Learning Lie Groups for Invariant Visual Perception

By Rajesh P. N. Rao, Daniel L. Ruderman. 1998

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Citations in the corpus

Towards a Definition of Disentangled Representations (2018, background): “Earlier work in this area mostly focused on learning transformations in observation space, such as translation and in-plane rotation of objects [62, 70, 19].”
Unsupervised Transformation Learning via Convex Relaxations (2017, methodology): “Second, improvements in transformation learning have focused on problems with known transformation classes, such as orthogonal or rotational groups [3, 4], while algorithms for general transformations require solving a difﬁcult, nonconvex objective [12].”
An Unsupervised Algorithm For Learning Lie Group Transformations (2010, methodology): “Motivated by the problem of recognizing form invariants, [Rao and Ruderman, 1999] introduced the idea of learning a Lie, or continuous transformation, group representation of the dynamics which occur in the visual world.”
Non-Local Manifold Tangent Learning (2004, methodology): “In (Rao and Ruderman, 1999) the matrix exponential is approximated to first order by (I + Gt), and the authors estimate G for a simple signal undergoing translations, using as a criterion the minimization of x,˜ x min t ||(I + Gt)x − ˜ x|| 2 , where˜x is a neighbor of x in the data.”
Bilinear Sparse Coding for Invariant Vision (2005, methodology): “A fundamental problem in vision is to simultaneously recognize objects and their transformations (Anderson & Van Essen, 1987; Olshausen et al., 1995; Rao & Ballard, 1998; Rao & Ruderman, 1999; Tenenbaum & Freeman, 2000).”
Invariant Visual Object and Face Recognition: Neural and Computational Bases, and a Model, VisNet (2012, methodology): “algorithm for learning Lie group operators for in-plane transforms from input data was described (Rao and Ruderman, 1999).”
Learning to Represent Spatial Transformations with Factored Higher-Order Boltzmann Machines (2010, background): “When transformations are not known a priori, are not stationary, or are difficult to model, we can still perform invariant recognition using a system that can learn about allowable transformations from training examples, as suggested, for example, by Rao and Ruderman ( 1999 ), Olshausen, Cadieu, Cul”
Nonlocal Estimation of Manifold Structure (2006, background): “Unlike in (Rao and Ruderman, 1999), the manifold can be more than one-dimensional (they present results for 12 dimensions), but the manifold is locally linear around each prototype (hence must be globally smooth if the number of prototypes is signi(cid:12)cantly less than the number of examples).”