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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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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1answer
22 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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10 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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12 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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13 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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23 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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52 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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1answer
42 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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54 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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17 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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7 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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59 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
14 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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5 views

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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76 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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3answers
45 views

Is every point in $\mathbb R$ a cluster point of $\mathbb R$? [closed]

Could someone please tell me if all of the points in $\mathbb R$ are cluster points for $\mathbb R$ or not?
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1answer
47 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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36 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
29 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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57 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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72 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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108 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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33 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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53 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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26 views

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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26 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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26 views

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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35 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
52 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
22 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
31 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
62 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
74 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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87 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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37 views

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
73 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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27 views

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
119 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 ...
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97 views

K-means convergence to local maxima

I study K-means clustering algorithm. It's known that K-means algorithm converges to the local maximum, the problem is I cannot come up with the examples that shows this. If you know the simple ...
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597 views

Optimization / personalization within clusters

I have the following optimization problem: I have a (random and very noisy) objective function f(A, P), where A is a vector of "observable" parameters of the input and P is the parameters that I can ...
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1answer
179 views

how do I compute the eigenvectors for spectral clustering from a singular value decomposition?

I am implementing spectral clustering following A tutorial on spectral clustering. After preparing the Laplacian matrix $L^{n \times n}$, I compute the Singular Value Decomposition $U \Sigma V^{*}$. ...
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132 views

Size of connected regions on a randomly-colored infinite chessboard

Consider an infinite chessboard where each square is colored white with probability $p$ and black with probability $1-p$. Suppose without loss of generality that the square at $(0,0)$ is white. We ...
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1answer
56 views

Ensemble of Classifiers Method (Bagging)

I am reading a book about classification systems. They tell me that Bagging is a technique where "we perform sampling with replacement, building the classifier on each bootstrap sample. Each sample ...
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91 views

How to find “approximate most common” value from a list of RGB values

I have about 50 equally sized photos of magazine covers, which I'm attempting to blend into one composite image that shows the "average" cover. Each of the covers has a single face on it, so the ...
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1answer
345 views

Uncountable subset of $\mathbb{R}$ clusters at some point of $\mathbb{R}$ [duplicate]

It seems very intuitive and simple, but how would I go about proving something like this? Thanks.
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123 views

cluster validation and determining number of clusters

I want to find number of cluster in the real world data set. So, I validate the spectral clustering by using some indexes as shown in figures below? But as you seen in figures the results are very ...
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1answer
67 views

Unsupervised clustering in $10$ dimensions

I have a set of $\sim1000$ feature vectors in $\sim10$ dimensions and would like to cluster them in an unsupervised manner. I am expecting some of the vectors to bunch together in groups, but quite a ...
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210 views

Clusteranalyse bei Zeitreihen / Cluster analysis of time series

ich habe eine Frage zur Anwendung der Clusteranalyse bei Zeitreihen. Ich kenne mich grundsätzlich mit statischer Clusteranalyse aus. Jedoch soll ich eine grössere Anzahl von Firmen ($n=3000$) anhand ...