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# 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.

83 questions with no upvoted or accepted answers
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### Find a dynamic programming solution that minimize the sum of the diameters of two clusters?

I asked a question at this link, where I suggested a greedy algorithm for this problem: Suppose given $2n$ points in the plane and we want partition points into two clusters $C_1$ , $C_2$ such that ...
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1 vote
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### What might be a suitable clustering algorithm to split different parts in dense optical flow?

I want to split the main part(like people) in optical flow from the background, but I don't konw how to start. I think one way is to use some kind of clustering algorithm, first split the optical flow ...
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1 vote
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### grouping/clustering of lines using Hough transform

I am new to Hough transform, though I have some basic idea about it. I am currently trying to fit the best line to a cluster of points $\left(x_i, y_i\right), i = 1,2,\cdots , N$, where there are ...
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1 vote
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### Grouping only overlapping points into stacks

I have n number of files on a ScrollView. Every time a file is added, x/y coordinates are stored in an array. The user is able to drag and drop the files anywhere they like. Overlapping files (e.g. ...
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1 vote
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### Find clustering/partitioning based on edge weight

So I have a complete digraph with non-zero positive edge weights. The nodes represent locations and edge weights are the travel times between the two corresponding nodes. I have 2 or more agents ...
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1 vote
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### Finding highly-connected regions of graphs

I have a large network of 10,000 nodes and I am trying to identify subgraphs which are clique-like, in that they share many connections. I don't a priori know how many subgraphs fit this criteria. To ...
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### Cluster 3d points with constraints

I have some 3d point cloud I wish to cluster into some number of clusters. I have the probability of two points being in the same cluster given as some function of their relative locations, with the ...
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1 vote
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### How to group thousand of data points for each user

I have thousands of data points associated with users. So a single user can have 2000-10000 data points. These data points are identified by contiguous numbers (e.g. all numbers from 0 to 2000). Each ...
1 vote
51 views

### Is n-dimentional assignment problem for points NP-hard?

We have $n$ sets of $k$ points in $\mathbb R^d$ and we are trying to partition them to $k$ clusters of $n$ points such that from each set every point is mapped to a different cluster and the sum of ...
1 vote
52 views

### Clustering sets by set difference

Suppose you have $n$ nonequal sets $S_1, \ldots, S_n$ and some constant $0 \le k < n$. The goal of set clustering is to find a partition of the set $\mathbf{S} = \{S_1, \ldots, S_n\}$ such that the ...
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### Delivery Clustering based-on Pick-Drop & Driver locations

I'm reading some papers about Delivery Clustering to solve following generic problems: Given N orders (with its Pick-up and Drop location point) and M delivery-man (with his location). We are going ...
1 vote
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### How can one algorithmically define the required amount of centroids in K-Means clustering?

Say I have a dataset of n vectors. These are, by nature, clustered so that there is a significant distance difference between any two points within a cluster and any two points in separate clusters. ...
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### How to cluster N sets into N subsets ,so that we can determine which set a point is from by checking its nearest neighbor in aforementioned subsets?

Question 1: Given N sets of points $S_1$ ... $S_n$ (no intersection between $S_i$ and $S_j$ when i != j), I want to find subsets of $S_1$ ... $S_n$ (call them $T_1$ ... $T_n$ respectively) So that ...
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### Clustering customer with string data

I'm looking for a customer clustering solution. I have done a lot of research on the machine learning level to find algorithms that could fit my needs but I can't find much information when the data ...
1 vote
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### Finding fewest strings that cover $\Sigma^n$ up to $R$ edit operations

Let $\Sigma$ be the alphabet, $0<R<n$ be an integer and let $\Sigma^n$ denote the set of all strings of length $n$ over the alphabet. The task is to find the minimum $m$ such that there exist ...
1 vote
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### 2 stage clustering

The problem I am facing is clustering problem, needed for a Vehicle routing problem (VRP) I'm tackling. It is a heterogeneous VRP with Time Windows and a capacity utilization constraint, i.e. a truck ...
1 vote
33 views

### How can I express the similarity between a Bing and a Google search result?

I'm working on a "semantic" browser engine where all search engines should look the same. One way to do this is to hard-code parsing rules for each site; another is to use machine-learning. Of course ...
1 vote
32 views

### Point cloud clustering based on similarity in less than $O(n^2)$

not sure if this is the right place to ask this but here it goes. Let's assume I have some 2D points dataset consisting of facial landmarks, and I want to cluster these based on similarity so that I ...
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1 vote
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### Balanced $\epsilon$-separated partitioning by a hyperplane

Suppose we have $m$ points in $R^n$ and $\epsilon>0$ is a given constant. How can we find a hyperplane that the number of points that are $\epsilon$-close to it is minimum, with the constraint that ...
1 vote
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### Concrete/theoritical center of a cluster in a general metric space

What i call center is the point which minimize the distance to every points of a specific cluster. From what i know we can look for a concrete point in the cluster get an approximation of the center. ...
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### $k$ -center with outliers - but the points are on a line

The classic $k$-center with outliers problem is NP-hard and there exist approximation algorithms to solve it. However, what if we assume that the input point are on a line, rather than in an ...
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1 vote
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### Strict partitioning clustering of points in 2D space into variable (but fixed) length cluster in order to minimize distance from center

Given $\\N$ points in 2D space, one is required to cluster them into $\\M$ clusters, with each cluster of a given size $\\S_m$ such that $\sum S_m = N$, in order to minimize the sum of the distance of ...
1 vote
491 views

### Clustering via Max-Cut

I wonder if there are papers that uses max cut algorithm(s) to cluster data. For example, if an edge between two nodes $u$ and $v$ indicate that $u$ and $v$ are different, then the max-cut in some ...
1 vote
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### Spanning tree with equally separated edge weights

I have a fully-connected graph $G=(V,E)$ with edge weights $w(v)\in\mathbb{R};v\in V$ and I need to find a spanning tree $T=(V_t\subseteq V,E_t\subseteq E)$ where the set of edge weights in the tree ...
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### Is this version of clustering still NP-Hard?

Let the set $A = \{a_1,...,a_n\}$ of objects and $d(a_i,aj) \quad \forall i,j\in[n] \quad i\neq j$. Let $\;C=\{C_1,...,C_k\}$ the set of clusters, split the elements of $A$ into $C$ such as there is ...
1 vote
299 views

### Determine border points of a cluster

My question is as follow. Imagine a random shape cluster of high dimension in an euclidian space, how can i get points which are at the edge of the cluster where edge are defined as segments ...
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### Appropriate graph clustering algorithm

I'm looking for an appropriate technique to search for clusters. My underlying data is 70,000 respondents to about 2500 multiple choice questions. Most respondents have not answered most questions. I ...
1 vote
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### What are internal clustering index for binary data ? And if possible applicable to massive cluster ?

I was wondering what are the current existing internal clustering index for binary data. I know already the silhouette and Davis Bouldin for euclidian space, i suppose they work as well in binary ...
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