Spectral learning of graph distributions
نویسنده
چکیده
This work draws on previous works regarding spectral learning algorithm for structured data (see [5], [9], [2], [1], [8]). We present an extension of the Hidden Markov Models, called Graphical Weighted Models (GWM), whose purpose is to model distributions over labeled graphs. We describe the spectral algorithm for GWM, which generalizes the previous spectral algorithms for sequences and trees. We show that this algorithm is consistant, and we provide statistical convergence bounds for the parameters estimate and for the learned distribution.
منابع مشابه
SIGNLESS LAPLACIAN SPECTRAL MOMENTS OF GRAPHS AND ORDERING SOME GRAPHS WITH RESPECT TO THEM
Let $G = (V, E)$ be a simple graph. Denote by $D(G)$ the diagonal matrix $diag(d_1,cdots,d_n)$, where $d_i$ is the degree of vertex $i$ and $A(G)$ the adjacency matrix of $G$. The signless Laplacianmatrix of $G$ is $Q(G) = D(G) + A(G)$ and the $k-$th signless Laplacian spectral moment of graph $G$ is defined as $T_k(G)=sum_{i=1}^{n}q_i^{k}$, $kgeqslant 0$, where $q_1$,$q_2$, $cdots$, $q_n$ ...
متن کاملTHE SPECTRAL DETERMINATION OF THE MULTICONE GRAPHS Kw ▽ C WITH RESPECT TO THEIR SIGNLESS LAPLACIAN SPECTRA
The main aim of this study is to characterize new classes of multicone graphs which are determined by their signless Laplacian spectra. A multicone graph is defined to be the join of a clique and a regular graph. Let C and K w denote the Clebsch graph and a complete graph on w vertices, respectively. In this paper, we show that the multicone graphs K w ▽C are determined by their signless ...
متن کاملMathematical Chemistry Works of Dragos Cvetkovic
In addition to his countless contributions to spectral graph theory, some works of Dragos Cvetkovic are concerned with chemical problems. These are briefly outlined, with emphasis on his collaboration with the present author.
متن کاملSIGNED GENERALIZED PETERSEN GRAPH AND ITS CHARACTERISTIC POLYNOMIAL
Let G^s be a signed graph, where G = (V;E) is the underlying simple graph and s : E(G) to {+, -} is the sign function on E(G). In this paper, we obtain k-th signed spectral moment and k-th signed Laplacian spectral moment of Gs together with coefficients of their signed characteristic polynomial and signed Laplacian characteristic polynomial are calculated.
متن کاملSpectrally approximating large graphs with smaller graphs
How does coarsening affect the spectrum of a general graph? We provide conditions such that the principal eigenvalues and eigenspaces of a coarsened and original graph Laplacian matrices are close. The achieved approximation is shown to depend on standard graph-theoretic properties, such as the degree and eigenvalue distributions, as well as on the ratio between the coarsened and actual graph s...
متن کامل