n-Dimensional Vector

An n-Dimensional Vector is a vector with more than on dimension.

• Context:
  • It can be from an n-Dimensional Space.
• See: 2-Dimensional Vector, 3-Dimensional Vector.

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References

2003

• (Zelenko et al., 2003) ⇒ Dmitry Zelenko, Chinatsu Aone, and Anthony Richardella. (2003). “Kernel Methods for Relation Extraction.” In: Journal of Machine Learning Research, 3.
  • QUOTE: Most learning algorithms rely on feature-based representation of objects. That is, an object is transformed into a collection features [math]\displaystyle{ f_1,...,f_N }[/math], thereby producing a N-dimensional vector.

2001

• (Hand et al., 2001) ⇒ David J. Hand, Heikki Mannila, and Padhraic Smyth. (2001). “Principles of Data Mining.” In: MIT Press. ISBN:026208290X
  • QUOTE: A model structure, as defined here, is a global summary of a data set; it makes statements about any point in the full measurement space. Geometrically, if we consider the rows of the data matrix as corresponding to p-dimensional vectors (i.e., points in p-dimensional space), the model can make a statement about any point in this space (and hence, any object). For example, it can assign a point to a cluster or predict the value of some other variable. Even when some of the measurements are missing (i.e., some of the components of the p-dimensional vector are unknown), a model can typically make some statement about the object represented by the (incomplete) vector.

19995

• (Cortes & Vapnik, 1995) ⇒ Corinna Cortes, and Vladimir N. Vapnik. (1995). “Support Vector Networks.” In: Machine Learning, 20(3). doi:10.1007/BF00994018
  • QUOTE: More than 60 years ago R. A. Fisher (Fisher, 1936) suggested the first algorithm for pattern recognition. He considered a model of two normal distributed populations, [math]\displaystyle{ N(m_1, \Sigma_1) }[/math] and [math]\displaystyle{ N(m_2, \Sigma_2) }[/math] of [math]\displaystyle{ n }[/math] dimensional vectors [math]\displaystyle{ \mathbf{x} }[/math] with mean vectors [math]\displaystyle{ m_1 }[/math] and [math]\displaystyle{ m_2 }[/math] and co-variance matrices [math]\displaystyle{ \Sigma_1 }[/math] and [math]\displaystyle{ \Sigma_2 }[/math], and showed that the optimal (Bayesian) solution is a quadratic decision function: ...

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