# Tagged Questions

Clustering is grouping (partitioning) a set of objects so that items in the same group are more similar to each other than to items in different groups, where the notion of similarity may be variously defined.

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### Simultaneously Diagonalizable matrices using clustering

I'm interested in partitioning matrices into groups which are almost simultaneously diagonalizable. I'm aware that if matrices commute and one of them has no multiple eigenvalues then the matrices are ...
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### What is Spectral bisection ?

I had to look through a paper on text clustering, the algorithm is by "clustering the sentences based on modified repeated spectral bisection" which made zero sense to me, can some one please explain ...
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### The modularity formula of Newmann and Girvan

I have question concerning the modularity formula of Michelle Girvan and Mark Newman. It says that it measures the fraction of edges in a network, that connects nodes, within the same ...
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### Number of clusters in $k$-means clustering for higher-dimensional data.

I've read the Wikipedia article and a lot of posts on stackexchange (like this really thorough one) on determining the number of clusters in a data set. Based on that, I am currently using the ...
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### Dirichlet clustering and group assignment

As in the Dirichlet clustering, the dirichlet process can be represented by the following: Chinese Restaurant Process Stick Breaking Process Poly Urn Model For instance, if we consider ...
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### Is my entropy calculation correct? Clustering entropy example

I would like to calculate entropy of this example scheme http://nlp.stanford.edu/IR-book/html/htmledition/evaluation-of-clustering-1.html Equation of entropy Then the entropy is (the first line) ...
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### How to develop an algorithm to prioritize set members based on various criteria

I tried looking for responses and Google. It has been a while since I used math to any capacity and the lack of application is only surpassed by my inability to articulate the concepts. That's my ...
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### Clustering via U(-W)PGMA

Given paiwise distance between 5 taxa: {a,b,c,d,e} 0 3 12 12 9 - 0 13 13 10 - - 0 6 7 - - - 0 7 - - - - 0 Calculate evolutionary tree, using UPGMA and ...
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### Grouping a set of numbers

I have a set of numbers which I don´t know if they belong to the same group (I could also call it factor or treatment, but actually each group is suppose to identify the same biological event). I am ...
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### How many degrees of freedom exist in an agglomerative hierarchical clustering?

The computational complexity of generating an agglomerative hierarchical clustering from n vectors is $O(n^2)$ (calculating the pairwise distance matrix) dendrogram example However, the total number ...
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### Approximate values from point groupings

Say I am given a set of values: \begin{bmatrix}0.9&1.1&1&1.95&2&2.05&2.95&2.95&3.1&3\end{bmatrix} Is there a way I can get the 'center' or 'average' values 1, 2, ...
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### Find percentage of proximity to cluster in kmeans2

I am trying to clustering in python. This is my code as follows: ...
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### der(der(A)) and der(A)

I have a question about cluster points that would like to ask you, this question is one of the exercises in my textbook. Question: If $A$ is any subset of $R^d$, then $der(der($A$))$ is the set of ...
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### Class Scatter Fitness Function Calculation

I get a fitness function for class scatter, the equation: Click here to see the Fitness Function Where : T = Transpose of Matrics Mi = class mean Mo = grand mean The equation is based from ...
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### How to evaluate a point in a weighted Mixture of Gaussians model?

Example: I have a MoG comprised of 2 1-d gaussians. The first gaussian has a weight of 0.8 the other 0.2. I have a sample point which I can easily evaluate on each individual gaussian. The ...
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### Building agglomerative hierarchical clustering algorithm manually

I am currently trying to solve this problem but I'm quite unsure if my answer is correct. I've build the tree different types of measures, MIN, MAX and AVERAGE but I might have some of them wrong. Can ...
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### Clustering state-space models according to similarity

I have a plant that can be modeled with nonlinear equations as $$f(x,u,p)=0$$ where $x$ is the state vector, $u$ the control vector, and $p$ the model parameters. In order to control this system, I ...
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### Theoretical link between the graph diffusion/heat kernel and spectral clustering

The graph diffusion kernel of a graph is the exponential of its Laplacian $\exp(-\beta L)$ (or a similar expression depending on how you define the kernel). If you have labels on some vertices, you ...
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### Cluster sampling: Compare efficiencies

A company operates from 12 branches, and the numbers of cars, $N_i$ and means $\bar{X}_i$ and variances $S_i^2$ of miles driven last year for each brand, are as follows Branch: $N_i$; $\bar{X}_i$ ; ...
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### math background for using Total Variation Norm for an L1-regularized optimization problem (Rudin-Osher-Fatemi)

I am working with some geographic data, and I would like to apply total variation denoising in order to sharpen the boundaries of clusters in the data. I also have some C code to run the split bregman ...