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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mean number of links in adjacency matrix

I have converted from an individual-level adjacency matrix to one for clusters and I am trying to show mathematically how I programmed up determining the mean number of inter-cluster links. I am not ...
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15 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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10 views

compare different quantization methods on a line.

assuming we have $n$ points ${x_1,x_2,...,x_n }$ uniformly distributed (or any other distribution that's convenient, or even distribution-free) over an interval $[a,b]$. Now I quantize the interval ...
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8 views

Graph partitioning with constraints

Consider having $n$ data points ${{x}_{1}},..,{{x}_{N}}\in {{R}^{D}}$. Given an affinity matrix of the data, $W=[{{w}_{ij}}]$ where ${{w}_{ij}}$ is the affinity measure for data points ${{x}_{i}}$ and ...
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15 views

Need explanation for clustering coefficient formula

I need some explanation for clustering coefficient formula itsef firstly and why it can be used for detecting communities in a social network! Also I would like to know why it is not a good method for ...
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1answer
22 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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35 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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508 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
69 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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83 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
22 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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47 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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13 views

In classification algorithms what is the idea behing choosing the first n values?

I came across the cluster pruning algorithm the other day. The algorithm first chooses √N random leaders for N points and after that assigns the new points to the nearest leaders. What is the idea ...
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1answer
116 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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30 views

spoting wrong weak edges on a graph (Is there anything like that?)

I've a question that I don't even know how to ask in order to start searching a way to solve my problem. Here is the Minimum Working Example(MWE) i can think of my problem: I've a graph were the edges ...
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1answer
65 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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98 views

How to compare the similarity between two dendrograms with uneven clusters?

For comparing two hierarchical clusters, I have read the paper "A Method for Comparing Two Hierarchical Clusterings" (Fowlkes and Mallows, 1983), as advised in the following stack exchange question: ...
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1answer
52 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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1answer
111 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 ...
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1answer
46 views

Optimize database indexes, the sequel

Background For those not familiar with databases. Indices help to speed up database searches, but they come at the cost of memory. Since you like your database to be fast, they are best cached in RAM ...
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2answers
45 views

Optimize database indexes

Q: I have 14 columns, how many indexes do i need to create to cover all possibilities? Examples of possibilities: col1 col12 col5, col3, col4 col7, col2, col12, col1 all 14 columns -- Order can ...
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14 views

Fit several inverse functions to cloud of points

I have a cloud of points that can be clustered so that each set of points in the cluster can be fitted with an inverse function : $f(x) = cte / x$. What would be an approach for clustering my dataset ...
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1answer
20 views

Which is a better clustering technique for High dimensional data?

I have these clustering methods: 1. adaptive dimension reduction using the Linear discriminant analysis and K-means 2. adaptive dimension reduction clustering technique 3. Spectral clustering Which ...
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34 views

Difference between standard and spherical k-means algorithms

I would like to understand, what is the major implementation difference between standard and spherical k-means clustering algorithms. In each step, k-means computes distances between element vectors ...
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1answer
176 views

Mutual Information for clustering

I'm working on a document clustering application and decided to use Normalized Mutual Information as one of the measures of effectivenes. But I don't really understand how to implement this in that ...
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1answer
40 views

How can I geometrically (or geographically) group items together?

I'm a programmer, and I'm working on a project that takes a bunch of photos and separates them into groups by their gps coordinates. I have no experience in things like geometric group theory so I'm ...
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1answer
105 views

How would you quantify the closeness between sets.

How would you represent the closeness (distance?) between sets? For example: how close are the sets: {8,4,5} and {9,8,2}? Could it be a percentage? If there is no way to do this, would you need two ...
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107 views

How can I find a villain's hideout given a set of previous locations? (Or, how can I identify the centeroid of a cluster of datapoints?)

Imagine this... Batman has just retrieved a tracking device he placed on The Joker 150 days ago. The good news is that it has 150 coordinates — one from each day. The bad news is that all the data ...
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72 views

List of n objects & their similarities. How to group them in sets based on their similarities?

I have a list of $n$ objects, and I know the similarity (as an index from $0$ to $1$) between any two objects. Question: how to create $i$ groups ($i< n$) of objects based on their ...
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1answer
87 views

Weighted directed graph clustering

I had a really huge sets of molecules and it's I'd like to compare according to various factors. So I created a similarity measure which was very informative and fitted for comparing different types ...
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82 views

Big data: 3D clustering with over 40 groups

I am a computational neuroscientist and I struggling over a problem; I have around one hundred 3D matrices (I am working on MATLAB at the moment), each of them is 121x145x121. Any 'cell' stores a ...
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1answer
50 views

Probability of being in same bin in a random clustering scenario

I have a set of $N(\geq 2)$ objects which I randomly group in $C(\leq N)$ clusters i.e. all the $C$ clusters have atleast one object and all such clusterings are equally likely. What is the ...
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41 views

How to use Legendre polynomials in order to determine the (an)isotropy of an on-lattice cluster aggrgegate?

I am currently testing various models of on-lattice (square lattice in two dimensions) cluster growth for anisotropy. I end up with a cluster, the boundary of which, in case of a truly isotropic ...
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1answer
444 views

Stationary distribution for directed graph

I want to implement the algorithm of graph partitioning of sparse directed graph. In this algorithm after computing the transition matrix ,we should compute the stationary distribution of the random ...
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1answer
75 views

$K$-means - how to calculate minimum distance

I was reading this article on $K$-Means and I got lost when it was time to assign objects to clusters. After calculating the centroids distance to every object, how can I calculate the minimum ...
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1answer
432 views

Why doesn't k-means give the global minima?

I read that the k-means algorithm only converges to a local minima and not to a global minima. Why is this? I can logically think of how initialization could affect the final clustering and there is a ...
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1answer
81 views

What are the use cases related to cluster analysis of different distance metrics?

I'm trying to use different distance metrics like Euclidean, Manhattan, cosine, chebyshev among other distance metrics in my k-means algorithm to calculate distances between the data points and the ...
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1answer
42 views

Probability : Dividing a list into 2 classes

I have a list of integer numbers ($n$). I am dividing it into two parts $n_1$ (smaller) and $n_2$ (bigger) such that the length of $n_1 \ge a*n$; $a$ is positive and $a \lt 0.5$. What is the ...
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1answer
31 views

three-dimensional vector clustering

I am looking for one or more algorithms that cluster points in non-euclidian vector space. My axes, specifically, are X and Y in space and Z in time. I was thinking about first clustering in X and Y ...
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106 views

Can anyone clarify how a diverging sequence can have cluster points?

$p$ is a cluster point of $S\subset M$ if each neighborhood of $p$ contains infinitely many points. Here is my confusion, a cluster point is also a limit point of $S$, right? If so, then how does the ...
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349 views

What is the difference between an array and a vector?

Okay so I'm doing a little bit of vector calculus at university (mainly with neural networks and the ...
3
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1answer
419 views

Fuzzy C Means mathematics tutorial [closed]

Hello I am looking for help on understanding the maths of Fuzzy C Means as explained here: Fuzzy C Means I was hoping for a broken down explantion of the actual math. I have tryed googling for ...
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1answer
133 views

Explanation of this Cluster Entropy equation

I need to calcuate the cluster entropy to represent the distinctness of a phrase in a set of documents. I understand the meaning behind it but I don't understand the notation equation itself, as in ...
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1answer
75 views

Cluster Analysis Terminology question

Let's say that I have a set of datapoints. Let's say I also have a set of pairs of these points, where a single point can be in multiple pairs. Let's say I also have a set of triples, etc with the ...
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1answer
1k views

Why one would want to normalize a matrix by dividing it by its Frobenius norm?

I am currently reading a scientific paper about clustering of brain signals, which consist on long time series across many channels (each signal is a matrix of C channels by T time samples). In the ...
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3answers
1k views

What is the correct definition of Minkowski distance

I realy confused. In a book ISBN: 978-0-470-27680-8 is written: The Euclidean distance can be generalized as a special case of a family of metrics, called Minkowski distance or L p norm, defined ...
3
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1answer
156 views

Partitioning Points Into Regions

I have a list of points $p_1, p_2, ..., p_n$ in the plane where each point has a weight $w(p)$ and I want to partition the points into $k$ separate regions with the following constraints: The convex ...
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351 views

Clustering algorithm to cluster objects based on their relation weight

I have $n$ words and their relatedness weight that gives me an $n\times n$ matrix. I'm going to use this for a search algorithm but the problem is I need to cluster the entered keywords based on their ...
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1answer
622 views

using “princomp” in matlab for clustering

I have a set of matrices which should fall into 3 distinct set/groups/clusters. They are unlabelled. I wish to do unsupervised clustering with PCA. I am using matlab as well. At the end I would also ...
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1answer
104 views

Possibilistic clustering- what exectly is $\eta$ and how to calculate it

I'm curently studing the topic of Possibilistic shell clustering and I have a hard time with understanding the concept of variable $\eta$. Can somebody in simpe words explain me what exectly this ...