Diffusion Kernels on Statistical Manifolds

By John D. Lafferty, Guy Lebanon. 2005

288 citations recorded by the source corpus.

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Citations in the corpus

Generative and Latent Mean Map Kernels (2010, methodology): “The heat kernel [13] is not sensitive to the parameterization, but it is rarely computable in closed form; however, it can be approximated under certain conditions to yield a positive definite kernel, e.”
Beyond Sentiment: The Manifold of Human Emotions (2012, methodology): “This multinomial geometry outperforms the Euclidean geometry in a variety of text processing tasks, as described in (Laﬀerty and Lebanon, 2005; Lebanon, 2005b).”
Context-aware citation recommendation (2010, background): “diffusion: the candidates are ranked according to their topical similarities which are generated by the multinomial diffusion kernel [14] to the query manuscript, K(θ1, θ2) = (4πt)− |W | 2 exp (− 1 t arccos(2)( √ θ1 · √ θ2) ) , where θ1 and θ2 are topic distributions of the query manuscript d1 and t”
Universal Kernels on Non-Standard Input Spaces (2010, background): “• SVMs for text classification and web mining [15, 12, 16], • SVMs with kernels from computational biology, e.”
Hilbertian Metrics and Positive Definite Kernels on Probability Measures (2005, methodology): “Following [8] we used the five most frequent classes earn, acq, moneyFx, grain and crude.”
LanczosNet: Multi-Scale Deep Graph Convolutional Networks (2019, background): “The anisotropic diffusion is able to use the local statistics of the measurements to convey the geometric information on the underlying factors rather than the speciﬁc realization or measurements at hand [60, 61].”
Nonextensive Information Theoretic Kernels on Measures (2009, methodology): “Although Lafferty and Lebanon (2005) provide empirical evidence that the heat kernel outperforms the linear kernel, it is not guaranteed to be pd for an arbitrary choice of t, as we show in Appendix E.”
Proto-value Functions: A Laplacian Framework for Learning Representation and Control in Markov Decision Processes (2007, methodology): “Riemannian manifolds have been actively studied recently in machine learning in several contexts, namely in the context of designing new types of kernels for supervised machine learning (Lafferty and Lebanon, 2005) and faster policy gradient methods using the natural Riemannian gradient on a space o”
Like like alike — Joint Friendship and Interest Propagation in Social Networks Shuang (2011, methodology): “This is similar to the information diffusion kernel for graph [8, 11] in that both kernels inherent a Riemannian manifold for I defined by the friendship network S, rather than a flat Euclidean space as in traditional CF models (e.”