Implementing the Split-Apply-Combine model in Clojure and Incanter

Using Split-Apply-Combine for Data Analysis in Clojure

Bay Area Clojure GroupJune 6, 2013

Tom Faulhaber

twitter: @tomfaulhabergithub: tomfaulhaber

Saturday, June 8, 13

Data Structures for Data Analysis

The Vector

[265.0 259.98 266.89 262.22 ...]

The Vector

(mean[265.0 259.98 266.89 262.22 ...]) ➜ 263.697

The Vector

(apply min[265.0 259.98 266.89 262.22 ...]) ➜ 257.21

The Vector

(apply max[265.0 259.98 266.89 262.22 ...]) ➜ 269.75

The Vector

(sd[265.0 259.98 266.89 262.22 ...]) ➜ 3.815

The Vector

(quantile[265.0 259.98 266.89 262.22 ...]) ➜ [257.21 260.105 264.27 266.175 269.75]

The Vector

[265.0 259.98 266.89 262.22 ...]

The Vector

(histogram[265.0 259.98 266.89 262.22 ...]) ➜

The Vector

[265.0 259.98 266.89 262.22 ...]

The Vector

(line-chart[265.0 259.98 266.89 262.22 ...]) ➜

The Matrix

1 Dimension

0 1 2 3 4

The Matrix

1 Dimension

0 1 2 3 40 1 2 3 4 5 6 7

2 Dimensions

The Matrix

1 Dimension

0 1 2 3 40 1 2 3 4 5 6 7

2 Dimensions

0 1 2 3 4 5 6 7

3 Dimensions

Key-Value Pairs

{"IBM" [205.18 203.79 202.79 201.02 ...], "MSFT" [27.93 27.44 27.5 27.34 ...], "AMZN" [265.0 259.98 266.89 262.22 ...]}

Using Key-Value pairs can organize multiple data units (such as trials, customers, etc.) or collect parameter data

The Dataset

2013-02-05

2013-02-01

2013-02-04

2013-02-04 2013-02-04

2013-02-01

261.46 266.89 268.03AMZN 4012900262.00 266.89MSFT 27.44 27.87

50540000 27.03 28.02 27.42

203.57205.02 201.99IBM 204.19 3188800 203.79AMZN 259.98 264.68 259.98 3723600 259.07262.78

27.93 27.51MSFT 28.05

55565900 27.5527.67204.65 203.37IBM 203.84 3370700 205.35 205.18

265.00268.93 6115000AMZN 268.93 262.80 265.00Adj CloseVolumeCloseLowHighOpenSymbol

The Dataset

2013-02-05

2013-02-01

2013-02-04

2013-02-04 2013-02-04

2013-02-01

261.46 266.89 268.03AMZN 4012900262.00 266.89MSFT 27.44 27.87

50540000 27.03 28.02 27.42

203.57205.02 201.99IBM 204.19 3188800 203.79AMZN 259.98 264.68 259.98 3723600 259.07262.78

27.93 27.51MSFT 28.05

55565900 27.5527.67204.65 203.37IBM 203.84 3370700 205.35 205.18

Items in column have same type

The Dataset

2013-02-05

2013-02-01

2013-02-04

2013-02-04 2013-02-04

2013-02-01

261.46 266.89 268.03AMZN 4012900262.00 266.89MSFT 27.44 27.87

50540000 27.03 28.02 27.42

203.57205.02 201.99IBM 204.19 3188800 203.79AMZN 259.98 264.68 259.98 3723600 259.07262.78

27.93 27.51MSFT 28.05

55565900 27.5527.67204.65 203.37IBM 203.84 3370700 205.35 205.18

...Across a row, there may be different types

The Dataset

2013-02-05

2013-02-01

2013-02-04

2013-02-04 2013-02-04

2013-02-01

261.46 266.89 268.03AMZN 4012900262.00 266.89MSFT 27.44 27.87

50540000 27.03 28.02 27.42

203.57205.02 201.99IBM 204.19 3188800 203.79AMZN 259.98 264.68 259.98 3723600 259.07262.78

27.93 27.51MSFT 28.05

55565900 27.5527.67204.65 203.37IBM 203.84 3370700 205.35 205.18

The Dataset

2013-02-05

2013-02-01

2013-02-04

2013-02-04 2013-02-04

2013-02-01

261.46 266.89 268.03AMZN 4012900262.00 266.89MSFT 27.44 27.87

50540000 27.03 28.02 27.42

203.57205.02 201.99IBM 204.19 3188800 203.79AMZN 259.98 264.68 259.98 3723600 259.07262.78

27.93 27.51MSFT 28.05

55565900 27.5527.67204.65 203.37IBM 203.84 3370700 205.35 205.18

...Identifiers

The Dataset

2013-02-05

2013-02-01

2013-02-04

2013-02-04 2013-02-04

2013-02-01

261.46 266.89 268.03AMZN 4012900262.00 266.89MSFT 27.44 27.87

50540000 27.03 28.02 27.42

203.57205.02 201.99IBM 204.19 3188800 203.79AMZN 259.98 264.68 259.98 3723600 259.07262.78

27.93 27.51MSFT 28.05

55565900 27.5527.67204.65 203.37IBM 203.84 3370700 205.35 205.18

...Identifiers Measurements

Split-Apply-Combine

Pattern described by Hadley Wickham and implemented in the plyr library for R.

Home page: http://plyr.had.co.nz

JSS Journal of Statistical Software

April 2011, Volume 40, Issue 1. http://www.jstatsoft.org/

The Split-Apply-Combine Strategy for DataAnalysis

Hadley WickhamRice University

Abstract

Many data analysis problems involve the application of a split-apply-combine strategy,where you break up a big problem into manageable pieces, operate on each piece inde-pendently and then put all the pieces back together. This insight gives rise to a new R

package that allows you to smoothly apply this strategy, without having to worry aboutthe type of structure in which your data is stored.

The paper includes two case studies showing how these insights make it easier to workwith batting records for veteran baseball players and a large 3d array of spatio-temporalozone measurements.

Keywords: R, apply, split, data analysis.

1. Introduction

What do we do when we analyze data? What are common actions and what are commonmistakes? Given the importance of this activity in statistics, there is remarkably little researchon how data analysis happens. This paper attempts to remedy a very small part of that lack bydescribing one common data analysis pattern: Split-apply-combine. You see the split-apply-combine strategy whenever you break up a big problem into manageable pieces, operate oneach piece independently and then put all the pieces back together. This crops up in all stagesof an analysis:

During data preparation, when performing group-wise ranking, standardization, or nor-malization, or in general when creating new variables that are most easily calculated ona per-group basis.

When creating summaries for display or analysis, for example, when calculating marginalmeans, or conditioning a table of counts by dividing out group sums.

Combine

the object based on dimension(s) or identifiers (yielding segments of the same type)

Combine

a function to each segment producing a new segment of the target type. The function can aggregate or transform the segment.

Combine

a function to each segment producing a new segment of the target type. The function can aggregate or transform the segment.

the results into an output type (possibly of higher dimension)

Variations based on interface

Output

InputArray Data.Frame List Discarded

Data.Frame

aaply adply alply a_ply

daply ddply dlply d_ply

laply ldply llply l_ply

From: Wickham, The Split-Apply-Combine Strategy for Data Analysis

Splitting Matrices - 2D

0 1 2 3 4 5 6 7

Split each element to a scalar

Split each column to a vector

0 1 2 3 4 5 6 7

Split each row to a vector

0 1 2 3 4 5 6 7

Split each column to a vector

0 1 2 3 4 5 6 7

Split each row to a vector0 1 2 3 4 5 6 7

0 1 2 3 4 5 6 7

1 2 3 4 5 6 7

Split each row x=c1, y=c2 to a vector

Split each row x=c1, z=c2 to a vector

0 1 2 3 4 5 6 7

Split each row y=c1, z=c2 to a vector

0 1 2 3 4 5 6 7

Split each slice x=c to a 2D matrix

Split each slice y=c to a 2D matrix

0 1 2 3 4 5 6 7

Split each slice z=c to a 2D matrix

0 1 2 3 4 5 6 7

1 2 3 4 5 6 7

Split each row x=c1, y=c2 to a vector

Split each row x=c1, z=c2 to a vector0 1 2 3 4 5 6 7

0 1 2 3 4 5 6 7

Split each row y=c1, z=c2 to a vector

0 1 2 3 4 5 6 7

Split each slice x=c to a 2D matrix

Split each slice y=c to a 2D matrix0 1 2 3 4 5 6 7

0 1 2 3 4 5 6 7

Split each slice z=c to a 2D matrixSaturday, June 8, 13

Splitting a Dataset

Split by Symbol

2013-02-05

2013-02-01 Date

2013-02-04

2013-02-04 2013-02-04

2013-02-01

261.46 266.89 268.03AMZN 4012900262.00 266.89MSFT 27.44 27.87

50540000 27.03 28.02 27.42

203.57205.02 201.99IBM 204.19 3188800 203.79AMZN 259.98 264.68 259.98 3723600 259.07262.78

27.93 27.51MSFT 28.05

55565900 27.5527.67204.65 203.37IBM 203.84 3370700 205.35 205.18

2013-02-05

Date 2013-02-04 2013-02-01

261.46 266.89 268.03AMZN 4012900262.00 266.89AMZN 259.98 264.68 259.98 3723600 259.07262.78

2013-02-01 Date

2013-02-04 203.57205.02 201.99IBM 204.19 3188800 203.79204.65 203.37IBM 203.84 3370700 205.35 205.18

Adj CloseVolumeCloseLowHighOpenSymbol

Date 2013-02-042013-02-01

MSFT 27.44 27.87

50540000 27.03 28.02 27.42 27.93 27.51MSFT 28.05

55565900 27.5527.67

Adj CloseVolumeCloseLowHighOpenSymbol

Splitting a Dataset

Split by Date

... 2013-02-05

2013-02-01 Date

2013-02-04

2013-02-04 2013-02-04

2013-02-01

261.46 266.89 268.03AMZN 4012900262.00 266.89MSFT 27.44 27.87

50540000 27.03 28.02 27.42

203.57205.02 201.99IBM 204.19 3188800 203.79AMZN 259.98 264.68 259.98 3723600 259.07262.78

27.93 27.51MSFT 28.05

55565900 27.5527.67204.65 203.37IBM 203.84 3370700 205.35 205.18

2013-02-01 Date

2013-02-01

2013-02-01 27.93 27.51MSFT 28.05

55565900 27.5527.67204.65 203.37IBM 203.84 3370700 205.35 205.18

2013-02-04

2013-02-04 2013-02-04

MSFT 27.44 27.87

50540000 27.03 28.02 27.42 203.57205.02 201.99IBM 204.19 3188800 203.79

AMZN 259.98 264.68 259.98 3723600 259.07262.78Adj CloseVolumeCloseLowHighOpenSymbol

2013-02-05 Date

261.46 266.89 268.03AMZN 4012900262.00 266.89Adj CloseVolumeCloseLowHighOpenSymbol

Splitting a Dataset

Split by Date

... 2013-02-05

2013-02-01 Date

2013-02-04

2013-02-04 2013-02-04

2013-02-01

261.46 266.89 268.03AMZN 4012900262.00 266.89MSFT 27.44 27.87

50540000 27.03 28.02 27.42

203.57205.02 201.99IBM 204.19 3188800 203.79AMZN 259.98 264.68 259.98 3723600 259.07262.78

27.93 27.51MSFT 28.05

55565900 27.5527.67204.65 203.37IBM 203.84 3370700 205.35 205.18

2013-02-01 Date

2013-02-01

2013-02-01 27.93 27.51MSFT 28.05

55565900 27.5527.67204.65 203.37IBM 203.84 3370700 205.35 205.18

2013-02-04

2013-02-04 2013-02-04

MSFT 27.44 27.87

50540000 27.03 28.02 27.42 203.57205.02 201.99IBM 204.19 3188800 203.79

AMZN 259.98 264.68 259.98 3723600 259.07262.78Adj CloseVolumeCloseLowHighOpenSymbol

2013-02-05 Date

261.46 266.89 268.03AMZN 4012900262.00 266.89Adj CloseVolumeCloseLowHighOpenSymbol

We’ll see more advanced splitting in the case study

(func )

➜ result

(func )

result must be appropriate for output type

➜ result

Combine

Assemble apply results into output

Implementing ddply in Clojure

Implementing ddply(ns split-apply-combine.ply "Implementation of the split-apply-combine functions, similar to R's plyr library." (:use [incanter.core :only [$data col-names conj-rows dataset]]) (:require [split-apply-combine.core :as sac]))

(defn fast-conj-rows "A simple version of conj-rows that runs much faster" [& datasets] (when (seq datasets) (dataset (col-names (first datasets)) (mapcat :rows datasets))))

(defn expr-to-fn [expr] (let [row-param (gensym "row-") kw-map (sac/build-keyword-map expr)] `(fn [~row-param] (let [~@(apply concat (for [[kw sym] kw-map] [sym `(get ~row-param ~kw ~kw)]))] ~(sac/convert-keywords expr kw-map)))))

(defn exprs-to-fns [group-by] (if (coll? group-by) (vec (for [item group-by] (if (and (coll? item) (coll? (second item)) (not (#{'fn 'fn*} (first (second item))))) [(first item) (expr-to-fn (second item))] item))) group-by))

(defn split-ds "Perform a split operation on data, which must be a dataset, using the group-by-fns to choose bins. group-by-fns can either be a single function or a collection of functions. In the latter case, the results will be combined to create a key for the bin. Returns a map of the group-by-fns results to datasets including all the rows that had the given result.

Note that keyword column names are the most common functions to use for the group-by." [group-by-fns data] (let [cols (col-names data) group-by-fn (if (= 1 (count group-by-fns)) (first group-by-fns) (apply juxt group-by-fns))] (loop [cur (:rows data) row-groups {}] (if (empty? cur) (for [[group rows] row-groups] [group (dataset cols rows)]) (recur (next cur) (let [row (first cur) k (group-by-fn row) a (row-groups k)] (assoc row-groups k (if a (conj a row) [row]))))))))

(defn apply-ds "Apply fun to each group in grouped-data returning a sequence of pairs of the original group-keys and the result of applying the function the dataset. See split-ds for information on the grouped-data data structure." [fun grouped-data] (for [[group split-data] grouped-data] [group (fun split-data)]))

(defn combine-ds "Combine the datasets in grouped-data into a single dataset including the columns specified in the group-by argument as having the values found in the keys in the grouped data.

If there are columns that are in both the key and the dataset, the values in the key have precedence." [group-by grouped-data] (let [group-by (if (coll? group-by) group-by [group-by]) group-by-filter (complement (set group-by))] (apply fast-conj-rows (for [[group data] grouped-data] (let [grouped-cols (zipmap group-by group) union-cols (concat group-by (filter group-by-filter (col-names data)))] (dataset union-cols (map #(merge % grouped-cols) (:rows data))))))))

(defn ddply* "Split-apply-combine from datasets to datasets.

Splits data into a the group of datasets as specified by the group-by argument, applies fun to each of the resulting datasets and combines the result of that back into a single dataset.

The group-by argument can be a keyword or collection of keywords which specify the columns to group by. It can also include pairs [keyword keyfn] where the function keyfun is applied to each row to generate the key for that row. When the groups are combined, keyword is used as the column name for the resulting column. The two types of group-by specifications can be mixed.

The result of the apply function can contain the same columns names as the original dataset or different ones. It can contain the same number of rows as the original, a different number, or a single row.

If data is not specified, it defaults to the currently bound value of $data.

Examples:

(ddply* :Symbol (transform :Change = (diff0 :Close)) stock-data)

(ddply* [[:Month #((juxt year month) (:timestamp %)]] (colwise :Volume sum) stock-data)"

([group-by fun] (ddply* group-by fun $data)) ([group-by fun data] (let [group-by (if (coll? group-by) group-by [group-by]) group-by (for [item group-by] (if (coll? item) item [item item]))] (->> data (split-ds (map second group-by)) (apply-ds fun) (combine-ds (map first group-by))))))

(defmacro ddply "Split-apply-combine from datasets to datasets. This macro is a wrapper on ddply* which provides translation of simple column-referencing expressions in the group-by argument.

The group-by argument can be a keyword or collection of keywords which specify the columns to group by. It can also include pairs [keyword key-expr] where the exression key-expr is tranformed to a function and in expr are expanded to accessors on rows. The resulting function is applied to each row to generate the key for that row. When the groups are combined, keyword is used as the column name for the resulting column. The two types of group-by specifications can be mixed.

Examples:

(ddply :Symbol (transform :Change = (diff0 :Close)) stock-data)

(ddply [[:Month ((juxt year month) :timestamp]]] (colwise :Volume sum) stock-data)" ([group-by fun] `(ddply* ~(exprs-to-fns group-by) ~fun $data)) ([group-by fun data] `(ddply* ~(exprs-to-fns group-by) ~fun ~data)))

(defn d_ply* "Split-apply-combine from datasets to nothing. This version ignores the output of fun and is used for fun's side effects.

Splits data into a the group of datasets as specified by the group-by argument, applies fun to each of the resulting datasets and then drops the result.

Example:

(d_ply* :Symbol #(view (bar-chart :Date :Volume :data %)) stock-data)" ([group-by fun] (ddply* group-by fun $data)) ([group-by fun data] (let [group-by (if (coll? group-by) group-by [group-by]) group-by (for [item group-by] (if (coll? item) item [item item]))] (dorun (->> data (split-ds (map second group-by)) (apply-ds fun))))))

(defmacro d_ply "Split-apply-combine from datasets to nothing. This version ignores the output of fun and is used for fun's side effects. This macro is a wrapper on d_ply* which provides translation of simple column-referencing expressions in the group-by argument.

Example:

(d_ply :Symbol #(view (bar-chart :Date :Volume :data %)) stock-data)" ([group-by fun] `(d_ply* ~(exprs-to-fns group-by) ~fun $data)) ([group-by fun data] `(d_ply* ~(exprs-to-fns group-by) ~fun ~data)))

Implementing ddply - Split(ns split-apply-combine.ply "Implementation of the split-apply-combine functions, similar to R's plyr library." (:use [incanter.core :only [$data col-names conj-rows dataset]]) (:require [split-apply-combine.core :as sac]))

Examples:

Example:

(defn split-ds [group-by-fns data] (let [cols (col-names data) group-by-fn (if (= 1 (count group-by-fns)) (first group-by-fns) (apply juxt group-by-fns))] (loop [cur (:rows data) row-groups {}] (if (empty? cur) (for [[group rows] row-groups] [group (dataset cols rows)]) (recur (next cur) (let [row (first cur) k (group-by-fn row) a (row-groups k)] (assoc row-groups k (if a (conj a row) [row]))))))))

Implementing ddply - Apply(ns split-apply-combine.ply "Implementation of the split-apply-combine functions, similar to R's plyr library." (:use [incanter.core :only [$data col-names conj-rows dataset]]) (:require [split-apply-combine.core :as sac]))

Examples:

Example:

(defn apply-ds [fun grouped-data] (for [[group split-data] grouped-data] [group (fun split-data)]))

Implementing ddply - Combine(ns split-apply-combine.ply "Implementation of the split-apply-combine functions, similar to R's plyr library." (:use [incanter.core :only [$data col-names conj-rows dataset]]) (:require [split-apply-combine.core :as sac]))

Examples:

Example:

(defn combine-ds [group-by grouped-data] (let [group-by (if (coll? group-by) group-by [group-by]) group-by-filter (complement (set group-by))] (apply fast-conj-rows (for [[group data] grouped-data] (let [grouped-cols (zipmap group-by group) union-cols (concat group-by (filter group-by-filter (col-names data)))] (dataset union-cols (map #(merge % grouped-cols) (:rows data))))))))

Implementing ddply - Putting it all together(ns split-apply-combine.ply "Implementation of the split-apply-combine functions, similar to R's plyr library." (:use [incanter.core :only [$data col-names conj-rows dataset]]) (:require [split-apply-combine.core :as sac]))

Examples:

Example:

(defn ddply* ([group-by fun] (ddply* group-by fun $data)) ([group-by fun data] (let [group-by (if (coll? group-by) group-by [group-by]) group-by (for [item group-by] (if (coll? item) item [item item]))] (->> data (split-ds (map second group-by)) (apply-ds fun) (combine-ds (map first group-by))))))

(defmacro ddply ([group-by fun] `(ddply* ~(exprs-to-fns group-by) ~fun $data)) ([group-by fun data] `(ddply* ~(exprs-to-fns group-by) ~fun ~data)))

Support functions - colwise

(ddply :Symbol (colwise :num stats/mean) tech-stocks)

Support functions - transform

(ddply :Symbol (transform :Change = (diff0 :Close) :Date =* (time-format/parse (time-format/formatters :year-month-day) :Date)) tech-stocks)

A Case Study

“SpaceCurve delivers instantaneous intelligence for location-based services, commodities, defense, emergency services and other markets. The company is developing Big Data solutions that continuously store and immediately analyze massive amounts of multidimensional data.”

Performance analysis of large-scale geospatial-temporal ingest and query on the SpaceCurve multidimensional DB

Our Sample Problem

cpu23cpu11

cpu22cpu10

cpu09 cpu21

cpu20cpu08

cpu23cpu11

cpu22cpu10

cpu09 cpu21

cpu20cpu08

cpu23cpu11

cpu22cpu10

cpu09 cpu21

cpu20cpu08

cpu23cpu11

cpu22cpu10

cpu09 cpu21

cpu20cpu08

cpu23cpu11

cpu22cpu10

cpu09 cpu21

cpu20cpu08

cpu23cpu11

cpu22cpu10

cpu09 cpu21

cpu20cpu08

10GB/s/channelswitch

External Clients

10.0.1.101 10.0.1.102 10.0.1.107 10.0.1.109 10.0.1.111 10.0.1.112 ‣CPU load data‣6 systems‣24 cores/each‣6 data points‣1 sample/second‣~38 minutes run time

Total of ~2 million data points

Small subset of the overall SpaceCurve analysis

Time to see it work...

Where to?

• A full library implementation of Split-Apply-Combine and helpers

Where to?

• Add to Incanter?

Where to?

• Performance optimizations (mutable intermediate results, column-oriented datasets)

Where to?

• Implementation based on reducers and parallelism

Where to?

• Implementation based on reducers and parallelism

• Explore the continuum from data exploration tools (R, Incanter) to large-scale data analysis (Hadoop, Cascalog, SpaceCurve, etc.)

Discussion

References

• Source for this presentation: https://www.github.com/tomfaulhaber/split-apply-combine

• The R Project: http://www.r-project.org• The plyr home page: http://plyr.had.co.nz• Hadley Wickham, The Split-Apply-Combine Strategy for Data Analysis,

Journal of Statistical Software, April 2011, Volume 40, Issue 1• Incanter project: http://incanter.org• Eric Rochester, The Clojure Data Analysis Cookbook, Packt Publishing, 2013• Bruce Durling, Quick and Dirty Data Science with Incanter, talk from

EuroClojure 2012, http://confreaks.com/videos/2071-euroclojure2012-quick-and-dirty-data-science-with-incanter

• Spacecurve: http://www.spacecurve.comTom Faulhabertwitter: @tomfaulhabergithub: tomfaulhaber

Photo Credits

• Florida Home - anoldent on flickr (http://www.flickr.com/photos/anoldent/2405722434/)

• Midland Coal Mine - jasonwoodhead23 on flickr (http://www.flickr.com/photos/woodhead/8522679843/)

• Paradise - Antti Simonen on flickr (http://www.flickr.com/photos/anttisimonen/6041095682/)

• Traders on the Exchange - thetaxhaven on flickr (http://www.flickr.com/photos/83532250@N06/7651028854)

• Louvre - dynamosquito on flickr (http://www.flickr.com/photos/25182210@N07/2802458437/)

• Construction - Aapo Haapanen on flickr (http://www.flickr.com/photos/decade_null/214247988/)

• Server farm - from the Spacecurve website (http://www.spacecurve.com)

• Sailboat race - Ryk Van Toronto on flickr (http://www.flickr.com/photos/sydandsaskia/394507351)

• Arguing Philosophers - David Schroeter on flickr (http://www.flickr.com/photos/53477785@N00/92134612/)

Implementing the Split-Apply-Combine model in Clojure and Incanter

Technology

Transcript of Implementing the Split-Apply-Combine model in Clojure and Incanter

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