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.

learn more… | top users | synonyms

0
votes
0answers
10 views

Simultaneously Diagonalizable matrices using clustering

I'm interested in partitioning matrices into groups which are almost simultaneously diagonalizable. I'm aware that if matrices commute and one of them has no multiple eigenvalues then the matrices are ...
0
votes
0answers
20 views

What is Spectral bisection ?

I had to look through a paper on text clustering, the algorithm is by "clustering the sentences based on modified repeated spectral bisection" which made zero sense to me, can some one please explain ...
0
votes
0answers
16 views

The modularity formula of Newmann and Girvan

I have question concerning the modularity formula of Michelle Girvan and Mark Newman. It says that it measures the fraction of edges in a network, that connects nodes, within the same ...
0
votes
0answers
16 views

Number of clusters in $k$-means clustering for higher-dimensional data.

I've read the Wikipedia article and a lot of posts on stackexchange (like this really thorough one) on determining the number of clusters in a data set. Based on that, I am currently using the ...
0
votes
0answers
8 views

Dirichlet clustering and group assignment

As in the Dirichlet clustering, the dirichlet process can be represented by the following: Chinese Restaurant Process Stick Breaking Process Poly Urn Model For instance, if we consider ...
0
votes
0answers
39 views

Is my entropy calculation correct? Clustering entropy example

I would like to calculate entropy of this example scheme http://nlp.stanford.edu/IR-book/html/htmledition/evaluation-of-clustering-1.html Equation of entropy Then the entropy is (the first line) ...
0
votes
1answer
21 views

How to develop an algorithm to prioritize set members based on various criteria

I tried looking for responses and Google. It has been a while since I used math to any capacity and the lack of application is only surpassed by my inability to articulate the concepts. That's my ...
0
votes
0answers
10 views

Clustering via U(-W)PGMA

Given paiwise distance between 5 taxa: {a,b,c,d,e} 0 3 12 12 9 - 0 13 13 10 - - 0 6 7 - - - 0 7 - - - - 0 Calculate evolutionary tree, using UPGMA and ...
1
vote
0answers
28 views

Grouping a set of numbers

I have a set of numbers which I don´t know if they belong to the same group (I could also call it factor or treatment, but actually each group is suppose to identify the same biological event). I am ...
0
votes
0answers
13 views

How many degrees of freedom exist in an agglomerative hierarchical clustering?

The computational complexity of generating an agglomerative hierarchical clustering from n vectors is $O(n^2)$ (calculating the pairwise distance matrix) dendrogram example However, the total number ...
1
vote
0answers
19 views

Approximate values from point groupings

Say I am given a set of values: \begin{bmatrix}0.9&1.1&1&1.95&2&2.05&2.95&2.95&3.1&3\end{bmatrix} Is there a way I can get the 'center' or 'average' values 1, 2, ...
0
votes
0answers
13 views

Find percentage of proximity to cluster in kmeans2

I am trying to clustering in python. This is my code as follows: ...
0
votes
1answer
79 views

der(der(A)) and der(A)

I have a question about cluster points that would like to ask you, this question is one of the exercises in my textbook. Question: If $A$ is any subset of $R^d$, then $der(der($A$))$ is the set of ...
0
votes
0answers
26 views

Class Scatter Fitness Function Calculation

I get a fitness function for class scatter, the equation: Click here to see the Fitness Function Where : T = Transpose of Matrics Mi = class mean Mo = grand mean The equation is based from ...
0
votes
0answers
8 views

How to evaluate a point in a weighted Mixture of Gaussians model?

Example: I have a MoG comprised of 2 1-d gaussians. The first gaussian has a weight of 0.8 the other 0.2. I have a sample point which I can easily evaluate on each individual gaussian. The ...
0
votes
0answers
9 views

Building agglomerative hierarchical clustering algorithm manually

I am currently trying to solve this problem but I'm quite unsure if my answer is correct. I've build the tree different types of measures, MIN, MAX and AVERAGE but I might have some of them wrong. Can ...
0
votes
0answers
7 views

Clustering state-space models according to similarity

I have a plant that can be modeled with nonlinear equations as $$f(x,u,p)=0$$ where $x$ is the state vector, $u$ the control vector, and $p$ the model parameters. In order to control this system, I ...
5
votes
0answers
115 views

Theoretical link between the graph diffusion/heat kernel and spectral clustering

The graph diffusion kernel of a graph is the exponential of its Laplacian $\exp(-\beta L)$ (or a similar expression depending on how you define the kernel). If you have labels on some vertices, you ...
0
votes
0answers
25 views

Cluster sampling: Compare efficiencies

A company operates from 12 branches, and the numbers of cars, $N_i$ and means $\bar{X}_i$ and variances $S_i^2$ of miles driven last year for each brand, are as follows Branch: $N_i$; $\bar{X}_i$ ; ...
0
votes
2answers
44 views

How to make an Eigenvector orthonormal?

I am trying to figure out the PCA of a Data-set using calculation , and in one phase of this calculation I have the two eigenvectors : $V_1=(\frac{1}{\sqrt2} , -\frac{1}{\sqrt2} ,0)t $ ; $V_2 = ...
0
votes
0answers
24 views

How to compute low rank factorization of a symmetric matrix?

I was implementing NEO - KMeans which is described in the following paper. NEO- KMeans Clustering Paper talked about low rank factorization of a matrix Z of size $ n \times n$ such that ...
0
votes
0answers
12 views

Introducing weights into spectral clustering

Suppose I have a data set with points $x_i$ and a dissimilarity measure $d_{ij}$ between each pair, as well as a weight $w_{ij}$ that qualifies the quality of this dissimilarity. I have two problems: ...
0
votes
0answers
18 views

Non-negative tri-matrix factorization

If I would like to factorize a matrix $W$ ($0\leq W\leq 1$) into 3 matrices, like $W = UAU^T$, is this problem solvable or is there any approximate solution? Here, $U$ is binary, $A\geq 0$ and $U^T$ ...
0
votes
1answer
15 views

Find the cluster points: For each cluster point, find a sub-sequence converging to it.

The book I am using for my Advance Calculus course is Introduction to Analysis by Arthur Mattuck. Find the cluster points of: (a). {${sin(\frac{n+1}{n} \frac{n}{2})}$} (b). ...
0
votes
1answer
27 views

How to profile people using clustering

I have a data of customers and i want to split them to segment (profiling). The columns of the data are Amount-Spending, Amount-Bonus, Age, Churn-or-Not. So i clustered my data with k-means. to 3 ...
0
votes
0answers
23 views

Most probable number of clusters

I have a set S of N 2D points, each point P is associated with a doubly infinite cone ...
0
votes
0answers
33 views

How to group/cluster data based on pairwise comparsion?

I want to create a group of objects, which share similarity of a certain feature if the similarity score is 90% and higher. I have about 200 such objects. How do I merge them into groups/clusters? I ...
0
votes
0answers
20 views

Proving the transitivity of a clustering coefficient

I am taking an upper level special topics course on Network Science at my university. Every class, we are given team-exercise questions which we are meant to work on with partners towards the end of ...
0
votes
0answers
38 views

Finding a cluster of points where each member is within minimum distance of all other members of the cluster

I am currently looking for an algorithm that will help me search a data set for groups of points that are all mutually within a tolerance distance of each other. I have been thinking along the lines ...
0
votes
1answer
79 views

Optimizing sums of log det

I have a set of points $S$ which have to be clustered into $K$ cluster say, $S_k$, by minimizing the following function: $J = - \sum_{i=1}^{K} \log \det( \mathbf{I} + H_i H_i^T)$, Where $H_i$ is the ...
0
votes
1answer
20 views

What Laplacian should we use for spectral clustering?

The second eigenvector of the normalized Laplacian $I-D^{-1}W$ or the symmetric normalized Laplacian $I-D^{-1/2}WD^{-1/2}$ can be used to approximate a minmizer of the normalized cut problem. Which ...
0
votes
2answers
32 views

Define temperature by clustering with math operators

I can´t figure out how to cluster the temperature for the weather in 3 optimal cases: hot, mild, cold My data contains: air temperature(the average daily value), max air temperature(highest daily ...
3
votes
2answers
207 views

Measure of “how much diagonal” a matrix is

I have a (biological) computational system that outputs squared matrices. These matrices will sometimes have a tendency to be diagonal-like, with higher values at and around the diagonal. I would ...
0
votes
0answers
14 views

approach for clustering of huge networks

Can you give me some kind of direction on the best approach for clustering huge networks? (so large, that even the list of nodes cannot be stored in RAM) Thanks for anyone who helps.
0
votes
0answers
94 views

Displaying a graph with minimum overlapping edges

Context I am developing UI for a skill web for a mobile game. Each skill may have requirements from other skills, or sometimes no requirement at all. The problem The description above is ...
0
votes
0answers
21 views

How do you compute the weighted sum of data points for learning the centers of a hyper basis function network (HBF)?

I was reading the following paper on hyper basis function (HBF) (similar to radial basis function RBF network) and was trying to figure out how one learns the movable centers of the hyper basis ...
0
votes
1answer
88 views

Mathematical Intuition behind the tf-idf formula in Statistics

I was reading: https://en.wikipedia.org/wiki/Tf%E2%80%93idf#Definition But I cannot seem to understand exactly why the formula was constructed the way it is. What I do Understand: iDF should at ...
0
votes
0answers
35 views

Difference between Cosine similarity and Angular similarity

Both cosine similarity and angular similarity are measures of similarity between vectors. The cosine similarity is defined as $$\sigma(u,v)=\frac{u \cdot v}{\|u\|\|v\|}$$, while the angular ...
0
votes
0answers
45 views

Shortest distance of a location to X number of locations

Anyone have advice on this problem? "Shortest distance of a location to X number of locations" First lets assume X=3 (3 addresses) We know the following: Distance in Miles or KM of : A1 to A1, A1 ...
1
vote
0answers
11 views

Identify outliers in a set of elements

I have a set of elements that has been partitioned into clusters based on several criteria, one of which is the length of the elements. To be precise, element $x$ cannot belong to cluster A if ...
0
votes
1answer
24 views

How to convert table into a distance function?

Been stumped on this past paper question for a while, it's in the context of clustering and the next part is using single linkage bottom-up hierarchical clustering to form a dendrogram using your ...
0
votes
0answers
120 views

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 ...
2
votes
1answer
59 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 ...
0
votes
1answer
47 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 ...
1
vote
0answers
19 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 ...
0
votes
0answers
19 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 ...
0
votes
1answer
24 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 ...
0
votes
0answers
113 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 ...
1
vote
1answer
267 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 ...
0
votes
0answers
73 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 ...