Multiple View Geometry
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Mahalanobis Distance The Mahalanobis distance is based on the covariance among variables in the feature vectors which are compared. It has the advantage of utilizing group means and variances for each variable and the problems of scale and correlation inherent in the Euclidean distance are no longer an issue. When using Euclidean distance, the set of points equidistant from a given location is a sphere. The Mahalanobis distance stretches this sphere to correct the respective scales of different variables and to account for correlation among variables. ▶ Hand Shape ▶ Signature Matching
▶ Fingerprint Classification
Machine-Learning A type of algorithm that learns from past experience to make decisions. ▶ Incremental Learning ▶ Palmprint Matching
Magnification In optical imaging, the ratio of the dimensions of the image created by the optical system to the dimensions of the object that is imaged. The ratio can be less than one. ▶ Iris Device #
2009 Springer Science+Business Media, LLC
Malicious-code-free Operating System ▶ Tamper-proof Operating System
Manifold Manifold is a non-empty subset M of R N such that the neighborhood of every point p 2 M resembles a Euclidean space. A smooth manifold is associated with a set of homeomorphisms that map points from open subsets around every point p to points in open subsets in R m , where m is the intrinsic dimensionality of the manifold. ▶ Gait Recognition, Motion Analysis for ▶ Manifold Learning ▶ Non-linear Techniques for Dimension Reduction
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Manifold Embedding
Manifold Embedding Any manifold is embedded in an Euclidean space, e.g., a sphere in the 3D world is a two-dimensional manifold embedded in a three-dimensional space. ▶ Gait Recognition, Motion Analysis for
Manifold Learning 1
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P HILIPPOS M ORDOHAI , M EDIONI 1 Stevens Institute of Technology, PA, USA 2 University of Southern California, Los Angeles, CA, USA
Definition Manifold learning is the process of estimating the structure of a ▶ manifold from a set of samples, also referred to as observations or instances, taken from the manifold. It is a subfield of machine learning that operates in continuous domains and learns from observations that are represented as points in a Euclidean space, referred to as the ▶ ambient space. This type of learning, to Mitchell, is termed instance-based or memory-based learning [1]. The goal of such learning is to discover the underlying relationships between observations, on the assumption that they lie in a limited part of the space, typically a manifold, the ▶ intrinsic dimensionality of a manifold of which is an indication of the degrees of freedom of the underlying system.
Introduction Manifold learning has attracted considerable attention of the machine learning community, due to a wide spectrum of applications in domains such as pattern recognition, data mining, biometrics, function approximation and visualization. If the manifolds are linear, techniques such as the Principal Component Analysis (PCA) [2] and Multi-Dimensional Scaling (MDS) [3] ar
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