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14
votes
0answers
503 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 ...
6
votes
3answers
6k 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). ...
5
votes
3answers
732 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 ...
4
votes
2answers
2k 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 ...
2
votes
1answer
105 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 $...
2
votes
0answers
100 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 ...
2
votes
0answers
137 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 ...
1
vote
1answer
4k views

Weighted Jaccard Similarity

I'd like to calculate the similarity between two sets using Jaccard but temper the results using the relative frequency of each item within a corpus. Jaccard is defined as the magnitude of the ...
1
vote
2answers
699 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 ...
1
vote
2answers
495 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 ...
1
vote
0answers
66 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 ...
1
vote
0answers
162 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 ...
0
votes
2answers
83 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=...
0
votes
1answer
102 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 ...
0
votes
1answer
752 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 ...
0
votes
0answers
46 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 ...
0
votes
1answer
532 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 ...
-1
votes
0answers
23 views

distance between two graphs, or graph similarity

I have two graphs G1 and G2 which have the same number of nodes and edges. However the edges of both graphs have different values (assume those values are distance relations between the nodes), what ...
-4
votes
0answers
26 views

similarity metric for geometries [on hold]

I'm searching for a method to calculate the degree of similarity of two given geometries. These geometries can be of any type and can have an arbitrary shape. For the sake of simplicity, I primarily ...