Method and system for detecting difference between plural observed results

Abstract

A method and system for analyzing time series data. In an embodiment, a loop is executed and terminated upon a specified maximum number of iterations of the loop being performed or upon a difference between scores in successive iterations of the loop not being greater than a specified tolerance, wherein the score in each iteration is calculated as function of an absolute value of a difference between respective cumulative probability values of first and second cumulative probability distributions which are generated from respectively first and second time series data sets. In an embodiment, time series data is processed in a sequence of time periods, wherein a combined cumulative probability distribution is generated in each time period by combining a cumulative probability distribution of new time series data with previously combined cumulative probability distribution data according to a ratio of the number of new to previous observed values.

1 . A method for analyzing time series data for each observation variable of a plurality of observation variables through execution of a program by a processor of an information processing apparatus that comprises a display unit, said method comprising performing for each observation variable:
 acquiring an initial first time series data set consisting of a first plurality of first observed values over a first period of time, followed by generating an initial first cumulative probability distribution from the initial first time series data set, said initial first time series data set being designated as a previous first time series data set;   acquiring an initial second time series data set consisting of a second plurality of second observed or computed values over a second period of time, followed by generating an initial second cumulative probability distribution from the initial second time series data set, said initial second time series data set being designated as a previous second time series data set;   calculating an initial score as a function of an absolute value of a difference between respective cumulative probability values of the generated initial first cumulative probability distribution and the generated initial second cumulative probability distribution, said initial score being designated as a previous score;   performing operations on the previous first time series data set, including: generating a next first time series data set by adding newly-obtained first observed values at first additional times to the previous first time series data set, followed by generating a next first cumulative probability distribution from the next first time series data set;   performing operations on the previous second time series data set, including: generating a next second time series data set by adding newly-obtained second observed or computed values at second additional times to the previous second time series data set, followed by generating a next second cumulative probability distribution from the next second time series data set;   calculating a next score as said function of an absolute value of a difference between respective cumulative probability values of the generated next first cumulative probability distribution and the generated next second cumulative probability distribution;   ascertaining whether a condition exists,
 wherein the condition is that the next score has been calculated a specified maximum number of times equal to at least 1 or an absolute value of a difference between the next score and the previous score is not greater than a specified tolerance, and 
 wherein if said ascertaining ascertains that the condition exists then outputting the next score as a detection result to the display unit, otherwise setting the previous first time series data set equal to the next first time series data set, setting the previous second time series data set equal to the next second time series data set, setting the previous score equal to the next score, and again executing said performing operations on the previous first time series data set, said performing operations on the previous second time series data set, said calculating the next score, and said ascertaining. 
   
   
   
       2 . The method of  claim 1 , wherein upon the next score having been calculated only once, said ascertaining ascertains that the condition does not exist. 
   
   
       3 . The method of  claim 1 , wherein upon the next score having been calculated a fewer number of times than the specified maximum number of times, said ascertaining ascertains that the condition exists. 
   
   
       4 . The method of  claim 1 , wherein upon the next score having been calculated the specified maximum number of times and the absolute value of the difference between the next score and the previous score being greater than the specified tolerance, said ascertaining ascertains that the condition exists. 
   
   
       5 . The method of  claim 1 , wherein the specified maximum number of times is  1 , and wherein the number of newly-obtained first observed values and the number of newly-obtained second observed values each comprise more than a 10-fold higher number than both the number of first observed values of the first plurality of first observed values and the number of second observed values of the second plurality of second observed values. 
   
   
       6 . The method of  claim 1 ,
 wherein said function of the absolute value of the difference between respective cumulative probability values of the generated initial first cumulative probability distribution and the generated initial second cumulative probability distribution is a maximum value of the absolute value of the difference between the respective cumulative probability values of the generated initial first cumulative probability distribution and the generated initial second cumulative probability distribution, and   wherein said function of the absolute value of the difference between respective cumulative probability values of the generated next first cumulative probability distribution and the generated next second cumulative probability distribution is a maximum value of the difference between the respective cumulative probability values of the generated next first cumulative probability distribution and the generated next second cumulative probability distribution.   
   
   
       7 . The method of  claim 1 ,
 wherein said function of the absolute value of the difference between respective cumulative probability values of the generated initial first cumulative probability distribution and the generated initial second cumulative probability distribution is an average value of or a summation of the absolute value of the difference between the respective cumulative probability values of the generated initial first cumulative probability distribution and the generated initial second cumulative probability distribution, and   wherein said function of the absolute value of the difference between respective cumulative probability values of the generated next first cumulative probability distribution and the generated next second cumulative probability distribution is an average value of or a summation of the difference between the respective cumulative probability values of the generated next first cumulative probability distribution and the generated next second cumulative probability distribution.   
   
   
       8 . The method of  claim 1 , wherein the second plurality of second observed or computed values of the initial second time series data set is a vector u representing m time series, wherein m is at least 2, and wherein said acquiring the initial second time series data set comprises:
 providing the m time series, wherein time series r of the m time series is denoted as a p-dimensional vector x (r)  (r=1, 2, . . . , m) of p observed values respectively corresponding to p different times, and wherein p is at least 2; and   computing the vector u as a vector that minimizes a sum of squares over r from r=1 to r=m of inter-vector distances between u and x (r) .   
   
   
       9 . The method of  claim 8 , wherein said computing the vector u comprises solving an eigenvalue equation (HH T )u=λu for the maximum eigenvalue λ and its associated eigenvector u, wherein H is a p-by-m matrix expressed as H=[x (1) , x (2) , . . . , x (m) ] and wherein H T  is a transposed matrix of H. 
   
   
       10 . The method of  claim 1 , wherein the first period of time is unequal to the second period of time, and wherein the number of first observed values of the first plurality of first observed values is unequal to the number of second observed values of the second plurality of second observed values. 
   
   
       11 . The method of  claim 1 , wherein the method comprises displaying on the display unit a bar chart of the detection result versus observation variable, wherein the observation variable is ordered on the bar chart in descending order of the detection result. 
   
   
       12 . The method of  claim 1 , wherein the method comprises displaying on the display unit a three-dimensional bar chart in which the next score is plotted as a function of observation variable and number of calculations of the next score. 
   
   
       13 . A computer program product, comprising a computer usable storage medium having a computer readable program stored thereon, wherein the program when executed on a processor of the information processing apparatus performs the method of  claim 1 . 
   
   
       14 . A system comprising a processor and a computer readable memory unit coupled to the processor, said memory unit containing a program that when executed by the processor implement the method of  claim 1 , wherein the system comprises the information processing apparatus, and wherein the information processing apparatus comprises the processor and the computer readable memory unit. 
   
   
       15 . A method for analyzing time series data for each observation variable of a plurality of observation variables through execution of a program by a processor of an information processing apparatus that comprises a display unit, said method comprising, for each observation variable, processing time series data for an ordered sequence of time periods 1, 2, . . . , J such that J is at least 3,
 wherein said processing for time period 1 comprises acquiring a new time series data set 1 having N1 observed values for the time period 1 and generating a first cumulative probability distribution (Pcomb,1) from the new time series data set 1, and   wherein said processing for time period j (j=2, 3, . . . , J) comprises the steps of:   (a) acquiring a new time series data set j having N 1  observed values for the time period j;   (b) generating a new cumulative probability distribution (Pnew,j) from the new time series data set j;   (c) generating a combined cumulative probability distribution (Pcomb,j) equal to β*Pnew,j+(1−β)*Pcomb,j−1, wherein β=N 2 /(N 1 +N 2 ), and wherein N 2 =(j−1)*N 1 ;   (d) computing a score equal to the difference of Pcomb,j and Pcomb,j−1; and   (e) outputting the score as a detection result to the display unit.   
   
   
       16 . The method of  claim 15 , wherein N 1 =1. 
   
   
       17 . The method of  claim 15 , wherein N 1 >1. 
   
   
       18 . The method of  claim 15 , wherein said processing the time series data for the time periods 1, 2, . . . , J is performed in real time. 
   
   
       19 . A computer program product, comprising a computer usable storage medium having a computer readable program stored thereon, wherein the program when executed on a processor of the information processing apparatus performs the method of  claim 15 . 
   
   
       20 . A system comprising a processor and a computer readable memory unit coupled to the processor, said memory unit containing a program that when executed by the processor implement the method of  claim 15 , wherein the system comprises the information processing apparatus, and wherein the information processing apparatus comprises the processor and the computer readable memory unit.