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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What Laplacian should we use for spectral clustering?

The second eigenvector of the normalized Laplacian $I-D^{-1}W$ or the symmetric normalized Laplacian $I-D^{-1/2}WD^{-1/2}$ can be used to approximate a minmizer of the normalized cut problem. Which ...
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Define temperature by clustering with math operators

I can´t figure out how to cluster the temperature for the weather in 3 optimal cases: hot, mild, cold My data contains: air temperature(the average daily value), max air temperature(highest daily ...
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51 views

Measure of “how much diagonal” a matrix is

I have a (biological) computational system that outputs squared matrices. These matrices will sometimes have a tendency to be diagonal-like, with higher values at and around the diagonal. I would ...
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14 views

approach for clustering of huge networks

Can you give me some kind of direction on the best approach for clustering huge networks? (so large, that even the list of nodes cannot be stored in RAM) Thanks for anyone who helps.
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20 views

Displaying a graph with minimum overlapping edges

Context I am developing UI for a skill web for a mobile game. Each skill may have requirements from other skills, or sometimes no requirement at all. The problem The description above is ...
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17 views

How do you compute the weighted sum of data points for learning the centers of a hyper basis function network (HBF)?

I was reading the following paper on hyper basis function (HBF) (similar to radial basis function RBF network) and was trying to figure out how one learns the movable centers of the hyper basis ...
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36 views

Mathematical Intuition behind the tf-idf formula in Statistics

I was reading: https://en.wikipedia.org/wiki/Tf%E2%80%93idf#Definition But I cannot seem to understand exactly why the formula was constructed the way it is. What I do Understand: iDF should at ...
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15 views

Difference between Cosine similarity and Angular similarity

Both cosine similarity and angular similarity are measures of similarity between vectors. The cosine similarity is defined as $$\sigma(u,v)=\frac{u \cdot v}{\|u\|\|v\|}$$, while the angular ...
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37 views

Shortest distance of a location to X number of locations

Anyone have advice on this problem? "Shortest distance of a location to X number of locations" First lets assume X=3 (3 addresses) We know the following: Distance in Miles or KM of : A1 to A1, A1 ...
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Identify outliers in a set of elements

I have a set of elements that has been partitioned into clusters based on several criteria, one of which is the length of the elements. To be precise, element $x$ cannot belong to cluster A if ...
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1answer
21 views

How to convert table into a distance function?

Been stumped on this past paper question for a while, it's in the context of clustering and the next part is using single linkage bottom-up hierarchical clustering to form a dendrogram using your ...
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50 views

How to recompute the markov transition matrix given a reduction to the number of states? Clustering from a transistion matrix

I am been puzzled with this one for sometime. Given a transition matrix (as below) for a markov chain of N states; how do we calculate the transition matrix for N-1 states, where we combined stat n1 ...
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30 views

Can anyone recommend good resources to learn about Cluster Analysis?

I'm a Software Developer. I'd like to learn more about Cluster Analysis because I think it would be an extremely useful skill-set to incorporate into the products my company develops and supports. I ...
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1answer
27 views

Curve Pattern Similarity

I have sales data and I want to cluster it based on similarity. The term similarity here focus on the pattern of peak, valley or the slope. I have different scale on both side of time and sales. So ...
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16 views

Lagrange Multiplier for clustering with size constrains

I'm trying to solve a clustering problem with size constrains. Minimize $J=\sum_{i=1}^c\sum_{j=1}^n {{u_i}_j}^2{d_i}_j$ Subject to $\forall 1\le j\le n : \sum_{i=1}^c {{u_i}_j}=1$ and ...
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16 views

Find all groups that meets the condition

I have $n$ elements, each of them have two unsigned int attributes $x$ and $y$. Now I'd like to find out all the groups that fit the following condition: $A.x \geq B.y$ and $B.x \geq A.y$. The ...
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1answer
24 views

A question about stability of clustering

I'm reading a paper about interactive clustering, and I'm stuck with a definition about stability property of a clustering (based on this paper): What I understand is that $A$ and $A$ are samples ...
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71 views

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 ...
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77 views

Cluster algorithm with max range and variable point size

Let's take the simplest example: I have a non-defined amount of points with x- and y-coordinates and want to cluster them under following premises: A point can only be part of one cluster. The ...
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64 views

How to calculate the critical density estimation for “continuum” percolation model in “3D space” when we have “spatial correlation”?

I want to approximately estimate the critical density (lower bound for density) of balls in a cube to make sure that the upper and lower surfaces of the cube will be connected to each other through ...
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22 views

which distance function is better to use

I have large data sets with large features space. I'm hesitating between finding the distance between each of those data sets to cluster them into 4 or 5 clusters. or just apply a method by using a ...
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9 views

K cluster structure in Kronecker product type matrix

I have this Kronecker product type matrix: $C =\begin{bmatrix} B_{1,1} A_{1,1} & B_{1,2} A_{1,2} & \dots & B_{1,K} A_{1,K} \\ B_{2,1} A_{2,1} & B_{2,2} A_{2,2} & \dots & ...
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63 views

Do I have to be a mathematician to understand the following papers?

I come from a CS&Machine Learning discipline. I have been looking to understand the core idea of Non-Negative Matrix Factorization. While most of the ML based work is understandable, mostly the ...
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1answer
34 views

Explanation of Information double summation within Normalized Mutual Information

The Normalized Mutual Information NMI calculation is described in deflation-PIC paper with the applicable formula copied to the screenshot shown below. My question is specifically about the double ...
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Meaning of coherence measure $\frac{n}{s}\max_{1 \le i \le n}\sum_{j=1}^n U_{ij}^2$

In the paper Extracting Certainty from Uncertainty: Transductive Pairwise Classification from Pairwise Similarities, the authors use a coherence measure defined as $$ \mu_s=\frac{n}{s}\max_{1 \le i ...
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106 views

Find the radius of a cluster, given that its center is the average of the centers of two other clusters

I do not know if it is possible to find it, but I am using Kmeans clustering with Mahout, and I am stuck to the following. In my implementation, I create with two different threads the following ...
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80 views

What is the meaning of |⋯| notation for an index subset?

I am currently working on a research project. In the attached image what does the capital $|I|$ and $|J|$ mean ?
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65 views

What is the definition of “convex” and “relaxation” concepts in clustering?

I have following text from a paper i am trying to understand: I don't understand what does below sentence refers to as being convex/non-convex The problem is that even though the objectives ...
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1answer
33 views

Measure for presence of several poorly interconnected components in undirected graph

Is there a measure to classify networks regarding whether or not they are composed of several (internally closely connected) groups which are poorly connected (i.e. few links between groups). That ...
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60 views

Proving symmetry of metric (single linkage between clusters using arbitrary dissimilarity measure)

I am told to assume that our dissimilarity measure $d$ satisfies the properties required of it, what seems to be the definition of a metric: $d(x,y) \geq0 $ and $d(x,y)=0 \Longleftrightarrow x=y$ ...
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82 views

Calculating Euclidean dissimilarity for a given cluster with itself

Suppose I have clusters $$A= \{(1,1)^T, (1,2)^T\} $$ $$B=\{(2,3)^T, (3,4)^T\} $$ $$C= \{(4,5)^T, (5,6)^T, (1,2)^T\} $$ I wish to use the Euclidean dissimilarity and Average linkage to calculate a ...
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155 views

Is k-means clustering guaranteed to converge if using Manhattan distance?

The k-means algorithm is an iterative clustering algorithm that partitions the data points into K clusters (with centroids {$\mu_1, ... , \mu_k$}, minimizing the Sum-of-Squared-Error: $$ SSE = ...
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34 views

finding clusters in a network from eigengaps

I have a usual Laplacian matrix, which describes a network. From the matrix I get the eigenvalues and from these I can compute a metric of modularity in my network based on the largest eigengap. Let's ...
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1answer
58 views

Measure of the clusters quality in a graph

Suppose we have a graph $G=(V,E)$ with $n$ non-overlapping subgraphs, the clusters $C_1, C_2, \dots, C_n$ which covers the graph $C_1 \cup \dots \cup C_n = G$. I'm looking for a good metric to ...
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UPGMA: Distance between clusters for multi-dimensional data

How would you calculate the distance for multi-dimensional data? From wikipedia: ...
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probability of clusters for iid points

Consider that $X_1^{(n)},...,X_n^{(n)}$ are iid uniform random variables on $[0,n]$. For $T >0$, let $N_n(T) = \sup_{t \in [0,n]} \# \{ i: |X_i^{(n)} - t| \leq T \}$ be the maximum number of points ...
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1answer
31 views

Identifying the k points in 2D geographic space which are 'most distant' from each other

I have a set of DNA samples from Y plants in a given geographic area. I'm going to be doing DNA sequencing on individuals in this population (and a number of other, separate populations), however due ...
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Looking for an algo to “sorta” diagonalize a similarity matrix.

I've got a big fat similarity matrix. The rows and columns represent people, and the values represent some positive measure of their closeness (0 meaning no connection at all). The n-th row and n-th ...
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40 views

Clustering Coefficient of A Transitive Graph/Network

Whats the difference of a transitive network's clustering coefficient and a non-transitive networks coefficient? more precisely is the clustering coefficient of a transitive network is as high as ...
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1answer
55 views

Are minimum cut communities maximal?

I am looking at the paper Graph Clustering and Minimum Cut Trees by Flake et al. Let $G(V, E)$ be some undirected weighted graph. Definition. Let $s, t\in V$ be given. Let $(S, T)$ be the minimum ...
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1answer
27 views

Cluster points so that within each cluster holds a certain maximum distance between points

Currently I'm struggling with a (for me) new field, namely clustering. I would really appreciate any help I could get! The starting situation is that a data set $(x_k)_{k\in\{1,\dots,n\}} \subseteq ...
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1answer
44 views

Sampling with an “oversampling” factor, in K-Means||

I'm trying to understand K-Means||, a scalable version of K-Means++, which itself is an "improved" version of the clustering algorithm K-Means. Please find here the link to K-Means|| paper ...
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2answers
71 views

Finding similarity between elements using statistics

I have a dataset of DJs in which I'm trying to find DJs similar to a specific DJ. Each DJ has a set of a genres with a certain percentage. How can I find the similarity between 2 DJs? The following is ...
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1answer
62 views

Clustering analysis of a weighted graph

My data consists of a large weighted undirected graph of $n$ nodes. I need to group the nodes into $m$ clusters ($m < n$), such that nodes in a cluster are connected with heavy weights. What ...
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1answer
83 views

Percolation Theory Basics: Open cluster size decay (Square Lattice)

I am trying to learn some stuff about percolation. On wiki (http://en.wikipedia.org/wiki/Percolation_theory) it says: "when $p<p_{c}$, the probability that a specific point (for example, the ...
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93 views

Triangulation of clusters of points

I am trying to solve a triangulation problem, but I am not really sure what is the best way to tackle it. I have a series of points $P$ in an $n$-dimensional space. These points are clustered in $k$ ...
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Machine learning algorithm for relative similarity

I'm trying to find a good starting place (or existing algorithm) to determine the similarity of various items to one another based on subjective assessments of two items' relative similarity to a ...
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1answer
80 views

In Cluster Analysis, how do we calculate Purity?

In cluster analysis how do we calculate purity? What's the equation? I'm not looking for a code to do it for me. Let $\omega_k$ be cluster k, and $c_j$ be class j. So is purity practically ...
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voronoi graph generated by $k$-means clustering

assume I correctly find the optimal centroids $c_i$ in the kmeans clustering problem, which finds $k$ centroids that minimizes: $$ \min \sum_i \sum_{x_j\in C_i } \|x_j - \mu_i\|^2 $$where $\mu_i, \ ...
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1answer
150 views

Normalized Mutual Information results in log(0) with non-overlapping clusters - how to deal with that?

I want to evaluate how well my flat soft clustering method works, compared to a gold standard. After some research I found that Normalized Mutual Information would most likely be a good measure, for ...