Non-Local Manifold Tangent Learning

By Yoshua Bengio, Monperrus Martin. 2004

104 citations recorded by the source corpus.

Subfields: Representation & Self-Supervised Learning

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In Representation & Self-Supervised Learning

Citations in the corpus

A Generative Process for Contractive Auto-Encoders (2012, methodology): “ng algorithms is that they are based on local generalization: they infer these local tangent planes based mostly on the training examples in the neighborhood of the point of interest. As discussed in Bengio and Monperrus (2005) and Bengio et al. (2006b), this raises a curse of dimensionality issue: ”
Representation Learning: A Review and New Perspectives (2012, background): “Examples of such general-purpose priors are the following: • Smoothness: assumes the function to be learned f is s.t. x ≈ y generally implies f(x) ≈ f(y).”
The Manifold Tangent Classifier (2011, background): “See Bengio and Monperrus (2005) for a critique of local non-parametric manifold algorithms: they might require a number of training examples which grows exponentially with manifold dimension and curvature (more crooks and valleys in the manifold will require more examples).”
Scaling learning algorithms towards AI (2007, methodology): “In Bengio et al. [2005] we present similar results that apply to unsupervised learning algorithms such as non-parametric manifold learning algorithms [Roweis and Saul, 2000, Tenenbaum et al.”
Unsupervised Feature Learning and Deep Learning: A Review and New Perspectives (2012, background): “Unfortunately, as argued at length previously (Bengio and Monperrus, 2005; Bengio et al. , 2006a; Bengio and LeCun, 2007; Bengio, 2009; Bengio et al. , 2010), most of these algorithms only exploit the principle of local generalization , i.e., the assumption that the target function (to be learned)…”
Unsupervised Transformation Learning via Convex Relaxations (2017, background): “Both works model a manifold by predicting the linear neighborhoods around points using nonlinear functions (radial basis functions in Dollár et al. [7] and a one-layer neural net in Bengio and Monperrus [1]).”
Non-Local Manifold Parzen Windows (2005, methodology): “In (Bengio and Monperrus, 2005) a manifold learning algorithm was introduced in which the tangent plane of a d-dimensional manifold at x is learned as a function of x ∈ R D , using globally estimated parameters.”
A review of novelty detection (2014, methodology): “The proposed approach builds upon the Manifold Parzen density estimator [96] that associates a regularised Gaussian with each training point, and upon previous work on non-local estimators of the tangent plane of a manifold [86].”
On the Expressive Power of Deep Architectures (2011, background): “Bengio and Monperrus (2005) argued that many real-world manifolds (such as the one generated by translations or rotations of images, when the image is represented by its pixel intensities) are highly curved (translating by 1 1 but of course additional noisy dimensions, although they do not change…”
Dimensionality Reduction: A Comparative Review (2008, methodology): “It has been suggested that the susceptibility to the curse of dimensionality may be addressed using techniques in which the global structure of the data manifold is represented in a number of linear models [14].”