Skip to main content

Questions tagged [similarity]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0 votes
0 answers
43 views

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 ...
k99's user avatar
  • 1
6 votes
0 answers
230 views

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 &...
Yemon Choi's user avatar
  • 25.6k
1 vote
0 answers
109 views

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?
Styles's user avatar
  • 113
8 votes
0 answers
262 views

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 $\mathbb{Z}^{n\times n}$)? ...
darij grinberg's user avatar
3 votes
1 answer
215 views

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 ...
Student88's user avatar
  • 503
1 vote
0 answers
178 views

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,...
Shaun Han's user avatar
  • 141
0 votes
0 answers
72 views

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 ...
twofiveone's user avatar
1 vote
0 answers
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 ...
AKA's user avatar
  • 11
4 votes
0 answers
218 views

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: ...
user avatar
7 votes
1 answer
495 views

Discriminant of elliptic curve (Frey-Hellegouarch), j-invariant and positive definite kernels, similarities?

Consider the Frey-Hellegouarch curve given $a,b$ natural numbers: $$y^3= x(x-\frac{a}{\gcd(a,b)})(x+\frac{b}{\gcd(a,b)})$$ Then the discriminant is given by $\Delta = \Delta(a,b) = 16 \left(\frac{ab(a+...
user avatar
0 votes
0 answers
384 views

Comparison of two similarity matrices

English is not my first language, so please excuse any mistakes. I'm working with two similarity matrices on the same data set: Suppose I have $n$ items, and I calculated the similarity of each item ...
Catasaur's user avatar
3 votes
0 answers
111 views

Symmetrization of pentadiagonal matrices

Nonsymmetric tridiagonal matrices $T_3$ can easily be symmetrized via a (diagonal) similarity transformation $D=\text{diag}(d_1, \dots, d_n)$ (i.e. see Wikipedia) $$ J_3=D^{-1} T_3 D \,. $$ Is there ...
jack's user avatar
  • 213
3 votes
1 answer
142 views

Efficient eigen-decomposition of a real matrix with all real eigenvalues

I'm optimising a radar algorithm that results in real matrices which are not symmetric but which are guaranteed to have real eigenvalues. Each matrix is therefore similar to a symmetric matrix. I am ...
Mark Pedley's user avatar
3 votes
0 answers
117 views

Sparsest similar matrix

Given a square matrix A (say with complex entries), which is the sparsest matrix which is similar to A? I guess it has to be its Jordan normal form but I am not sure. Remarks: A matrix is sparser ...
Nacho Garcia Marco's user avatar
5 votes
0 answers
362 views

Shapes defined by points

Can shapes determined by some number of points? From an amazing theorem in plane curves geometry we know that vertices of triangles similar to arbitrary triangle $T$ is dense on every closed jordan ...
MasM's user avatar
  • 289
1 vote
1 answer
191 views

Are there two tetrahedrons with the same volume that share their opposite edge lengths and arent the same or a different chirality of the same? [closed]

I have been coming up with an efficient way to decide if two tetrahedrons are similar. I believe that it is enough for a computer to check for the ordered by length list of pairs of opposite edges on ...
The_Turtle's user avatar
3 votes
1 answer
168 views

Similarity via symmetric matrix

Let $K$ be a field extension of $F$. If two $n\times n$ matrices $A,B \in M_n(F)$ are similar via a matrix $P \in GL_n(K)$ (that is, $A=PBP^{-1}$), then there exists a matrix $Q\in GL_n(F)$ such that $...
Oliver's user avatar
  • 367
0 votes
2 answers
146 views

Simultaneous special orthogonal similarity problem

Given matrices $A,B,C,D\in\Bbb K^{n\times n}$ where $\Bbb K$ is a ring is there an efficient technique to compute set $O$ with $OO'=I$ where $'$ is transpose and $\mathsf{Det}(O)=\pm1$ such that $$A=...
user avatar
0 votes
0 answers
63 views

Eigenvalues of sum of two fuchsian matrices

Dear mathoverflow users, I am trying to solve a problem concerning eigenvalues and sum of matrices. In particular: consider the expression $$ A=\frac{E}{x-x_1}+\frac{F}{x-x_2}, $$ and suppose to know ...
Marco B.'s user avatar
0 votes
1 answer
142 views

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 ...
Michael Hardy's user avatar
2 votes
0 answers
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 ...
Cali's user avatar
  • 29
1 vote
0 answers
202 views

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 ...
np20's user avatar
  • 111
5 votes
3 answers
1k views

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 ...
user avatar
2 votes
0 answers
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 ...
kerzol's user avatar
  • 335
13 votes
4 answers
24k views

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). ...
web_ninja's user avatar
  • 281
2 votes
2 answers
1k views

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 ...
EJA's user avatar
  • 23
6 votes
2 answers
4k views

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 ...
Xiao Junhui's user avatar
23 votes
0 answers
8k views

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). ...
Sungjin Kim's user avatar
  • 3,320
1 vote
2 answers
1k views

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 ...
Francesco's user avatar
1 vote
0 answers
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 ...
Jagra's user avatar
  • 111
0 votes
1 answer
1k views

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 ...
graus's user avatar
  • 11
0 votes
1 answer
652 views

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 ...
user17528's user avatar
  • 103
14 votes
0 answers
620 views

Some questions on unitarisability of discrete groups

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 ...
Kate Juschenko's user avatar