the above is an overview of several illustrated embodiments implementing the machine method of the present invention and provides exemplary translation examples utilizing selected aspects described in connection with certain embodiments of the present invention . fig1 - a , 1 - b , and 1 - c provide illustration of applying the k - means ++ algorithm to sample data generated using the david arthur software . fig1 - a , 1 - b , and 1 - c illustrate setting the desired number of clusters ( groups ) as input to the k - means ++ algorithm to 4 , 5 , and 6 respectively . the y - axis is the data values for the data points and the x - axis is the number of data points placed into each cluster by application of the k - means ++ algorithm with the desired number of groups . the cross - hatching of each group indicates to which cluster the data points have been assigned by the k - means ++ clustering . examination and comparison of fig1 - a , 1 - b , and 1 - c will give an idea of how the k - means ++ algorithm works . fig2 provides illustration of the experimental results shown in fig1 - a , 1 - b , and 1 - c with a “ quality indicator ” calculated or computed for a desired grouping of one to twenty groups ( clusters ). that is , fig1 - a , 1 - b , and 1 - c illustrate only desired number of clusters of 4 , 5 , and 6 . examining the value of the quality indicator as k ( number of desired groups or clusters ) varies from 1 to 20 shows that the quality indicator goes down rapidly as k increases from 1 to 5 , and then improves less rapidly from 6 to 20 . it will be noted that in this example a “ lower ” quality indicator is better . that is , since in this illustration the quality indicator is the average distance from the centroid of each group for all data in all groups , therefore the lower the number the better the grouping . in this example choosing a number of groups , and then choosing a small sample of representative data from each of these five groups to be examined will likely provide a good overview of all the data , without missing any exceptional data . note that instead of using an average distance from the centroid as a quality indicator , it may be advantageous to use or select a maximum distance to try to be sure that “ outlying ” data points are not missed in the summary . it may also be advantageous to choose a few or the “ most ” outlying points in each cluster for further examination as sample data to be sure that exceptional data is not missed . fig4 provides illustration of the operational flow performed by a computing apparatus 400 controlled by a control program stored within storage of the computing apparatus according to one illustrated embodiment of the method of the present invention . the method providing for summarized viewing of a large number of observation data points ( as indicated by reference numeral 401 ) each having a characterizing value . the observation data points each have a characterizing value stored in memory or storage of the computing apparatus , or as records on a file or in memory of the computing apparatus . the clustering begins ( as indicated by reference numeral 410 ) by selecting a starting number of desired number of clusters ( dnc ), which might typically be one ( just to get started ) or two or more , or possibly some starting number based upon user input or a calculation based on the number of data points . the k - means ++ algorithm ( or other clustering algorithm ) is then applied ( as indicated by reference numeral 420 ) to the observation data points for achieving a first clustering . a quality indicator value , or indication of goodness of the current number of clusters is then calculated or computed by the computing apparatus ( as indicated by reference numerals 430 and 440 or 441 ). the quality indicator value can be based , for example , on the “ distance ” of the characterizing values of each data point compared to the “ average ” or “ centroid ” of all data points in that cluster . the quality indicator could be computed or calculated in other ways as could be determined by those skilled in the art , and this described illustration of quality indicator is not meant to be limiting . for each number of clusters , the quality indicator is calculated and saved ( in storage of the computing apparatus ). after a few quality indicators have been calculated by the computing apparatus , the pattern of change as the number of clusters is increasing can then be observed ( displayed ) ( as indicated by reference numeral 460 ) for determining if any further increase in the number of clusters is likely to produce much improved values of the overall quality indicator , or not . if the number of clusters is determined to be not yet large enough ( as indicated by reference numeral 470 ), then the desired number of clusters is further increased and everything ( all the above described steps ) is repeated by the computing apparatus . if the quality indicator improvement seems to be leveling off ( as indicated by reference numeral 471 ) then the repeated clustering can be stopped . once the proper number of clusters is determined , the clustering information can optionally be saved 490 to a file or storage of the computing apparatus , or displayed on a computer screen for further use in evaluating the data . it is important to note also that one may want to go beyond any first indication of slowing improvement in the quality indicator , especially at the beginning , to avoid any local minimums or anomalies in starting up the clustering with low numbers of clusters . these problems and solutions are well known in the art of clustering and alterations to the algorithm while still applying principles of the present invention can be made . it is further noted that the order of the steps in the claimed invention may be altered without changing the concept of the invention , and the order of the steps is not meant to be limiting . thus , while the principles of the invention have been made clear and described relative to a number of embodiments or implementations , it will be immediately obvious to those skilled in the art the many modifications or adaptations which can be made without departing from those principles . while the invention has been shown and described with reference to specific illustrated embodiments , it should be understood by those skilled in the art that various changes in form and detail may be made such implementations without departing from the spirit and scope of the invention as defined by the following claims . having described the embodiments of the present invention , it will now become apparent to one of skill in the arts that other embodiments or implementations incorporating the teachings of the present invention may be used . accordingly , these embodiments should not be construed as being limited to the disclosed embodiments or implementations but rather should be limited only by the spirit and scope of the following claims .