US2017091282A1PendingUtilityA1

A method for identifying clusters of fluorescence-activated cell sorting data points

Assignee: UNIV LELAND STANFORD JUNIORPriority: Apr 25, 2003Filed: Dec 13, 2016Published: Mar 30, 2017
Est. expiryApr 25, 2023(expired)· nominal 20-yr term from priority
G06F 17/30336G06F 17/30507G06F 16/35G16B 5/00G06F 16/355G06F 16/90G16B 25/10G06F 16/2272G06F 16/55G06F 16/24564
54
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Claims

Abstract

A method and/or system for analyzing data using population clustering through density based merging.

Claims

exact text as granted — not AI-modified
What is claimed: 
     
         1 . A computer implemented method of identifying clusters of data items, wherein a data item is associated with one or more values using an information system comprising:
 defining a plurality of lattice points in a data space able to contain some of said data items of interest, said lattice points spaced according to a lattice rule;   calculating weights for said lattice points using one or more of said data items according to a weighting rule;   determining a density at said lattice points relating a weight at a lattice point to weights at nearby lattice points using a density function;   creating, for a lattice point, a directional association with at least one other lattice point using an association rule;   following directional associations between lattice points to determine terminal states for one or more pointer paths;   assigning each data item to a lattice point according to an assignment rule; and   using terminal states of said pointer paths to determine a cluster for said data item.   
     
     
         2 . The method of  claim 1  wherein said data items are groups of values each associated with an individual cell and said cluster is a cell subpopulation. 
     
     
         3 . The method of  claim 1  wherein:
 said data items each represent market participants in an economic market; 
 said values represent obtainable characteristic measures of a market participant; and 
 said clusters each represent a category of market participants. 
 
     
     
         4 . The method of  claim 1  further wherein:
 said one or more values are effectively continuous. 
 
     
     
         5 . The method of  claim 1  wherein said identifying one or more clusters uses directional associations of a plurality of lattice points and a density estimated at each lattice point and does not use weights assigned to lattice points or original data values. 
     
     
         6 . An apparatus for creating groupings from data comprising:
 means for assigning each piece of data from said set of data to a point on a lattice;   means for assigning weights to each lattice point based on the data near said lattice point;   means for determining for each of said lattice points if each of said lattice points should be associated with one of its surrounding lattice points and if so creating a pointer from the individual lattice point to the surrounding lattice point it is associated with; and   means for creating clusterings of the lattice points.   
     
     
         7 . A set of application program interfaces embodied on a computer-readable medium for execution on a computer in conjunction with an application program that determines clusters within a set of data, comprising:
 a first interface that receives data;   a second interface that receives parameters; and   returns groupings of said data.   
     
     
         8 . A method of clustering data items, wherein a data item is associated with one or more semi-continuous values, using an information system comprising:
 creating a reduction data item set, each reduction data item associated with one or more quantized values correlated with said one or more semi-continuous values;   assigning each data item to a reduction data item according to an assignment rule;   calculating weights for said reduction data items using one or more data items according to a weighting rule;   determining for a plurality of reduction data items if it should be associated with another reduction data item according to an association rule;   for at least one reduction data item, creating a directional association with at least one other reduction data item; and   identifying one or more clusters of said reduction data items using one or more directional associations and/or one or more of said weights.   
     
     
         9 . A method enabling analysis of large sets of data observation points, each point having multiple parameters comprising:
 performing a first automated clustering of data points using a subset of said parameters using an information system, said first clustering providing one or more data clusters;   selecting a first selected cluster;   successively performing subsequent automated child clusterings on selected clusters, while option ally choosing different parameters allowing for said clustering.   
     
     
         10 . A method enabling analysis o(large sets of data observation points, each point having multiple parameters using an information system comprising:
 displaying to a user results of an automated clustering of data points using a subset of said parameters, said first clustering indicating one or more data clusters;   registering an input from said user selecting a first selected cluster from which to generate children clusters;   providing an interface allowing a user to optionally choose different parameters allowing for said children clusters; and   displaying a hierarchy of clustering results.   
     
     
         11 . The method of  claim 8 , wherein the step of calculating weights includes linear binning in accordance with the formula: 
       
         
           
             
               
                 w 
                 m 
               
               = 
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   n 
                 
                  
                 
                   
                     ∏ 
                     
                       j 
                       = 
                       1 
                     
                     d 
                   
                    
                   
                     max 
                      
                     
                       ( 
                       
                         0 
                         , 
                         
                           1 
                           - 
                           
                             
                                
                               
                                 
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                                     i 
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                                     j 
                                   
                                 
                                 - 
                                 
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                                   mj 
                                 
                               
                                
                             
                             / 
                             
                               Δ 
                               j 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
     
         12 . The method of  claim 1 , wherein the step of determining a density includes computing an estimate of a density surface {circumflex over (f)}(y m ) wherein the Gaussian kernel is denoted by φ(b)=1/√{square root over (2)}πexp(−b 2 /2) and the estimated density y m  is computed by the formula: 
       
         
           
             
               
                 
                   
                     
                       f 
                       ^ 
                     
                      
                     
                       ( 
                       
                         y 
                         m 
                       
                       ) 
                     
                   
                   = 
                   
                     
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                         … 
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                                 ∏ 
                                 
                                   j 
                                   = 
                                   1 
                                 
                                 d 
                               
                                
                               
                                 
                                   φ 
                                    
                                   
                                     ( 
                                     
                                       
                                         l 
                                         j 
                                       
                                        
                                       
                                         
                                           Δ 
                                           j 
                                         
                                         / 
                                         
                                           h 
                                           j 
                                         
                                       
                                     
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                                 / 
                                 
                                   h 
                                   j 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
                 , 
                 
                   
 
                 
                  
                 
                   
                     where 
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                      
                     l 
                   
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                     ( 
                     
                       
                         l 
                         1 
                       
                       , 
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                       , 
                       
                         l 
                         d 
                       
                     
                     ) 
                   
                 
                 , 
                 
                   
                     Z 
                     j 
                   
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                      
                     
                       ( 
                       
                         
                           
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                        
                       
                         ( 
                         
                           { 
                           
                             
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                         ) 
                       
                     
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                           ( 
                           
                             d 
                             + 
                             4 
                           
                           ) 
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
       where SD denotes standard deviation. 
     
     
         13 . The method of  claim 12 , wherein the formula: 
       
         
           
             
               
                 
                   
                     
                       
                         f 
                         ^ 
                       
                        
                       
                         ( 
                         
                           y 
                           m 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         1 
                         / 
                         n 
                       
                        
                       
                         
                           ∑ 
                           
                             
                               l 
                               1 
                             
                             = 
                             
                               - 
                               
                                 Z 
                                 1 
                               
                             
                           
                           
                             Z 
                             1 
                           
                         
                          
                         
                             
                         
                          
                         
                           … 
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                            
                           
                             
                               ∑ 
                               
                                 
                                   l 
                                   1 
                                 
                                 = 
                                 
                                   - 
                                   
                                     Z 
                                     1 
                                   
                                 
                               
                               
                                 Z 
                                 d 
                               
                             
                              
                             
                               
                                 ω 
                                 
                                   m 
                                   - 
                                   1 
                                 
                               
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                                   ∏ 
                                   
                                     j 
                                     = 
                                     1 
                                   
                                   d 
                                 
                                  
                                 
                                   
                                     φ 
                                      
                                     
                                       ( 
                                       
                                         
                                           l 
                                           j 
                                         
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                                             Δ 
                                             j 
                                           
                                           / 
                                           
                                             h 
                                             j 
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                   / 
                                   
                                     h 
                                     j 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     
                       where 
                        
                       
                           
                       
                        
                       l 
                     
                     = 
                     
                       ( 
                       
                         
                           l 
                           1 
                         
                         , 
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                         , 
                         
                           l 
                           d 
                         
                       
                       ) 
                     
                   
                   , 
                   
                     
                       Z 
                       j 
                     
                     = 
                     
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                        
                       
                         ( 
                         
                           
                             
                               ⌊ 
                               
                                 4 
                                  
                                 
                                   
                                     h 
                                     j 
                                   
                                   / 
                                   
                                     Δ 
                                     j 
                                   
                                 
                               
                               ⌋ 
                             
                             / 
                           
                           , 
                           
                             M 
                             - 
                             1 
                           
                         
                         ) 
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     
                       and 
                        
                       
                           
                       
                        
                       
                         h 
                         j 
                       
                     
                     = 
                     
                       
                         SD 
                          
                         
                           ( 
                           
                             { 
                             
                               
                                 x 
                                 
                                   i 
                                   , 
                                   j 
                                 
                               
                               , 
                               
                                 i 
                                 = 
                                 1 
                               
                               , 
                               … 
                                
                               
                                   
                               
                               , 
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                             } 
                           
                           ) 
                         
                       
                        
                       
                         n 
                         
                           
                             - 
                             1 
                           
                           / 
                           
                             ( 
                             
                               d 
                               + 
                               4 
                             
                             ) 
                           
                         
                       
                     
                   
                 
                 ) 
               
               , 
             
           
         
       
       is computed by the Fast Fourier Transform (FFT). 
     
     
         14 . The method of  claim 1 , wherein the step of determining a density includes calculating an estimate of the standard deviation of the density estimate in accordance with the formula: 
       
         
           
             
               
                 
                   σ 
                   ^ 
                 
                 m 
                 2 
               
               = 
               
                 
                   
                     1 
                     
                       n 
                        
                       
                         ( 
                         
                           n 
                           - 
                           1 
                         
                         ) 
                       
                     
                   
                    
                   
                     
                       ∑ 
                       
                         
                           l 
                           1 
                         
                         = 
                         
                           - 
                           
                             Z 
                             1 
                           
                         
                       
                       
                         Z 
                         1 
                       
                     
                      
                     
                         
                     
                      
                     
                       … 
                        
                       
                           
                       
                        
                       
                         
                           ∑ 
                           
                             
                               l 
                               d 
                             
                             = 
                             
                               - 
                               
                                 Z 
                                 d 
                               
                             
                           
                           
                             Z 
                             d 
                           
                         
                          
                         
                           
                             w 
                             
                               m 
                               - 
                               1 
                             
                           
                            
                           
                             
                               ∏ 
                               
                                 j 
                                 = 
                                 1 
                               
                               d 
                             
                              
                             
                               
                                 
                                   φ 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       l 
                                       j 
                                     
                                      
                                     
                                       
                                         Δ 
                                         j 
                                       
                                       / 
                                       
                                         h 
                                         j 
                                       
                                     
                                   
                                   ) 
                                 
                               
                               / 
                               
                                 h 
                                 j 
                                 2 
                               
                             
                           
                         
                       
                     
                   
                 
                 - 
                 
                   
                     1 
                     
                       n 
                       - 
                       1 
                     
                   
                    
                   
                     
                       
                         f 
                         ^ 
                       
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                         ( 
                         
                           y 
                           m 
                         
                         ) 
                       
                     
                     2 
                   
                 
               
             
           
         
       
       and defining an index set S={m∈{1, . . . M} d : {circumflex over (f)}(y m )>4.3*√{square root over ({circumflex over (σ)} m   2 )}}. 
     
     
         15 . The method of  claim 14 , wherein the step of creating a directional association includes establishing and removing pointers between neighboring lattice points by successively executing a series of evaluations for all lattice points y m , where m is an element of S, in turn:
 considering all neighboring lattice points p 1  . . . , p nm  which are defined as the set of all lattice points contained in a s-dimensional rectangular volume. Let p be an element of {p 1 , . . . , p nm } such that {circumflex over (f)}(p)=max k=1, . . . nm {circumflex over (f)}(p k ), splitting ties in an arbitrary manner; then a pointer is established from y m  to p provided:   
       
         
           
             
               
                 
                   
                     f 
                     ^ 
                   
                    
                   
                     ( 
                     p 
                     ) 
                   
                 
                 > 
                 
                   
                     f 
                     ^ 
                   
                    
                   
                     ( 
                     
                       y 
                       m 
                     
                     ) 
                   
                 
               
               ; 
               and 
             
           
         
         
           
             
               
                 
                   
                     ∂ 
                     
                       ∂ 
                       e 
                     
                   
                    
                   
                     
                       f 
                       ^ 
                     
                      
                     
                       ( 
                       
                         y 
                         m 
                       
                       ) 
                     
                   
                 
                 > 
                 
                   λ 
                   m 
                 
               
               , 
               
                 
                   where 
                    
                   
                       
                   
                    
                   e 
                 
                 = 
                 
                   
                     ( 
                     
                       p 
                       - 
                       
                         y 
                         m 
                       
                     
                     ) 
                   
                   / 
                   
                      
                     
                       p 
                       - 
                       
                         y 
                         m 
                       
                     
                      
                   
                 
               
               , 
               
                  
                 · 
                  
               
             
           
         
       
       denotes Euclidean norm, and 
       
         
           
             
               
                   
               
                
               
                 
                   
                     
                       ∂ 
                       
                         ∂ 
                         e 
                       
                     
                      
                     
                       
                         f 
                         ^ 
                       
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                         ( 
                         
                           y 
                           m 
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         
                           ? 
                         
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                       d 
                     
                      
                     
                       e 
                        
                       
                         ∂ 
                         
                           ∂ 
                           y 
                         
                       
                        
                       
                         
                           f 
                           ^ 
                         
                          
                         
                           ( 
                           
                             y 
                             m 
                           
                           ) 
                         
                       
                     
                   
                 
                 , 
                 
                   
 
                 
                  
                 
                   
                     ? 
                   
                    
                   
                     indicates text missing or illegible when filed 
                   
                 
               
             
           
         
       
       which indicates a gradient of the density estimate, 
       
         
           
             
               
                 
                   
                     
                       
                         
                           ∂ 
                           
                             ∂ 
                             
                               y 
                               
                                 m 
                                 a 
                               
                             
                           
                         
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                             ^ 
                           
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                               y 
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                             ) 
                           
                         
                       
                       = 
                       
                         
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                             ∑ 
                             
                               
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                                   w 
                                   
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                                        
                                       
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                         m 
                       
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                                   m 
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                                     e 
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                                     [ 
                                     
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                                           ∂ 
                                           
                                             ∂ 
                                             
                                               y 
                                               
                                                 m 
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                         A 
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                             1 
                             / 
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                            
                           
                             
                               ∑ 
                               
                                 
                                   l 
                                   1 
                                 
                                 = 
                                 
                                   - 
                                   
                                     Z 
                                     1 
                                   
                                 
                               
                               
                                 Z 
                                 1 
                               
                             
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                                   ∑ 
                                   
                                     
                                       l 
                                       d 
                                     
                                     = 
                                     
                                       - 
                                       
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                                         1 
                                       
                                     
                                   
                                   
                                     Z 
                                     d 
                                   
                                 
                                  
                                 
                                   
                                     w 
                                     
                                       m 
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                                       1 
                                     
                                   
                                    
                                   
                                     
                                       
                                         l 
                                         a 
                                       
                                        
                                       
                                         l 
                                         b 
                                       
                                        
                                       
                                         Δ 
                                         a 
                                       
                                        
                                       
                                         Δ 
                                         b 
                                       
                                     
                                     
                                       
                                         h 
                                         a 
                                         2 
                                       
                                        
                                       
                                         h 
                                         b 
                                         2 
                                       
                                     
                                   
                                    
                                   
                                     
                                       ∏ 
                                       
                                         ϕ 
                                         = 
                                         1 
                                       
                                       δ 
                                     
                                      
                                     
                                       
                                         
                                           φ 
                                           2 
                                         
                                          
                                         
                                           ( 
                                           
                                             
                                               l 
                                               j 
                                             
                                              
                                             
                                               
                                                 Δ 
                                                 j 
                                               
                                               / 
                                               
                                                 h 
                                                 j 
                                               
                                             
                                           
                                           ) 
                                         
                                       
                                       / 
                                       
                                         h 
                                         j 
                                         2 
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                       
                       , 
                     
                   
                 
                 
                   
                       
                   
                 
               
             
           
         
       
       A being an estimate of 
       
         
           
             
               
                 ∂ 
                 
                   ∂ 
                   
                     y 
                     
                       m 
                       a 
                     
                   
                 
               
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       and q(x) denotes the 100*xth percentile of the standard normal distribution. 
     
     
         16 . The method of  claim 15 , wherein from each lattice point y m , where m is not an element of S, a pointer is established that points to a state representing background noise. 
     
     
         17 . The method of  claim 16 , wherein the step of following directional associations further includes the evaluation: for all lattice points y m , where m is an element of S, in turn: if a pointer originates at y m , then it will point to a different lattice point, which itself may have a pointer originating from it; following a succession of pointers until a lattice point y z  is reached that either (a) does not have any pointer originating from it or (b) has a pointer originating from it that points to a state representing a cluster or background noise; in the event (a) removing all pointers visited in the succession and establishing new pointers originating from each lattice point to the background noise state, provided {circumflex over (f)}(y z )<q(0.95 1/κ )√{square root over ({right arrow over (σ)} z   2 )}, otherwise only the pointer originating from y z  is removed and a new pointer is established that originates from y z  (if any) is removed and a new pointer is establishes that originates from y z  and points to a new cluster state, in the event (b) no pointers are removed or established. 
     
     
         18 . The method of  claim 17 , wherein the step of following directional associations further includes the following steps:
 Let {y m(1) , . . . y m(k) } be the set of all lattice points which have a pointer originating from them to a dummy state representing a cluster, enumerated such that {circumflex over (f)}(y m(1) )≧ . . . ≧{circumflex over (f)}(y m(k) ) and for i=1, . . . , k do:
 Set A={m(i), and iterate the following loop until no more indices are added to A: 
   (Begin loop)
 For each index a which is an element of A in turn, add all the indices p to A that satisfy: 
 Yp is a neighbor or ya as defined in  claim 15 , and 
 No pointer originates from yp, and
   {circumflex over ( f )}( y   p )+{circumflex over (σ)} p   ≧{circumflex over (f)} ( y   m(i) )+{circumflex over (σ)} m(i)  
 
 
   (End loop)
 Denote by B the set of indices of lattice points from which a pointer originates to a cluster state and that also have some y p , p being an element of as neighbor. If B is not empty, then do the following: 
 Define q by {circumflex over (f)}(y q )=max r∈B {circumflex over (f)}(y r ), breaking ties arbitrarily; 
 Establish a pointer from each y p , p an element of A\{m(i)} to y q ; 
   For each r which is an element of B, if r≠q, remove the pointer from y r  to the state representing a cluster and establish a new pointer from y r  to y q      
     
     
         19 . The method of  claim 18 , wherein the steps recited in  claim 18  are repeated until there are no more additions or deletions of pointers to cluster state. 
     
     
         20 . The method of  claim 19 , wherein from each lattice point that does not have a pointer originating from it, a pointer is established pointing to the background noise state.

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