# Questions tagged [clustering]

Clustering is the problem of finding groups of data points (often modelled as nodes in a graph) that are closer to each other than to other points.

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### Finding the “most modular” subset of graph vertices, i.e. that minimize disagreement inside and outside

Let $G = (V, E)$ be a graph. I want to find the subset of vertices of $G$ that minimizes a certain modularity cost. In our setting, the modularity cost of a subset $X$ is defined as the number of ...
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### Persistent Homology vs Clustering Methods

How do persistent homology and clustering methods for data point clouds differ? I'm specifically interested in the application to gene expression data of cancer patients, but any example works. I ...
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### How to cluster similar objects into fixed size groups?

I have $n$ people each of which can meet on certain days of the week. I want to group them into $\frac{n}{k}$ groups of size $k$ such that all people in a group can meet on a day. eg - Suppose there ...
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### Algorithm to separate single contour of glyph into several strokes?

A glyph contour contains points set {p}, a point contains tuple (x,y,on_curve). Now, think about this need, converting contour of glyph X, for example, into to two contour parts or two strokes, point ...
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### How to map points in high-dimensional space into dense grid in lower-dimensional space?

A formal description of the problem: Given a set $P$ of $n^k$ points in $d$ dimensional space, what algorithm can I use to find a mapping between them and points on a $n \times n \times n...$ grid in ...
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### Document clustering for summarization

I am curious as to what steps one would reasonably need to take to perform an extraction-based text summarizer. I've taken a look at some papers I've found on Google such as this one, which explains ...
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### Separating labelled points with a plane, minimizing label variance

Suppose we have observations with associated labels $\{({\bf x}_1, y_1), ({\bf x}_2, y_2), \dots, ({\bf x}_n, y_n)\}$ where ${\bf x}_i \in \mathbb{R}^d$ and $y_i \in \mathbb{R}$. Can we efficiently ...
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### How to calculate delta Q (modularity increase matrix) in graphs?

I've been trying to implement the Three-stage Algorithm to compare its results with our new proposed algorithm with different datasets than those mentioned in the article. I've succeeded in ...
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### Algorithms / heuristics for a distributed sorting problem

The setting: There's a cluster of $k$ computers (= nodes). For simplicity, assume their hardware is identical. The network topology can be complicated, but let's simplify and assume it's a clique ...
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### Enumerate subtrees of a given size in a graph

Given a graph $G$ with $n$ nodes, is there an algorithm to find $m$ subtrees, each with $\lfloor n/m\rfloor$ or $\lceil n/m\rceil$ nodes, such that every node of $G$ is in exactly one tree? Other ...
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### How to cluster nodes based on the number of dependencies

I have a problem where, there are a set of nodes and dependencies between them. I want to cluster them based on the maximum number of dependencies. Dependencies can be thought of as number of edges ...
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### Dimensional reduction of quadtree influence on clustering with dbscan

Let's say we take a quadtree of 50 dimension and apply dimension reduction(Assume the dimension reduction works well). Why does the dimension reduction not influence the clustering with DBSCAN(Mintpts:...
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### Euclidean space vs metric space in density clustering algorithms

I'm trying to find out if these algorithm still work if i replace the Euclidean space with metric space defined on the input point set. But i'm having some trouble figuring it out for some of them. I ...
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### Using Restricted Boltzmann Machines for clustering data

I want to use RBMs as a clustering model and the idea is to use an RBM for clustering a 16 class clustering problem with 4 nodes in the hidden layer. The clustering is done by updating the hidden ...
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### How to solve this grouping problem heuristically?

There are $S$ servers in the system. There are also $M$ computers in the system. Each computer shows different efficiencies when they are connected to different servers. Lets say, for computer $m$, ...