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Alhazen and the Nearest Neighbor Rule

Alhazen and the Nearest Neighbor Rule. Marcello Pelillo, PRL 348, 34-37, 2014. (On the origin of the nearest neighbor rule). Marcello Pelillo Italy. Thomas Cover 1938-2012, USA. Peter Hart 1940, USA. Alhazen, 965-1040, Egypt. Cover and Hart Result.

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Alhazen and the Nearest Neighbor Rule

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  1. Alhazen and the Nearest Neighbor Rule Marcello Pelillo, PRL 348, 34-37, 2014 (On the origin of the nearest neighbor rule) Marcello Pelillo Italy Thomas Cover 1938-2012, USA Peter Hart 1940, USA Alhazen,965-1040, Egypt Coffee Talk

  2. Coffee Talk

  3. Cover and Hart Result • Based on densities, assuming equal pdfs for training and testing. however …. • The NN rule is the only classifier using only distances and no densities. • It is untrained and relies on the choice of a proper distance measure. Who invented distance based classification?? Coffee Talk

  4. Early distance based classification rules • Nilsson, 1965, p16-17: minimum distance classifier • Sebestyen, 1962 p91: proximity algorithm • Fix and Hodges, 1951: Discriminatory Analysis: Nonparametric Discrimination • Ockham, 1287 – 1347: Choose the simplest solution • Alhazen, 965-1040, Optics in the eye  template Coffee Talk

  5. Recognition according to Alhazen Sight perceives what kind of thing a visible object is through recognition exclusively. (Smith, 2001, p. 431) … recognition is the perception of similarity between two forms …… recognition will occur through defining features … (p. 432) That universal forms of visible aspects occur in the soul and are impressed in the imagination is due to the fact that there are certain kinds of visible characteristics, such as form or shape, according to which individuals of a certain kind will be identical, whereas those individuals vary according to [other] particular characteristics that are perceived by the sense of sight. (Smith, 2001, p. 518) Smith, A.M., 2001. Alhacen’s Theory of Visual Perception. American Philosophical society, Philadelphia Coffee Talk

  6. Recognition according to Alhazen (2) It is thus through the effect of perceiving individuals of the same kind by sight that the universal form of their kind will recur [in the soul] along with the various particular forms of those individuals. (p. 518) Hence, when sight perceives some visible object, the faculty of discrimination immediately seeks its counterpart among the forms persisting in the imagination, and when it finds some form in the imagination that is like the form of that visible object, it will recognize that visible object and will perceive what kind of object it is. (p. 519) Smith, A.M., 2001. Alhacen’s Theory of Visual Perception. American Philosophical society, Philadelphia Coffee Talk

  7. Nearest Neighbor Rule?? Universal forms are stored along with particular forms. Mixture of nearest neighbor and nearest mean?? Coffee Talk

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