Clustering on the Unit Hypersphere using von Mises-Fisher Distributions

By Arindam Banerjee, Inderjit S. Dhillon, Joydeep Ghosh, Suvrit Sra. 2005

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Citations in the corpus

General Incremental Learning with Domain-aware Categorical Representations (2022, background): “Moreover, the probability density function p(ṽ|z, y) = Cd(κ)e κμ̃y,zṽ follows the von Mises-Fisher(vMF) distribution [2], which can be considered as multivariate normal distribution for directional features on the hyper-sphere.”
Recurrent Pixel Embedding for Instance Grouping (2017, methodology): “Since our embedding vectors are unit norm, we instead use the von Mises-Fisher distribution, K(x,xi) ∝ exp(δxxi), which is the natural extension of the multivariate normal to the hypersphere [24, 5, 64, 41].”
Automated Scalable Bayesian Inference via Hilbert Coresets (2017, methodology): “For this purpose we employ a von Mises-Fisher (vMF) mixture model (Banerjee et al., 2005).”
Information theoretic measures for clusterings comparison: is a correction for chance necessary? (2009, background): “Another class of clustering comparison measures, which are information theoretic based, have also been employed more recently in the clustering literature (Banerjee et al., 2005; Strehl & Ghosh, 2002; Meilˇa, 2005).”
A Bayesian Hierarchical Topic Model for Political Texts: Measuring Expressed Agendas in Senate Press Releases (2010, methodology): “Previously developed unsupervised learning methods ignore this hierarchy and instead focus upon assigning documents to topics (Banerjee et al. 2005) or introduce structure designed to answer a different (but still important) question about how attention varies over time in the whole legislature…”
Compositional Convolutional Neural Networks: A Deep Architecture With Innate Robustness to Partial Occlusion (2020, methodology): “The parameters of the vMF distribution Λ can be learned by iterating between vMF clustering of the feature vectors of all training images and maximum likelihood parameter estimation [1] until convergence.”
Exploratory Learning (2013, methodology): “[1], who described an EM algorithm that is directly inspired by K-Means and TFIDF-based representations.”
Hidden Markov Model on a unit hypersphere space for gesture trajectory recognition (2014, methodology): “The derivation of parameter re-estimation formulae of the MvMF HMM follows the EM approach for MvMF parameter estimation of Banerjee et al. (2005). In the MvMF-HMM case it can be estimated by maximizing Baum’s auxiliary function which is defined as”
topicmodels: An R Package for Fitting Topic Models (2011, methodology): “…the performance of topic models for clustering documents to other approaches such as using mixtures of von Mises-Fisher distributions to model the term distributions of the documents (Banerjee, Dhillon, Ghosh, and Sra 2005) where the R package movMF (Hornik and Grün 2011) is available on CRAN .”
A web-based kernel function for measuring the similarity of short text snippets (2006, methodology): “Such distributions, which are defined based on direction or angle, fall into the general class of circular distributions and a full discussion of them is beyond the scope of this paper (we refer the interested reader to work on document analysis using circular distributions, such as the von Mises di”
Transductive Multi-view Embedding for Zero-Shot Recognition and Annotation (2014, background): “In particular, extensive evidences in text analysis and information retrieval have shown that high-dimensional embedding vectors are naturally directional and using cosine similarity provides significant robustness against noise [2, 13, 14].”
Exact risk improvement of bandwidth selectors for kernel density estimation with directional data (2013, methodology): “(5) The second element is the Expectation–Maximization (EM) algorithm of Banerjee et al. (2005) for fitting mixtures of directional von Mises.”
Hyperspherical Variational Auto-Encoders (2018, methodology): “…used to infer structure from motion (Guan and Smith, 2017) in spherical video, or structure from texture (Wilson et al., 2014), to natural language processing, where it is utilized in text analysis (Banerjee et al., 2003, 2005) and topic modeling (Banerjee and Basu, 2007; Reisinger et al., 2010).”