I'm looking into political redistricting, and wonder what would be the best model
A sample problem would be:
7000 census tracts, each with coordinates and population,
to be assigned to 53 districts.
constraint: populations of all districts to be within 1%
maximize: "compactness" of districts (ie: minimize gerrymandering)
For a simple measure of compactness I might use mean/median of distances from the centroid.
This seems to be a fairly straightforward clustering problem with constraints,
but in the tutorial I see no mention of clustering problems.
The knapsack model of the tutorial wouldn't seem to accommodate the compactness requirement.
What would be the best model compatible with Minizinc?
Related
Is is possible to model a general trend from a population using GPflow and also have individual predictions, as in Hensman et al?
Specifically, I am trying to fit spatial data from a bunch of individuals from a clinical assessment. For each individual, am I dealing with approx 20000 datapoints (different number of recordings for each individual), which definitely restricts myself to a sparse implementation. In addition to this, there also seemes that I need an input dependent noise model, hence the heteroskedasticity.
I have fitted a hetero-sparse model as in this notebook example, but I am not sure how to scale it to perform the hierarchical learning. Any ideas would be welcome :)
https://github.com/mattramos/SparseHGP may be helpful. This repo is gives GPFlow2 code for modelling a sparse hierarchical model. Note, there are still some rough edges in the implementation that require an expensive for loop to be constructed.
I am new to machine learning and now I am interested in document clustering (short texts with different lengths) according to their semantic similarity (I just want to go beyond the standard TF/IDF approach). I read the paper http://proceedings.mlr.press/v37/kusnerb15.pdf where the Word Mover's distance for word embeddings is explained. In the paper they used it for classification. My question is now - can I use it for clustering? If so, is there a paper where this kind of usage is discribed?
P.S.: I am basically interested in clustering which takes into account the semantic similarity, so even a word2vec or doc2vec approach will do the job - I just couldn't find any papers where they are used in a clustering problem.
If you could afford to compute an entire distance matrix, then you could do hierarchical clustering, for example.
It's easy today find other clusterings that accept any distance and use a threshold. These could even use the bounds for performance. But it's not obvious that they will work on such data.
I am working on instances from the TSPLIB, which are simply coordinates of nodes in a plan. I'm looking to analyze spatial characteristics and features of a set of instances (e.g. clustered, not clustered, dispersed, etc) and I would like to implement some code in Matlab to analyze and compute specific features.
For example, so far, I have used Nearest Neighbor analysis to identify clusters, as well as quadrant analysis. Can anyone suggest any other spatial features and patterns that could be computed with some relatively simple code? Anybody maybe expert in the Traveling Salesman Problem. Thank you so much!
K-means is a very useful clustering tool that you can use.
https://www.mathworks.com/help/stats/kmeans.html
Nearest Neighbor is a classification methods. if you want to do classification you can use K Nearest Neighbors, SVM or Neural Networks Pattern recognition toolbox. these are all already in Matlab.
Also, check out Matlab Apps. there are some very cool clustering tools available as well with examples.
I have a data set which consists of data points having attributes like:
average daily consumption of energy
average daily generation of energy
type of energy source
average daily energy fed in to grid
daily energy tariff
I am new to clustering techniques.
So my question is which clustering algorithm will be best for such kind of data to form clusters ?
I think hierarchical clustering is a good choice. Have a look here Clustering Algorithms
The more simple way to do clustering is by kmeans algorithm. If all of your attributes are numerical, then this is the easiest way of doing the clustering. Even if they are not, you would have to find a distance measure for caterogical or nominal attributes, but still kmeans is a good choice. Kmeans is a partitional clustering algorithm... i wouldn't use hierarchical clustering for this case. But that also depends on what you want to do. you need to evaluate if you want to find clusters within clusters or they all have to be totally apart from each other and not included on each other.
Take care.
1) First, try with k-means. If that fulfills your demand that's it. Play with different number of clusters (controlled by parameter k). There are a number of implementations of k-means and you can implement your own version if you have good programming skills.
K-means generally works well if data looks like a circular/spherical shape. This means that there is some Gaussianity in the data (data comes from a Gaussian distribution).
2) if k-means doesn't fulfill your expectations, it is time to read and think more. Then I suggest reading a good survey paper. the most common techniques are implemented in several programming languages and data mining frameworks, many of them are free to download and use.
3) if applying state-of-the-art clustering techniques is not enough, it is time to design a new technique. Then you can think by yourself or associate with a machine learning expert.
Since most of your data is continuous, and it reasonable to assume that energy consumption and generation are normally distributed, I would use statistical methods for clustering.
Such as:
Gaussian Mixture Models
Bayesian Hierarchical Clustering
The advantage of these methods over metric-based clustering algorithms (e.g. k-means) is that we can take advantage of the fact that we are dealing with averages, and we can make assumptions on the distributions from which those average were calculated.
I'm using WEKA for my thesis and have over 1000 lines of data. The database includes demographical information (Age, Location, status etc.) followed by name of products (valued 1 or 0). The end results is a recommender system.
I used two methods of clustering, K-Means and DBScan.
When using K-means I tried 3 different number of cluster, while using DBscan I chose 3 different epsilons (Epsilon 3 = 48 clusters with ignored 17% of data, Epsilone 2.5 = 19 clusters while cluster 0 holds 229 items with ignored 6%.) Meaning i have 6 different clustering results for same data.
How do I choose what's best suits my data ?
What is "best"?
As some smart people noticed:
the validity of a clustering is often in the eye of the beholder
There is no objectively "better" for clustering, or you are not doing cluster analysis.
Even when a result actually is "better" on some mathematical measure such as separation, silhouette or even when using a supervised evaluation using labels - its still only better at optimizing towards some mathematical goal, not to your use case.
K-means finds a local optimal sum-of-squares assignment for a given k. (And if you increase k, there exists a better assignment!) DBSCAN (it's actually correctly spelled all uppercase) always finds the optimal density-connected components for the given MinPts/Epsilon combination. Yet, both just optimize with respect to some mathematical criterion. Unless this critertion aligns with your requirements, it is worthless. So there is no best, until you know what you need. But if you know what you need, you would not need to do cluster analysis.
So what to do?
Try different algorithms and different parameters and analyze the output with your domain knowledge, if they help you with the problem you are trying to solve. If they help you solving your problem, then they are good. If they do not help, try again.
Over time, you will collect some experience. For example, if the sum-of-squares is meaningless for your domain, don't use k-means. If your data does not have meaningful density, don't use density based clustering such as DBSCAN. It's not that these algorithms fail. They just don't solve your problem, they solve a different problem that you are not interested in. And they might be really good at solving this other problem...