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BEGIN:VEVENT
UID:42aafc0efb5f48d4230886bc397fcead
CATEGORIES:Experimental Mathematics Seminar
CREATED:20210426T133007
SUMMARY:Data analysis in high-dimensional spaces
LOCATION:Zoom
DESCRIPTION:<p>&nbsp;</p><p style="text-align: left; color: #000000; text-transform: no
 ne; text-indent: 0px; letter-spacing: normal; font-family: Times New Roman;
  font-size: 16px; font-variant: normal; font-weight: 400; text-decoration: 
 none; word-spacing: 0px; white-space: normal; orphans: 2;">1. The unreliabi
 lity of the Euclidean distance in high-dimension, making a proximity query 
 meaningless and unstable because there is poor discrimination between the n
 earest and furthest neighbor [3], see also [4].</p><p style="text-align: le
 ft; color: #000000; text-transform: none; text-indent: 0px; letter-spacing:
  normal; font-family: Times New Roman; font-size: 16px; font-variant: norma
 l; font-weight: 400; text-decoration: none; word-spacing: 0px; white-space:
  normal; orphans: 2;">2. The uniform probability distribution on the n-dime
 nsional unit sphere S_n, and some non-intuitive results for large $n$. For 
 example, if x is any point in S_n, taken as the "north pole", then most of 
 the area of S_n is concentrated in the "equator".</p><p style="text-align: 
 left; color: #000000; text-transform: none; text-indent: 0px; letter-spacin
 g: normal; font-family: Times New Roman; font-size: 16px; font-variant: nor
 mal; font-weight: 400; text-decoration: none; word-spacing: 0px; white-spac
 e: normal; orphans: 2;">3. The advantage of the $ell_1$-distance, which is 
 less sensitive to high dimensionality, and has been shown to "provide the b
 est discrimination in high-dimensional data spaces," [1, p. 427].</p><p sty
 le="text-align: left; color: #000000; text-transform: none; text-indent: 0p
 x; letter-spacing: normal; font-family: Times New Roman; font-size: 16px; f
 ont-variant: normal; font-weight: 400; text-decoration: none; word-spacing:
  0px; white-space: normal; orphans: 2;">4. Clustering high-dimensional data
  using the $ell_1$ distance, [2].</p><p style="text-align: left; color: #00
 0000; text-transform: none; text-indent: 0px; letter-spacing: normal; font-
 family: Times New Roman; font-size: 16px; font-variant: normal; font-weight
 : 400; text-decoration: none; word-spacing: 0px; white-space: normal; orpha
 ns: 2;">References</p><p style="text-align: left; color: #000000; text-tran
 sform: none; text-indent: 0px; letter-spacing: normal; font-family: Times N
 ew Roman; font-size: 16px; font-variant: normal; font-weight: 400; text-dec
 oration: none; word-spacing: 0px; white-space: normal; orphans: 2;">[1] C.C
 . Aggarwal et al, On the surprising behavior of distance metrics in high di
 mensional space, Lecture Notes in Computer Science, vol 1973(2001), Springe
 r, <a href="https://doi.org/10.1007/3-540-44503-X_27">https://doi.org/10.10
 07/3-540-44503-X_27</a></p><p style="text-align: left; color: #000000; text
 -transform: none; text-indent: 0px; letter-spacing: normal; font-family: Ti
 mes New Roman; font-size: 16px; font-variant: normal; font-weight: 400; tex
 t-decoration: none; word-spacing: 0px; white-space: normal; orphans: 2;">[2
 ] T. Asamov and A. Ben-Israel, A probabilistic $ell_1$ method for clusterin
 g high-dimensional data, Probability in the Engineering and Informational S
 ciences, 2021, 1-16</p><p style="text-align: left; color: #000000; text-tra
 nsform: none; text-indent: 0px; letter-spacing: normal; font-family: Times 
 New Roman; font-size: 16px; font-variant: normal; font-weight: 400; text-de
 coration: none; word-spacing: 0px; white-space: normal; orphans: 2;">[3] K.
  Beyer et al, When is "nearest neighbor" meaningful?, Lecture Notes in Comp
 uter Science, vol 1540(1999), Springer, <a href="https://doi.org/10.1007/3-
 540-49257-7_15">https://doi.org/10.1007/3-540-49257-7_15</a></p><p style="t
 ext-align: left; color: #000000; text-transform: none; text-indent: 0px; le
 tter-spacing: normal; font-family: Times New Roman; font-size: 16px; font-v
 ariant: normal; font-weight: 400; text-decoration: none; word-spacing: 0px;
  white-space: normal; orphans: 2;">[4] J.M. Hammersley, The distribution of
  distance in a hypersphere, The Annals of Mathematical Statistics 21(1950),
  447452.</p>
CONTACT:Adi Ben Israel, Rutgers University (RUTCOR)
X-EXTRAINFO:https://rutgers.zoom.us/j/94346444480#success\nPassword 6564120420  
DTSTAMP:20260829T151910
DTSTART;TZID=America/New_York:20210506T170000
DTEND;TZID=America/New_York:20210506T180000
SEQUENCE:0
TRANSP:OPAQUE
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