# Questions tagged [similarity]

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### How can I measure similarity between two graphs with identical topology but different edge weights

I have two graphs, G1 and G2, with exactly the same topology. Their only difference lies in the edge weights, which vary between 0 and 1. How can I measure the similarity between G1 and G2 under these ...
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### Are bounded groups of thin operators on Hilbert space similar to groups of unitaries?

QUESTION. Let $G$ be a group of bounded operators on $\ell^2$, satisfying $\sup_{x\in G} \lVert x\rVert <\infty$, whose elements are all of the form "identity+compact" (sometimes called &...
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1 vote
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### What is the status of The Halmos Similarity Problem?

What is the general status of "The Halmos Similarity Problem"(HSP) in Operator theory?For What conditions ,HSP has been solved?
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### How to check two matrices for similitude over $\mathbb{Z}$?

General question. Let $A$ and $B$ be two $n\times n$-matrices over $\mathbb{Z}$. How do I algorithmically check whether $A$ and $B$ are similar (i.e., conjugate in the ring $\mathbb{Z}^{n\times n}$)? ...
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### Comparing two distributions based of the ratio of their moments

I am looking for some metric for distribution with support on the interval $[0,1-\epsilon]$, that will be based on the ratio of their moments. That is, if $X\sim f(x)$, $Y\sim g(y)$, I'm looking for a ...
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1 vote
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### What is a good algorithm to measure similarity between isomorphic graphs with different node labels?

I am using graphs to represent some structured data. In my case, I have a time series of undirected unweighted graphs with the same topology (i.e. isomorphic graphs with same number of nodes and edges,...
• 141
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### Fast decay of eigenvector elements

Let A be a set of similar (symmetric) matrices, sharing the same eigenvalues. I understand that their eigenvectors would be different. Let us focus on one eigenvector (e.g. corresponding to the lowest ...
1 vote
57 views

### What is the name given to the solution to the equation $cU = Y U Y$ for a given symmetric, positive definite, real-valued matrix $Y$

Overarching question is: What is the name given to the solution to the equation $cU = Y U Y$ for a given symmetric, positive definite, real-valued matrix $Y$? And what procedure is used to solve this ...
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### Studying finite groups with Euclidean geometry?

Since each finite group $G$ can be considered as a subgroup of the symmetric group, by Cayley's theorem, we might see the elements of $G$ as permutations $\pi$. Consider for each $\pi \in G$ the set: ...
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### Sizes and shapes of Dedekind cuts

My geometric intuition has failed to tell me that there are different sizes and shapes of Dedekind cuts. I realized it in the course of writing this answer only by doing algebra. If we define a ...
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447 views

### What does similar eigenvectors and eigenvalues of two matrices really mean? [closed]

Empirically I've noticed that diagonally dominant matrix G and it's diagonal version D (diagonal elements of G on the diagonal and all other elements are set to zero) produce similar eigenvalues and ...
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1 vote
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### Quantification of the extent of periodicity in a time series using fractal analyses

I need metrics to quantify and compare the extent of periodicity between any two given time series, considering the time series were "almost periodic". By "almost periodic" I mean: if I were to take ...
• 111
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### Looking for techniques of How to measure the Similarity/Dissimilarity between two images?

I would like to compute the similarity/dissimilarity between two images L and R. I know one way which is : computing the histogram of blocks of each image, and then using Bhattacharyya measure I ...
240 views

### Is there an universal (dis)similarity measure between two structures?

I'm always wondering is there an universal (dis)similarity measure between two structures (let's say between two undirected simple graphs)? I mean, not "the measure with universal parameter that we ...
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### What is a good algorithm to measure similarity between two dynamic graphs?

I am using graphs to represent structure present in a scene. The vertices represent the objects in the scene and the edges represent the relationship between two nodes(touching, overlapping, none). ...
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### Appropriate histogram comparison distance measure

I am working with hyperspectral image data in R, so I have subset an image to a region of 5000 pixels, each containing a vector 254 bands in length. I would like to cluster this data in order to try ...
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### similarity transformation into symmetric matrices

I want to determine some structures of matrices that can be transformed into a symmetric matrices using similarity transformation, i.e., $B=T^{-1}AT$ where $T$ is the similarity transformation ...
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### An $n \times n$ matrix $A$ is similar to its transpose $A^{\top}$: elementary proof?

A famous result in linear algebra is the following. An $n \times n$ matrix $A$ over a field $\mathbb{F}$ is similar to its transpose $A^T$. I know one proof using the Smith Normal Form (SNF). ...
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1 vote
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### Similarity measure between 2 bi-partite graph.

Hello there, i need to solve this problem: I have 2 different bi-partite weighted graph, g1 and g2 and i would like to measure their similarity, g1 and g2 may have different number of vertex and edges ...
1 vote
191 views

### Universal Correlation measure — ranking correlations

I have time series data of experimental observations for two related processes. I want to measure correlation for use in further analysis. Correlation of the series changes over time and across ...
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### How to use node similarity to measure subgraph similarity

For a semantic annotation task I am trying to calculate the semantic similarity between two sets of annotations: S1 and S2. Both sets consist out of multiple nodes from within one graph (in my case an ...
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### Fuzzy vector similarity

Hi all, I have two multi-dimensional vectors representing documents $\vec{a}$ and $\vec{b}$. Considering cases where there is no overlap between $a$ and $b$ ($a \cap b = \emptyset$), traditional ...
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In this post I would like to ask several of questions related to Dixmier problem. I will try to make the post as self-contained as possible. A discrete group $G$ is unitarisable if for every Hilbert ...