Clustering is an unsupervised learning problem. It deals with finding "clusters" or groups in a collection of unlabeled data. A cluster is therefore a collection of objects which are “similar” and are “dissimilar” to the objects belonging to other clusters.

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an axiomatic framework for clustering by jon kleinberg may have a problem?

In the paper An Impossibility Theorem for Clustering, Jon Kleinberg introduced an axiomatic framework for clustering and showed that his set of axioms are inconsistent. One of the axioms is the ...
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148 views

Bisecting a set of points into two optimal subsets

I want to divide a set of points into two equally-sized subsets such that the within-cluster sum of squares is minimized. We can assume that the points are in two-dimensional Euclidian space. I'm ...
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updating clusters in NCut spectral clustering

Are there any methods to update the clusters formed in k-way NCut when new data points arrive or any change in the similarity matrix??
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155 views

Splitting a graph into size constrained clusters

I ran across a problem while working on an algorithm for a game I'm making on the side. It's basically a clustering problem where we have a graph G and want to split it into clusters of equal size ...
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46 views

Quality measure for clusters of a metric space embedding of a graph?

When evaluating clustering algorithms for networks, we have well-established metrics like Modularity and Surprise for evaluating the quality of the resulting partition. If we then embed our graph ...
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417 views

Time complexity analysis of random forest and k-means?

I am working with random forest for a supervised classification problem, and I am using the k-means clustering algorithm to split the data at each node, where $n$ is the number of points, $K$ is ...
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105 views

The non-metric k-median problem

It is well-known that the non-metric $k$-median problem cannot be approximated better than $O(\log(n))$ (by a gap preserving reduction from the set cover problem). Is there any logarithmic ...
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138 views

Time complexity of clustering based on random walk

What is the time complexity of the following algorithm (from this paper suggested by Zhou) to partition directed graph? Can I use the complexity of eigen vector computation for this purpose? The ...
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122 views

Grouping a set of rectangles in larger rectangular regions

I have a set of rectangles, which I want to cluster (group) as shown here(I can not post images yet, so please bear with me). The approach I took was to consider central points of each rectangle as a ...
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2answers
223 views

Hyperspherical nature of K-means and similar clustering methods

Jain, Murty, and Flynn state in their article Data Clustering: A Review all squared error based clustering methods like K-means tend to generate hyperspherical clusters. However, they do not give a ...
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256 views

canopy clustering: what should we do with samples in overlapping canopies?

In canopy clustering http://www.kamalnigam.com/papers/canopy-kdd00.pdf, if a sample falls in an overlap of 2 canopies, how do we choose its cluster?
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1answer
155 views

Clustering massive data sets in practice

If you have a very large data set of $n$ vectors and you want to cluster them according to some metric measure, what is the current state of the art when you can not afford to do more than $\Theta(n)$ ...
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106 views

PTAS Algorithm for K-Clustering when Distance Computation is Costly

Can anyone throw any light on any PTAS algorithm that I can apply for K-Clustering algorithm when the distance computation between the clustering points is costly. In details, I have a set of N ...
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141 views

Classic parallel clustering algorithms

I'm starting a research about parallel clustering. I see a ton of articles on this topic, so that I don't know where to start. I'd like to get familiar with classic methods of parallelizing ...
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304 views

K-Clustering of a Graph maximizing intra-cluster weights?

I would like to know if the following problem has already been studied, and if so how is it called. In particular I'm interested in approximability results. Input: A complete graph G with ...
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93 views

Clustering without specifying the number of clusters apriori

Does anyone know of an algorithm that can perform the following tasks: Unsupervised clustering without specifying the number of clusters apriori. For example if all the buildings in wide ...
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92 views

Finding most informative feature subsets given dataset, clustering algorithm and gold standard partition

I have an $n \times m$ matrix of data $\mathbf{D}$ as well as a $k$-partition $P$ of $n$ indices each representing a row in a dataset. Assuming an arbitrary clustering algorithm $A$, I would like to ...
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100 views

Rigid-body matching algorithm and clustering algorithm with groups of lines in 3D [closed]

I've been struggling with this problem for weeks, and couldn't find an appropriate algorithm to solve it. Could you guys please give me some advices or suggestions in addressing this question. Or if ...
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82 views

Techniques to get nodes in the best Markov Cluster?

I was using Markov Clustering to cluster nodes in my bidirectional graph, and overall the results were great. However, there were a couple instances where a weakly connected node would attract a node ...
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1answer
543 views

Simple k-nearest-neighbor algorithm for euclidean data with highly variable density?

An elaboration on this question, but with more constraints. The idea is the same, to find a simple, fast algorithm for k-nearest-neighbors in 2 euclidean dimensions. The bucketing grid seems to work ...
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251 views

Divide-and-conquer approach for hierarchical clustering

I have a huge data set (33K), each represented as a bit-vector of 275-dimensions. Basically my data set can be represented as a $33000 \times 275$ matrix. I want to cluster these bit-vectors. I have ...
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150 views

Fuzzy K-modes clustering how to find the cluster centers

I'm trying to understand [fuzzy k-modes][1] algorithm (look mainly at page 3) in order to implement it. I'm stuck at the calculation of cluster centers they said as shown in the link ...
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214 views

k-clustering problems

I'm interested in open questions from the book Approximation Algorithms for NP-Hard Problemss dedicated to k-clustering. They are: Is Euclidean max cut solvable in polynomial time? If not, how ...
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190 views

K-means with centres outside the data?

Say we want to split a cube in $\mathbb{R}^{64}$ into 10 pieces. NN, nearest-neighbor or Voronoi splits, take 10 cluster centres $c_0, \ldots, c_9$ in the cube, e.g. from K-means, then classify a new ...
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237 views

Higher-order and black-box clustering

As far as I understand a large number of clustering problems can be formulated as: $\underset{\textbf{P}}{ \text{argmin}} \; \sum_{i,j} f \left(x_i, x_j\right)$ where $\textbf{P}$ is a partitioning ...
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1answer
103 views

Scoring set of points based on clustering

I have a sparse set of points with unpredictable locations. I need a way of "scoring" each set of points such that clustering is rewarded. My working case is actually one dimensional, but a two ...
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113 views

Clustering of letters - what approach would give the best results?

I am working on letter recognition program. I have a text and divide it into letters, every single letter is written to separate file. Now I want to apply a clustering algorithm to these images to ...
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111 views

A better way to cluster items

I am working on a text processer which gives out similarities between a set of strings. After weighted LCS, Levenshtein distance and double metaphone matching, I get buckets of strings such as ...
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3answers
172 views

clustering (lat,lng) pairs, with clusters having the same number of elements

Imagine you have a list of (lat,lng) pairs. You have k employees. And you want each employee to visit roughly the same number of places, making the least distance possible. I've tried to solve this ...
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2answers
400 views

Euclidean-squared max-cut in low dimensions

Let $x_1, \ldots, x_n$ be points in the plane $\mathbb{R}^2$. Consider a complete graph with the points as vertices and with edge weights of $\|x_i - x_j\|^2$. Can you always find a cut of weight that ...
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2answers
1k views

Computational complexity of clustering algorithms

My wish is to describe the time complexity of several clustering approaches. For example, suppose we have $n$ data points in $m$ dimensional space. Suppose further that the pairwise dissimilarity ...
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1answer
212 views

K-NN or matrix factorization for discovering correlated features?

I am looking to cluster users together in a database, with each user represented by a number of features that are both discrete and continuous in nature. "Similar" users should be clustered together ...
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2answers
289 views

Clustering formalizations other than K-means for separable data

Real world data sometimes has a natural number of clusters (trying to cluster it into a number of cluster lesser than some magic k will cause a dramatic increase the clustering cost). Today I attended ...
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450 views

clustering algorithm for non-dimensional data

i have a dataset of thousands of points and a means of measuring the distance between any two points, but the data points have no dimensionality. i want an algorithm to find cluster centers in this ...
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999 views

DAG partitioning to subgraphs

Given a DAG with $|V| = n$ and has $s$ sources, we have to present subgraphs such that each subgraph has approximately $k_1=\sqrt{s}$ sources and approximately $k_2=\sqrt{n}$ nodes. (Note: ...
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315 views

Continuous Clustering

So I have an issue I'm facing in regards to clustering with live, continuously streaming data. Since I have an ever-growing data set I'm not sure what is the best way to run efficient and effective ...