Learning over Sets using Kernel Principal Angles

By Lior Wolf, Amnon Shashua. Journal of machine learning research, 2003

304 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/84497fd95b90e5bfe3ee0ed701808a8ec4c28690

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Citations in the corpus

Face recognition with image sets using manifold density divergence (2005, background): “We believe that this restriction explains the variable results attributed to these methods [24, 27], since it does not capture non-linear variation in appearance due to illumination and pose changes.”
Face recognition in unconstrained videos with matched background similarity (2011, methodology): “Different choices of similarity measures are then used to compare two sets [19, 20, 24].”
Covariance discriminative learning: A natural and efficient approach to image set classification (2012, background): “…( , ) q d G to a Euclidean space: : ( , ) , q d G The inner product in the Euclidean space d d × spanned by d d × projection matrices thus induces a Grassmann kernel function on the manifold ( , ) q d G , as discussed in [8],[29]: It is also easy to check that Proj k is a valid Mercer kernel.”
The Pyramid Match Kernel: Efficient Learning with Sets of Features (2007, methodology): “In the method of Wolf and Shashua (2003), similarity is measured in terms of the principal angle between the linear subspaces spanned by two sets' vector elements; the kernel has a cubic complexity and is only positive-definite for sets of equal cardinality.”
Semigroup Kernels on Measures (2005, methodology): “Finally, Wolf and Shashua (2003) recently proposed a formulation rooted in kernel canonical correlation analysis (Bach and Jordan, 2002, Melzer et al., 2001, Akaho, 2001) which makes use of the principal angles between the subspaces generated by the two sets of points to be compared when considered…”
Object Classification from a Single Example Utilizing Class Relevance Metrics (2004, background): “Extensions of the principal angles kernel that have the additional capacity to incorporate knowledge on the accurate location matching, might enhance the kernel’s descriptive power [16].”
Discriminative Learning and Recognition of Image Set Classes Using Canonical Correlations (2007, background): “Most recently, the concept of canonical correlations has attracted increasing attention for image set matching in [36], [8], [23], [24], [37], [27], [39], following the early works [1], [3], [5], [2].”
Graph embedding discriminant analysis on Grassmannian manifolds for improved image set matching (2011, methodology): “Grassmannian kernels [13, 14, 27] allow us to treat the Grassmannian space as if it were a Euclidean vector space.”
From sample similarity to ensemble similarity: probabilistic distance measures in reproducing kernel Hilbert space (2006, background): “For example, alternative representations include strings [14], graphs [15], lattices [16], statistical manifolds [17], [18], [19], and so on [20], [21].”
The pyramid match kernel: discriminative classification with sets of image features (2005, methodology): “The authors of [27] measure similarity in terms of the principal angle between the two linear subspaces spanned by two sets’ vector elements.”
Manifold-Manifold Distance with application to face recognition based on image set (2008, methodology): “Representative methods include [10], [17], [27], [28], following the early works in [3], [8].”
Mathematics of Deep Learning (2017, background): “…data [59], [60], [61], deep networks with random weights are a universal system that separates any data (belonging to a low-dimensional model) according to the angles between the data points, where the general assumption is that there are large angles between different classes [62], [63].”
Projection Metric Learning on Grassmann Manifold with Application to Video based Face Recognition (2015, background): “Nowadays, linear subspaces have proven a powerful representation for video based face recognition [43, 41, 10, 30, 27, 12, 11, 16, 7], where each video can be treated as a set of face images without considering temporal information.”
On classification with bags, groups and sets (2014, background): “This setup is common for face recognition [42, 57, 24, 58].”