Compute Summary Statistics by Group Using MapReduce

This example shows how to compute summary statistics organized by group using mapreduce. It demonstrates the use of an anonymous function to pass an extra grouping parameter to a parameterized map function. This parameterization allows you to quickly recalculate the statistics using a different grouping variable.

Prepare Data

Create a datastore using the airlinesmall.csv data set. This 12-megabyte data set contains 29 columns of flight information for several airline carriers, including arrival and departure times. For this example, select Month, UniqueCarrier (airline carrier ID), and ArrDelay (flight arrival delay) as the variables of interest.

ds = datastore('airlinesmall.csv', 'TreatAsMissing', 'NA');
ds.SelectedVariableNames = {'Month', 'UniqueCarrier', 'ArrDelay'};

The datastore treats 'NA' values as missing, and replaces the missing values with NaN values by default. Additionally, the SelectedVariableNames property allows you to work with only the selected variables of interest, which you can verify using preview.

preview(ds)

ans=8×3 table
    Month    UniqueCarrier    ArrDelay
    _____    _____________    ________

     10         {'PS'}            8   
     10         {'PS'}            8   
     10         {'PS'}           21   
     10         {'PS'}           13   
     10         {'PS'}            4   
     10         {'PS'}           59   
     10         {'PS'}            3   
     10         {'PS'}           11   

Run MapReduce

The mapreduce function requires a map function and a reduce function as inputs. The mapper receives blocks of data and outputs intermediate results. The reducer reads the intermediate results and produces a final result.

In this example, the mapper computes the grouped statistics for each block of data and stores the statistics as intermediate key-value pairs. Each intermediate key-value pair has a key for the group level and a cell array of values with the corresponding statistics.

This map function accepts four input arguments, whereas the mapreduce function requires the map function to accept exactly three input arguments. The call to mapreduce (below) shows how to pass in this extra parameter.

Display the map function file.

function statsByGroupMapper(data, ~, intermKVStore, groupVarName)
  % Data is a n-by-3 table. Remove missing values first
  delays = data.ArrDelay;
  groups = data.(groupVarName);
  notNaN =~isnan(delays);
  groups = groups(notNaN);
  delays = delays(notNaN);

  % Find the unique group levels in this chunk
  [intermKeys,~,idx] = unique(groups, 'stable');

  % Group delays by idx and apply @grpstatsfun function to each group
  intermVals = accumarray(idx,delays,size(intermKeys),@grpstatsfun);
  addmulti(intermKVStore,intermKeys,intermVals);

  function out = grpstatsfun(x)
    n = length(x); % count
    m = sum(x)/n; % mean
    v = sum((x-m).^2)/n; % variance
    s = sum((x-m).^3)/n; % skewness without normalization
    k = sum((x-m).^4)/n; % kurtosis without normalization
    out = {[n, m, v, s, k]};
  end
end

After the Map phase, mapreduce groups the intermediate key-value pairs by unique key (in this case, the airline carrier ID), so each call to the reduce function works on the values associated with one airline. The reducer receives a list of the intermediate statistics for the airline specified by the input key (intermKey) and combines the statistics into separate vectors: n, m, v, s, and k. Then, the reducer uses these vectors to calculate the count, mean, variance, skewness, and kurtosis for a single airline. The final key is the airline carrier code, and the associated values are stored in a structure with five fields.

Display the reduce function file.

function statsByGroupReducer(intermKey, intermValIter, outKVStore)
  n = [];
  m = [];
  v = [];
  s = [];
  k = [];

  % Get all sets of intermediate statistics
  while hasnext(intermValIter)
    value = getnext(intermValIter);
    n = [n; value(1)];
    m = [m; value(2)];
    v = [v; value(3)];
    s = [s; value(4)];
    k = [k; value(5)];
  end
  % Note that this approach assumes the concatenated intermediate values fit
  % in memory. Refer to the reducer function, covarianceReducer,  of the
  % CovarianceMapReduceExample for an alternative pairwise reduction approach

  % Combine the intermediate results
  count = sum(n);
  meanVal = sum(n.*m)/count;
  d = m - meanVal;
  variance = (sum(n.*v) + sum(n.*d.^2))/count;
  skewnessVal = (sum(n.*s) + sum(n.*d.*(3*v + d.^2)))./(count*variance^(1.5));
  kurtosisVal = (sum(n.*k) + sum(n.*d.*(4*s + 6.*v.*d +d.^3)))./(count*variance^2);

  outValue = struct('Count',count, 'Mean',meanVal, 'Variance',variance,...
                 'Skewness',skewnessVal, 'Kurtosis',kurtosisVal);

  % Add results to the output datastore
  add(outKVStore,intermKey,outValue);
end

Use mapreduce to apply the map and reduce functions to the datastore, ds. Since the parameterized map function accepts four inputs, use an anonymous function to pass in the airline carrier IDs as the fourth input.

outds1 = mapreduce(ds, ...
    @(data,info,kvs)statsByGroupMapper(data,info,kvs,'UniqueCarrier'), ...
    @statsByGroupReducer);

********************************
*      MAPREDUCE PROGRESS      *
********************************
Map   0% Reduce   0%
Map  16% Reduce   0%
Map  32% Reduce   0%
Map  48% Reduce   0%
Map  65% Reduce   0%
Map  81% Reduce   0%
Map  97% Reduce   0%
Map 100% Reduce   0%
Map 100% Reduce  10%
Map 100% Reduce  21%
Map 100% Reduce  31%
Map 100% Reduce  41%
Map 100% Reduce  52%
Map 100% Reduce  62%
Map 100% Reduce  72%
Map 100% Reduce  83%
Map 100% Reduce  93%
Map 100% Reduce 100%

mapreduce returns a datastore, outds1, with files in the current folder.

Read the final results from the output datastore.

r1 = readall(outds1)

r1=29×2 table
       Key           Value    
    __________    ____________

    {'PS'    }    {1x1 struct}
    {'TW'    }    {1x1 struct}
    {'UA'    }    {1x1 struct}
    {'WN'    }    {1x1 struct}
    {'EA'    }    {1x1 struct}
    {'HP'    }    {1x1 struct}
    {'NW'    }    {1x1 struct}
    {'PA (1)'}    {1x1 struct}
    {'PI'    }    {1x1 struct}
    {'CO'    }    {1x1 struct}
    {'DL'    }    {1x1 struct}
    {'AA'    }    {1x1 struct}
    {'US'    }    {1x1 struct}
    {'AS'    }    {1x1 struct}
    {'ML (1)'}    {1x1 struct}
    {'AQ'    }    {1x1 struct}
      ⋮

Organize Results

To organize the results better, convert the structure containing the statistics into a table and use the carrier IDs as the row names. mapreduce returns the key-value pairs in the same order as they were added by the reduce function, so sort the table by carrier ID.

statsByCarrier = struct2table(cell2mat(r1.Value), 'RowNames', r1.Key);
statsByCarrier = sortrows(statsByCarrier, 'RowNames')

statsByCarrier=29×5 table
              Count     Mean      Variance    Skewness    Kurtosis
              _____    _______    ________    ________    ________

    9E          507     5.3669     1889.5      6.2676      61.706 
    AA        14578     6.9598       1123      6.0321      93.085 
    AQ          153     1.0065     230.02      3.9905      28.383 
    AS         2826     8.0771        717      3.6547      24.083 
    B6          793     11.936     2087.4      4.0072       27.45 
    CO         7999      7.048     1053.8      4.6601      41.038 
    DH          673      7.575     1491.7      2.9929      15.461 
    DL        16284     7.4971     697.48      4.4746      41.115 
    EA          875     8.2434     1221.3      5.2955      43.518 
    EV         1655     10.028     1325.4      2.9347      14.878 
    F9          332     8.4849     1138.6      4.2983      30.742 
    FL         1248     9.5144     1360.4      3.6277      21.866 
    HA          271    -1.5387     323.27      8.4245      109.63 
    HP         3597     7.5897     744.51      5.2534      50.004 
    ML (1)       69    0.15942     169.32      2.8354      16.559 
    MQ         3805     8.8591     1530.5       7.054      105.51 
      ⋮

Change Grouping Parameter

The use of an anonymous function to pass in the grouping variable allows you to quickly recalculate the statistics with a different grouping.

For this example, recalculate the statistics and group the results by Month, instead of by the carrier IDs, by simply passing the Month variable into the anonymous function.

outds2 = mapreduce(ds, ...
    @(data,info,kvs)statsByGroupMapper(data,info,kvs,'Month'), ...
    @statsByGroupReducer);

********************************
*      MAPREDUCE PROGRESS      *
********************************
Map   0% Reduce   0%
Map  16% Reduce   0%
Map  32% Reduce   0%
Map  48% Reduce   0%
Map  65% Reduce   0%
Map  81% Reduce   0%
Map  97% Reduce   0%
Map 100% Reduce   0%
Map 100% Reduce  17%
Map 100% Reduce  33%
Map 100% Reduce  50%
Map 100% Reduce  67%
Map 100% Reduce  83%
Map 100% Reduce 100%

Read the final results and organize them into a table.

r2 = readall(outds2);
r2 = sortrows(r2,'Key');
statsByMonth = struct2table(cell2mat(r2.Value));
mon = {'Jan','Feb','Mar','Apr','May','Jun', ...
       'Jul','Aug','Sep','Oct','Nov','Dec'};
statsByMonth.Properties.RowNames = mon

statsByMonth=12×5 table
           Count     Mean     Variance    Skewness    Kurtosis
           _____    ______    ________    ________    ________

    Jan     9870    8.5954     973.69      4.1142      35.152 
    Feb     9160    7.3275     911.14      4.7241       45.03 
    Mar    10219    7.5536     976.34      5.1678      63.155 
    Apr     9949    6.0081     1077.4      8.9506      170.52 
    May    10180    5.2949     737.09      4.0535      30.069 
    Jun    10045    10.264     1266.1      4.8777        43.5 
    Jul    10340    8.7797     1069.7      5.1428      64.896 
    Aug    10470    7.4522     908.64      4.1959       29.66 
    Sep     9691    3.6308     664.22      4.6573      38.964 
    Oct    10590    4.6059     684.94      5.6407      74.805 
    Nov    10071    5.2835     808.65      8.0297      186.68 
    Dec    10281    10.571     1087.6      3.8564      28.823 

Local Functions

Listed here are the map and reduce functions that mapreduce applies to the data.

function statsByGroupMapper(data, ~, intermKVStore, groupVarName)
  % Data is a n-by-3 table. Remove missing values first
  delays = data.ArrDelay;
  groups = data.(groupVarName);
  notNaN =~isnan(delays);
  groups = groups(notNaN);
  delays = delays(notNaN);

  % Find the unique group levels in this chunk
  [intermKeys,~,idx] = unique(groups, 'stable');

  % Group delays by idx and apply @grpstatsfun function to each group
  intermVals = accumarray(idx,delays,size(intermKeys),@grpstatsfun);
  addmulti(intermKVStore,intermKeys,intermVals);

  function out = grpstatsfun(x)
    n = length(x); % count
    m = sum(x)/n; % mean
    v = sum((x-m).^2)/n; % variance
    s = sum((x-m).^3)/n; % skewness without normalization
    k = sum((x-m).^4)/n; % kurtosis without normalization
    out = {[n, m, v, s, k]};
  end
end
%---------------------------------------------------------------------
function statsByGroupReducer(intermKey, intermValIter, outKVStore)
  n = [];
  m = [];
  v = [];
  s = [];
  k = [];

  % Get all sets of intermediate statistics
  while hasnext(intermValIter)
    value = getnext(intermValIter);
    n = [n; value(1)];
    m = [m; value(2)];
    v = [v; value(3)];
    s = [s; value(4)];
    k = [k; value(5)];
  end
  % Note that this approach assumes the concatenated intermediate values fit
  % in memory. Refer to the reducer function, covarianceReducer,  of the
  % CovarianceMapReduceExample for an alternative pairwise reduction approach

  % Combine the intermediate results
  count = sum(n);
  meanVal = sum(n.*m)/count;
  d = m - meanVal;
  variance = (sum(n.*v) + sum(n.*d.^2))/count;
  skewnessVal = (sum(n.*s) + sum(n.*d.*(3*v + d.^2)))./(count*variance^(1.5));
  kurtosisVal = (sum(n.*k) + sum(n.*d.*(4*s + 6.*v.*d +d.^3)))./(count*variance^2);

  outValue = struct('Count',count, 'Mean',meanVal, 'Variance',variance,...
                 'Skewness',skewnessVal, 'Kurtosis',kurtosisVal);

  % Add results to the output datastore
  add(outKVStore,intermKey,outValue);
end
%---------------------------------------------------------------------