MATLAB Examples

# 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 = 8x3 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 chunks 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 chunk 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)
% Mapper function for the StatisticsByGroupMapReduceExample.

% Copyright 2014 The MathWorks, Inc.

% 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);

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]};

```

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)
% Reducer function for the StatisticsByGroupMapReduceExample.

% Copyright 2014 The MathWorks, Inc.

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

```

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 = 29x2 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] 'MQ' [1x1 struct] 'OO' [1x1 struct] 'XE' [1x1 struct] 'TZ' [1x1 struct] 'EV' [1x1 struct] 'FL' [1x1 struct] 'B6' [1x1 struct] 'DH' [1x1 struct] 'HA' [1x1 struct] 'OH' [1x1 struct] 'F9' [1x1 struct] 'YV' [1x1 struct] '9E' [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 = 29x5 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 NW 10097 5.4265 977.64 8.616 172.87 OH 1414 7.7617 1224 3.57 24.52 OO 3010 5.8618 1010.4 4.4263 32.783 PA (1) 313 5.3738 692.19 3.2061 20.747 PI 861 11.252 1121.1 14.751 315.59 PS 82 5.3902 454.51 2.9682 14.383 TW 3718 7.411 830.76 4.139 30.67 TZ 215 1.907 814.63 2.8269 13.758 UA 12955 8.3939 1046.6 3.9742 28.187 US 13666 6.8027 760.83 4.6905 47.975 WN 15749 5.4581 562.49 4.0439 30.403 XE 2294 8.8082 1410.1 3.7114 23.235 YV 827 12.376 2192.6 3.9315 26.446 ```

## 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 = 12x5 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 ```