{"title": "Familiarity Discrimination of Radar Pulses", "book": "Advances in Neural Information Processing Systems", "page_first": 875, "page_last": 881, "abstract": null, "full_text": "Familiarity  Discrimination of Radar \n\nPulses \n\nEric  Grangerl,  Stephen Grossberg2 \n\nMark A.  RUbin2 ,  William W.  Streilein2 \n\n1 Department of Electrical and Computer Engineering \n\nEcole Poly technique de  Montreal \nMontreal,  Qc.  H3C  3A 7 CAN ADA \n\n2Department of Cognitive and Neural Systems,  Boston University \n\nBoston,  MA  02215 USA \n\nAbstract \n\nThe  ARTMAP-FD  neural  network  performs  both  identification \n(placing  test  patterns in  classes  encountered during  training)  and \nfamiliarity  discrimination  (judging  whether a  test  pattern belongs \nto  any  of  the  classes  encountered  during  training).  The  perfor(cid:173)\nmance of ARTMAP-FD  is  tested  on  radar pulse  data obtained in \nthe field,  and compared to that of the nearest-neighbor-based NEN \nalgorithm and to a  k  > 1 extension of NEN. \n\n1 \n\nIntroduction \n\nThe recognition process involves both identification and familiarity  discrimination. \nConsider, for  example, a neural network designed to identify aircraft based on their \nradar reflections and trained on sample reflections from ten types of aircraft A . . . J. \nAfter  training,  the network  should  correctly  classify  radar reflections  belonging to \nthe familiar  classes  A . .. J,  but  it  should  also  abstain  from  making  a  meaningless \nguess when presented with a radar reflection from  an object belonging to a different, \nunfamiliar class.  Familiarity discrimination is also referred to as \"novelty detection,\" \na  \"reject option,\"  and  \"recognition in  partially exposed environments.\" \n\nARTMAP-FD, an extension of fuzzy  ARTMAP  that performs familiarity  discrimi(cid:173)\nnation,  has shown  its effectiveness on  datasets  consisting of simulated radar range \nprofiles  from  aircraft  targets  [1,  2].  In  the  present  paper  we  examine  the  perfor(cid:173)\nmance of ARTMAP-FD  on  radar pulse data obtained in  the field , and  compare it \n\n\f876 \n\nE.  Granger,  S.  Grossberg,  M.  A.  Rubin and W.  W.  Streilein \n\nto that of NEN,  a  nearest-neighbor-based familiarity  discrimination algorithm,  and \nto a  k  > 1 extension of NEN. \n2  Fuzzy  ARTMAP \n\nFuzzy  ARTMAP  [3]  is  a  self-organizing  neural  network  for  learning,  recognition, \nand prediction.  Each input a  learns to predict an output class  K.  During training, \nthe  network  creates  internal  recognition  categories,  with  the number  of categories \ndetermined  on-line  by  predictive  success.  Components  of  the  vector  a  are  scaled \nso  that  each  ai  E  [0,1]  (i  =  1 ... M).  Complement  coding  [4]  doubles  the number \nof  components  in  the  input  vector,  which  becomes  A  = (a, a C ),  where  the  ith \ncomponent of a C  is ai = (I-ad. With fast learning, the weight vector w) records the \nlargest  and smallest  component  values  of input  vectors placed in  the /h category. \nThe  2M-dimensional  vector  Wj  may  be  visualized  as  the  hyperbox  R j  that  just \nencloses  all  the vectors a  that selected category j  during training. \n\nActivation  of  the  coding  field  F2  is  determined  by  the Weber  law  choice  function \nTj(A)  =1  A  1\\  Wj  1 /(0:+  1 Wj  I),  where  (P 1\\  Q)i  =  min(Pi , Qj)  and  1 P  1= \nL;~ 1 Pi  I\u00b7  With  winner-take-all  coding,  the  F2  node  J  that  receives  the  largest \nFl  -+  F2  input Tj  becomes active.  Node J  remains active if it satisfies the matching \ncriterion:  1 Al\\wj  1/ 1 A  1 = 1 Al\\wj 1 /M  >  p,  where p E  [0,1]  is the dimensionless \nvigilance  parameter.  Otherwise, the network resets the active F2  node and searches \nuntil  J  satisfies  the  matching  criterion.  If node  J  then  makes  an  incorrect  class \nprediction,  a  match  tracking  signal raises  vigilance just enough  to induce  a  search, \nwhich  continues  until  either  some  F2  node  becomes  active  for  the  first  time,  in \nwhich  case  J  learns  the correct output class label  k( J)  =  K;  or  a  node  J  that has \npreviously  learned  to  predict  K  becomes  active.  During testing,  a  pattern  a  that \nactivates  node  J  is  predicted to belong to the class  K  =  k( J). \n3  ARTMAP-FD \n\nFamiliarity  measure.  During testing,  an  input  pattern  a  is  defined  as  familiar \nwhen  a  familiarity  function  \u00a2(A)  is  greater  than  a  decision  threshold  T  Once  a \ncategory choice has been made by the winner-take-all rule, fuzzy  ARTMAP ignores \nthe  size  of the  input TJ.  In contrast,  ARTMAP-FD  uses  TJ  to  define  familiarity, \ntaking \n\n\u00a2(A) = TJ(A)  =  1 A  1\\ WJ  1 \n\nTjlAX \n\n1 WJ  1 \n\n' \n\n(1) \n\nwhere  TjlAX  =1  WJ  1 /(0:+  1 WJ  I)\u00b7  This  maximal  value  of TJ  is  attained  by  each \ninput  a  that  lies  in  the  hyperbox  RJ,  since  1 A  1\\  W J  1 = 1 W J  1 for  these  points. \nAn  input  that  chooses  category  J  during  testing  is  then  assigned  the  maximum \nfamiliarity  value 1 if and only if a  lies  within RJ. \n\nFamiliarity  discrimination  algorithm.  ARTMAP-FD  is  identical  to  fuzzy \nARTMAP during training.  During testing, \u00a2(A) is  computed after fuzzy  ARTMAP \nIf \u00a2(A)  >  I, \nhas  yielded  a  winning  node  J  and  a  predicted  class  K  =  k(J). \nARTMAP-FD  predicts  class  K  for  the  input  a.  If \u00a2(A)  ::;  I, a  is  regarded  as \nbelonging to an  unfamiliar class and the network makes  no  prediction. \n\nNote  that  fuzzy  ARTMAP  can  also  abstain from  classification,  when  the  baseline \n\nvigilance  parameter 15  is  greater than  zero  during  testing.  Typically  15  = \u00b0 during \n\ntraining,  to  maximize  code  compression.  In  radar  range  profile  simulations  such \n\n\fFamiliarity Discrimination of Radar Pulses \n\n877 \n\nas  those described  below,  fuzzy  ARTMAP  can  perform  familiarity  discrimination \nwhen  p >  0  during  both  training  and  testing.  However,  accurate  discrimination \nrequires that p be close  to  1,  which  causes category proliferation during training. \nRange profile simulations have also set p =  0 during both training and testing,  but \nwith  the familiarity  measure set equal  to the fuzzy  ARTMAP  match function: \n\n(2) \n\nThis  approach  is  essentially  equivalent  to  taking p =  0  during training  and  p > 0 \nduring  testing,  with  p =,.  However,  for  a  test  set  input  a  E  RJ,  the  function \ndefined  by  (2)  sets  \u00a2(A)  =1  w J  1 / M,  which  may  be large  or small  although  a  is \nfamiliar.  Thus this function  does not provide as  good familiarity  discrimination  as \nthe one defined  by  (1),  which  always sets \u00a2(A) =  1 when a  E  RJ.  Except as  noted, \nall the simulations  below employ the function  (1),  with p =  O. \n\nSequential  evidence  accumulation.  ART-EMAP  (Stage 3)  [5]  identifies  a  test \nset  object's class  after  exposure  to  a  sequence  of input  patterns,  such  as  differing \nviews,  all  identified  with  that  one  object.  Training  is  identical  to  that  of  fuzzy \nART MAP,  with  winner-take-all  coding  at  F2 .  ART-EMAP  generally  employs  dis(cid:173)\ntributed  F2  coding  during testing.  With  winner-take-all  coding  during  testing  as \nwell as training, ART-EMAP predicts the object's class to be the one selected by the \nlargest  number of inputs  in  the sequence.  Extending this approach,  ARTMAP-FD \naccumulates familiarity measures for each predicted class K  as the test set sequence \nis  presented.  Once  the winning  class  is  determined,  the object's familiarity  is  de(cid:173)\nfined  as  the average accumulated familiarity  measure of the predicted  class  during \nthe test sequence. \n4  Familiarity discrimination simulations \n\nSince  familiarity  discrimination  involves  placing  an input  into one  of two  sets,  fa(cid:173)\nmiliar  and  unfamiliar,  the  receiver  operating  characteristic  (ROC)  formalism  can \nbe  used  to evaluate  the  effectiveness  of ARTMAP-FD  on  this  task.  The  hit  rate \nH  is  the fraction of familiar  targets the network correctly identifies  as  familiar  and \nthe  false  alarm  rate  F  is  the fraction  of unfamiliar targets the network  incorrectly \nidentifies  as  familiar.  An  ROC  curve  is  a  plot  of H  vs.  F,  parameterized  by  the \nthreshold'Y  (i.e.,  it is equivalent to the two curves Fh) and Hh)) . The area under \nthe ROC curve is the  c-index, a  measure of predictive accuracy that is  independent \nof both  the fraction of positive  (familiar)  cases in the test set and the positive-case \ndecision  threshold 'Y. \n\nAn  ARTMAP-FD  network  was  trained  on  simulated  radar range  profiles  from  18 \ntargets  out  of  a  36-target  set  (Fig. \nla).  Simulations  tested  sequential  evidence \naccumulation  performance  for  1,  3,  and  100  observations,  corresponding  to  0.05, \n0.15,  and  5.0  sec.  of  observation  (smooth  curves,  Fig. \nIb) .  As  in  the  case  of \nidentification  [6],  a  combination  of multiwavelength  range  profiles  and  sequential \nevidence  accumulation  produces  good  familiarity  discrimination,  with  the c-index \napproaching 1 as  the number of sequential observations grows. \n\nFig.  Ib also  demonstrates the  importance of the proper choice  of familiarity  mea(cid:173)\nsure.  The jagged ROC  curve was  produced by  a familiarity discrimination simula(cid:173)\ntion identical  to that  which  resulted  in  the  IOO-sequential-view  smooth  curve,  but \nusing the match function  (2)  instead of \u00a2  as given by  (1). \n\n\f878 \n\nE.  Granger,  S.  Grossberg,  M  A. Rubin and W.  W.  Streilein \n\nIO , - - - - - ----r \n\nI \n' F \n~_~~~II \n\n\u00b7\"\"'\\\"MA \n'-\"-.. \n\no  o \n\n0.2 \n\n0.4 \n\n0.6 \n\n08 \n\nF \n(b) \n\nT. \n\n'Y \n(c) \n\nFigure  l:(a)  36  simulation  targets  with  6  wing  positions  and  6  wing  lengths,  and  100 \nscattering centers per target.  Boxes indicate randomly selected familiar  targets.  (b)  ROC \ncurves  from  ARTMAP-FD  simulations,  with  multiwavelength  range  profiles  having  40 \ncenter frequencies.  Sequential evidence accumulation for  1,  3 and 100 views uses familiarity \nmeasure (1)  (smooth curves); and for  100 views uses the match function  (2)  (jagged curve). \n(c)  Training and test curves of miss rate M  = (1- H) and false  alarm rate F  vs  threshold \n1',  for  36  targets  and  one  view,  Training  curves  intersect  at  the  point  where  \"y  = r p \n(predicted); and test curves intersect near the point where l' =  ra (optimal).  The training \ncurves  are  based  on  data  from  the  first  training  epoch,  the  test  curves  on  data from  3 \ntraining epochs. \n\n5  Familiarity threshold selection \nWhen a system is placed in operation, one particular decision threshold 'Y  = r  must \nbe  chosen.  In  a  given  application,  selection  of r  depends  upon  the  relative  cost \nof errors  due to  missed  targets  and  false  alarms.  The optimal r  corresponds to  a \npoint on the parameterized ROC curve that is  typically close to the upper left-hand \ncorner of the unit square, to maximize correct selection of familiar targets (H)  while \nminimizing incorrect selection of unfamiliar  tar gets  (F) . \nValidation  set  method.  To  determine  a  predicted  threshold  r p ,  the  training \ndata  is  partitioned  into  a  training  subset  and  a  validation  subset.  The  network \nis  trained  on  the  training  subset,  and  an  ROC  curve  (F(r) , H(r))  is  calculated \nfor  the  validation  subset.  r p  is  then  taken  to  be  the  point  on  the  curve  that \nmaximizes  [H(r)  - F(r)].  (For  ease  of computation  the  symmetry  point  on  the \ncurve, where  1 - H('y)  =  F(r), can yield a  good approximation.)  For a  familiarity \ndiscrimination  task the validation set  must include examples of classes not  present \nin the training set.  Once rp is determined , the training subset and validation subset \nshould be recombined and the network retrained on the complete training set.  The \nretrained network and the predicted threshold r p  are then employed for  familiarity \ndiscrimination on the test set. \n\nOn-line  threshold  determination.  During  ARTMAP-FD  training,  category \nnodes  compete  for  new  patterns  as  they  are  presented.  When  a  node  J  wins  the \ncompetition,  learning  expands  the  category  hyperbox  RJ  enough  to  enclose  the \ntraining pattern a.  The familiarity  measure \u00a2  for  each  training set  input  then  be(cid:173)\ncomes  equal  to  1.  However,  before  this  learning  takes  place,  \u00a2  can  be less  than  1, \nand  the  degree  to  which  this  initial  value  of \u00a2  is  less  than  1  reflects  the  distance \nfrom  the training pattern to RJ.  An event of this type- a  training pattern success(cid:173)\nfully  coded  by  a  category  node-is  taken  to  be  representative  of familiar  test-set \npatterns.  The corresponding initial values of \u00a2  are thus used to generate a  training \n\n\fFamiliarity Discrimination of Radar Pulses \n\n879 \n\nhit  rate curve,  where  H(\"()  equals the fraction of training inputs with  cp  > ,. \nWhat about false  alarms?  By definition,  all  patterns presented  during training are \nfamiliar.  However,  a  reset  event  during  training  (Sec.  2)  resembles  the  arrival  of \nan  unfamiliar  pattern  during testing.  Recall  that  a  reset  occurs  when  a  category \nnode that predicts class K  wins the competition for  a  pattern that actually belongs \nto  a  different  class  k.  The corresponding  values  of cp  for  these  events  can  thus  be \nused  to generate a  training false-alarm  rate curve,  where F(\"()  equals  the fraction \nof match-tracking inputs with  initial cp  > \"(. \nPredictive accuracy is  improved by use of a  reduced set of cp  values  in  the training(cid:173)\nset  ROC  curve  construction  process.  Namely,  training  patterns  that  fall  inside \nRJ,  where  cp  = I,  are  not  used  because  these  exemplars  tend  to  distort  the  miss \nrate curve.  In  addition,  the  first  incorrect  response  to  a  training input  is  the best \npredictor of the network's response to an unfamiliar  testing input,  since sequential \nsearch  will  not  be  available  during testing.  Finally,  giving  more  weight  to  events \noccurring later in the training process improves accuracy.  This can be accomplished \nby  first  computing  training  curves  H(\"()  and  F(\"()  and  a  preliminary  predicted \nthreshold r p  using  the reduced  training set;  then  recomputing the curves  and r p \nfrom  data  presented  only  after  the  system  has  activated  the  final  category  node \nof the  training process  (Fig.  Ic).  The final  predicted threshold r p  averages  these \nvalues.  This calculation can still be made on-line,  by taking the  \"final\"  node to be \nthe last one activated. \n\nTable  I  shows  that  applying  on-line  threshold  determination  to  simulated  radar \nrange profile data gives good predictions for the actual hit and false alarm rates, H A \nand  FA.  Furthermore, the HA  and FA  so obtained are close to optimal, particularly \nwhen the ROC curve has a c-index close to one.  The method is  effective even when \ntesting involves sequential evidence accumulation, despite the fact  that the training \ncurves  use  only  single views of each  target. \n6  NEN \n\nNear-enough-neighbor  (NEN)  [7,  8]  is  a  familiarity  discrimination algorithm  based \non  the single  nearest  neighbor  classifier.  For each familiar  class  K,  the familiarity \nthreshold  t:l.K  is  the largest  distance  between  any  training pattern of class  K  and \nits  nearest  neighbor  also  of  class  K.  During  testing,  a  test  pattern  is  declared \nunfamiliar if the distance to its  nearest neighbor is  greater than the threshold  t:l.K \ncorresponding to the class  K  of that nearest  neighbor. \nWe  have  extended  NEN  to  k  >  I  by  retaining  the  above  definition  of the  t:l.K's, \nwhile  taking  the  comparison  during  testing  to  be  between  t:l.K  and  the  distance \nbetween  the test  pattern and  the closest  of its  k  nearest  neighbors  which  is  of the \nclass  K  to which  the test pattern is deemed to belong. \n7  Radar  pulse data \n\nIdentifying  the  type  of emitter  from  which  a  radar  signal  was  transmitted  is  an \nimportant  task for  radar electronic support  measures  (ESM)  systems.  Familiarity \ndiscrimination  is  a  key component of this task, particularly as  the continual prolif(cid:173)\neration of new  emitters outstrips the ability  of emitter libraries  to document  every \nsort of emitter which  may be encountered. \n\nThe data analyzed here, gathered by Defense Research Establishment Ottawa, con-\n\n\f880 \n\nE.  Granger,  S.  Grossberg,  M.  A. Rubin and W  W Streilein \n\nhit  rate \nfalse  alarm rate \naccuracy \n\n3x3 \n\noptimal \n\n0.86 \n0.14 \n1.00 \n\nactual \n0.81 \n0.11 \n0.95 \n\n6x6 \n\noptimal \n\n0.77 \n0.23 \n1.00 \n\nactual \n0.77 \n0.24 \n0.93 \n\n6x6* \n\noptimal \n\n0.98 \n0.02 \n1.00 \n\nactual \n0.99 \n0.06 \n1.00 \n\nla) ,  testing  on  all  target  classes.  (In  3x3  case,  4  classes  out  of  9  to(cid:173)\n\nTable  1:  Familiarity  discrimination,  using  ARTMAP-FD  with  on-line  threshold  predic(cid:173)\ntion,  of simulated  radar  range  profile  data.  Training  on  half  the  target  classes  (boxed \n\"aircraft\"  in  Fig. \ntal  used  for  training.)  Accuracy  equals  the  fraction  of correctly-classified  targets  out  of \nfamiliar  targets  selected  by  the network  as  familiar.  The results  for  the  6x6'  dataset  in(cid:173)\nvolve  sequential  evidence  accumulation,  with  100  observations  (5  sec.)  per  test  target. \nRadar  range  profile  simulations  use  40  center  frequencies  evenly  spaced  between  18GHz \nand  22GHz,  and  wp  x  wl  simulated  targets,  where  wp  =number  of  wing  positions  and \nwi  =number of wing  lengths.  The number of range  bins  (2/3  m.  per  bin)  is  60 , so  each \npattern vector  has  (60  range bins)  x  (40  center frequencies)  =  2400  components.  Training \npatterns  are  at  21  evenly  spaced  aspects  in  a  10\u00b0  angular  range  and,  for  each  viewing \nangle,  at  15  downrange  shifts  evenly  spaced  within  a  single  bin  width.  Testing  patterns \nare  at  random  aspects  and  downrange  shifts  within  the  angular  range  and  half the  total \nrange  profile  extent of (60  bins)  x  (2/3 m.)  =40 m. \n\nmethod \n\nARTMAP-FD \n\nNEN \n\ncity-block  metric \n\nEuclidean metric \n\nhit rate \nf.  a.  rate \naccuracy \n[memory \n\n[I \n\n0.95 \n0.02 \n1.00 \n21 \n\nk-l  k-5 \n0.94 \n0.94 \n0.04 \n0.13 \n1.00 \n1.00 \n\nII \n\nk  - 25  k-l  k-5 \n0.93 \n0.93 \n0.02 \n0.05 \n1.00 \n1.00 \n\n0.94 \n0.14 \n0.99 \n\nk  - 25 \n0.92 \n0.02 \n1.00 \n\n446 \n\nTable 2:  Familiarity discrimination of radar pulse data set,  using ARTMAP-FD and NEN \nwith  different  metrics  and  values  of k.  Figure  given  for  memory  is  twice  number  of F2 \nnodes  (due  to  complement  coding)  for  ARTMAP-FD,  number  of  training  patterns  for \nNEN. Training  (single epoch)  on first  three quarters of data in classes 1-9, testing on other \nquarter  of  data  in  classes  1-9  and  all  data  in  classes  10-12.  (Values  given  are  averages \nover  four  cyclic  permutations  of the  the  12  classes.)  ARTMAP-FD  familiarity  threshold \ndetermined by  validation-set  method with  retraining. \n\nsist  of  radar  pulses  from  12  ship borne  navigation  radars  [9].  Fifty  pulses  were \ncollected  from  each  radar,  with  the  exception  of  radars  #7  (100  pulses)  and  #8 \n(200 pulses).  The pulses were preprocessed to yield 800 I5-component vectors. with \nthe components taking  values  between a and l. \n8  Results \n\nFrom Table  2,  ARTMAP-FD is  seen  to perform effective familiarity  discrimination \non  the  radar pulse data.  NEN  (k  =  1)  performs  comparatively poorly.  Extensions \nof  NEN  to  k  >  1  perform  well.  During  fielded  operation  these  would  incur  the \ncost  of the  additional  computation  required  to find  the  k  nearest  neighbors  of the \ncurrent test  pattern , as  well  as the cost  of higher memory requirements]  relative to \nARTMAP-FD.  The combination of low  hit  rate with  low false  alarm  rate obtained \nby  NEN  on  the  simulated  radar range profile datasets  (Table  3)  suggests  that  the \nalgorithm  performs  poorly  here  because  it  selects  a  familiarity  threshold  which  is \n\n1 The  memory  requirements  of  kNN  pattern  classifiers  can  be  reduced  by  editing \n\ntechniques[8],  but  how  the  use  of  these  methods  affects  performance  of  kNN-based  fa(cid:173)\nmiliarity  discrimination  methods is  an open question. \n\n\fFamiliarity Discrimination of Radar Pulses \n\n881 \n\nmethod \n\ndataset \nhit rate \nfalse  alarm rate \naccuracy \nI memory \n\nII  ARTMAP -FD  Ill-rk -----.-1 .,.....,_...-,--,-N_E ...... N....,..-...--.-_..---r-.----..-i \nk - 1  I k - 5 \n__ \nII  3x3  I  6x6 \n0.77 \n0.24 \n0.93 \n88 \n\nk - 5 \n3x3 \n0.11 \n0.00 \n1.00 \n1260 \n\n0.14 \n0.00 \n1.00 \n\n0.14 \n0.00 \n1.00 \n\n0.81 \n0.11 \n0.95 \n\nII  12  I \n\nk - 99 \n\n0.11 \n0.00 \n1.00 \n\n6x6 \n\n5670 \n\n__ \nII \n\nII \n\n0.11 \n0.00 \n1.00 \n\nTable 3:  Familiarity discrimination of simulated radar range  profiles using ARTMAP-FD \nand  NEN  with  different  values  of k.  Training  and  testing  as  in  Table  1.  ARTMAP-FD \nfamiliarity  threshold  determined  by  on-line  method.  City-block  metric  used  with  NEN; \nresults with  Euclidean metric were  slighlty poorer. \n\ntoo  high.  ARTMAP-FD  on-line  threshold  selection,  on  the  other  hand,  yields  a \nvalue  for  the  familiarity  threshold  which  balances  the  desiderata of high  hit  rate \nand low false  alarm rate. \n\nThis  research  was  supported in  part  by  grants  from  the  Office  of Naval  Research,  ONR \nNOOOI4-95-1-0657  (S . G.) and ONR NOOOI4-96-1-0659  (M.  A.  R ., W. W. S.) , and by a grant \nfrom  the Defense  Advanced Research  Projects  Agency  and the  Office  of Naval  Research, \nONR  NOOOI4-95-1-0409  (S.  G. ,  M.  A.  R. ,  W  W.  S.).  E.  G.  was  supported  in  part  by \nthe  Defense  Research  Establishment  Ottawa  and  the  Natural  Sciences  and  Engineering \nResearch  Council of Canada. \nReferences \n[1]  Carpenter,  G.  A.,  Rubin,  M.  A. ,  &  Streilein,  W .  W .,  ARTMAP-FD:  Familiarity \ndiscrimination  applied  to  radar  target  recognition,  in  ICNN'97:  Proceedings  of the \nIEEE International  Conference  on  Neural  N etworks,  Houston, June 1997; \n\n[2]  Carpenter,  G.  A.,  Rubin,  M.  A.,  &  Streilein,  W.  W .,  Threshold  Determination  for \nARTMAP-FD Familiarity  Discrimination, in C . H.  Dagli  et  al.,  eds.,  Intelligent  En(cid:173)\ngineering  Systems  Through  Artificial  Neural  Networks,  1,  23-28,  ASME,  New  York, \n1997. \n\n[3]  Carpenter,  G.  A.,  Grossberg,  S. ,  Markuzon,  N.,  Reynolds,  J .  H.,  &  Rosen,  D.  E ., \nFuzzy  ARTMAP:  A  neural  network  architecture  for  incremental supervised learning \nof analog multidimensional maps, IEEE Transactions  on N eural  Networks, 3, 698-713, \n1992. \n\n[4]  Carpenter,  G.  A., Grossberg, S.,  & Rosen . D. B. , Fuzzy ART: Fast stable learning and \ncategorization of analog patterns by  an  adaptive resonance system,  Neural  Networks, \n4,759-771,  1991. \n\n[5]  Carpenter,  G.  A.,  &  Ross,  W .  D. ,  ART-EMAP :  A  neural  network  architecture  for \nobject recognition by evidence accumulation , IEEE Transactions  on Neural  Networks, \n6,  805-818,  1995. \n\n[6]  Rubin,  M.  A.,  Application of fuzzy  ARTMAP  and ART-EMAP  to automatic target \n\nrecognition  using radar range  profiles,  Neural  Networks ,  8,  1109-1116,  1995. \n\n[7]  Dasarathy, E. V.,.Is your nearest neighbor near enough a neighbor?, in Lainious, D.  G. \nand  Tzannes,  N.  S.,  eds.  Applications  and  Research  in  Informations  Systems  and \nSciences,  1,  114-117, Hemisphere Publishing Corp. , Washington,  1977. \n\n[8]  Dasarathy, B.  V.,  ed.,  Nearest  Neighbor(NN)  Norm:  NN Pattern  Classification  Tech(cid:173)\n\nniques,  IEEE  Computer Society Press, Los  Alamitos,  CA, 1991. \n\n[9]  Granger, E. , Savaria, Y, Lavoie, P.,  &  Cantin, M.-A .,  A comparison of self-organizing \nneural  networks  for  fast  clustering  of radar  pulses,  Signal  Processing ,  64,  249-269, \n1998. \n\n\f", "award": [], "sourceid": 1548, "authors": [{"given_name": "Eric", "family_name": "Granger", "institution": null}, {"given_name": "Stephen", "family_name": "Grossberg", "institution": null}, {"given_name": "Mark", "family_name": "Rubin", "institution": null}, {"given_name": "William", "family_name": "Streilein", "institution": null}]}