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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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 ...
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How to calculate distance between two or more vector with Euclidean Distance [on hold]

I know how to get distance between 2 vector (1 vector may have several points), however I want to get distance between 2 vectors where each object has several points. (See illustration on link below.) ...
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12 views

Most Efficient clustering for vectors

I am trying to learn unsupervised learning in Python. My data is stored in list of lists as follows: ...
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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 ...
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30 views

clustering for dummies

I am trying to understand clustering. I have a limited knowledge in math (basic Algebra I, and some basic geometry) but I still want to be able to learn and understand what this is. I don't need to ...
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7 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 ...
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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 ...
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105 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 ...
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24 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: $N_i$; $\bar{X}_i$ ; ...
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41 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 = ...
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16 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 ...
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8 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: ...
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15 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 $U^T$ ...
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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). ...
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1answer
22 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 ...
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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 ...
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31 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 ...
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19 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 ...
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29 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 ...
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1answer
74 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 ...
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1answer
14 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 ...
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31 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 ...
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120 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 ...
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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.
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51 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 ...
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18 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 ...
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1answer
72 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 ...
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30 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 ...
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41 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 ...
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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 ...
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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 ...
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93 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 ...
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1answer
51 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 ...
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40 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 ...
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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 ...
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18 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 ...
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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 ...
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99 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 ...
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1answer
174 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 ...
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71 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 ...
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27 views

which distance function is better to use

I have large data sets with large features space. I'm hesitating between finding the distance between each of those data sets to cluster them into 4 or 5 clusters. or just apply a method by using a ...
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10 views

K cluster structure in Kronecker product type matrix

I have this Kronecker product type matrix: $C =\begin{bmatrix} B_{1,1} A_{1,1} & B_{1,2} A_{1,2} & \dots & B_{1,K} A_{1,K} \\ B_{2,1} A_{2,1} & B_{2,2} A_{2,2} & \dots & ...
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Do I have to be a mathematician to understand the following papers?

I come from a CS&Machine Learning discipline. I have been looking to understand the core idea of Non-Negative Matrix Factorization. While most of the ML based work is understandable, mostly the ...
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1answer
47 views

Explanation of Information double summation within Normalized Mutual Information

The Normalized Mutual Information NMI calculation is described in deflation-PIC paper with the applicable formula copied to the screenshot shown below. My question is specifically about the double ...
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1answer
117 views

What is the meaning of |⋯| notation for an index subset?

I am currently working on a research project. In the attached image what does the capital $|I|$ and $|J|$ mean ?
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152 views

What is the definition of “convex” and “relaxation” concepts in clustering?

I have following text from a paper i am trying to understand: I don't understand what does below sentence refers to as being convex/non-convex The problem is that even though the objectives ...
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1answer
33 views

Measure for presence of several poorly interconnected components in undirected graph

Is there a measure to classify networks regarding whether or not they are composed of several (internally closely connected) groups which are poorly connected (i.e. few links between groups). That ...
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75 views

Proving symmetry of metric (single linkage between clusters using arbitrary dissimilarity measure)

I am told to assume that our dissimilarity measure $d$ satisfies the properties required of it, what seems to be the definition of a metric: $d(x,y) \geq0 $ and $d(x,y)=0 \Longleftrightarrow x=y$ ...
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96 views

Calculating Euclidean dissimilarity for a given cluster with itself

Suppose I have clusters $$A= \{(1,1)^T, (1,2)^T\} $$ $$B=\{(2,3)^T, (3,4)^T\} $$ $$C= \{(4,5)^T, (5,6)^T, (1,2)^T\} $$ I wish to use the Euclidean dissimilarity and Average linkage to calculate a ...
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322 views

Is k-means clustering guaranteed to converge if using Manhattan distance?

The k-means algorithm is an iterative clustering algorithm that partitions the data points into K clusters (with centroids {$\mu_1, ... , \mu_k$}, minimizing the Sum-of-Squared-Error: $$ SSE = ...