything when it comes to extrapolation.