Github user felixcheung commented on a diff in the pull request:

    https://github.com/apache/spark/pull/14980#discussion_r77733377
  
    --- Diff: R/pkg/vignettes/sparkr-vignettes.Rmd ---
    @@ -0,0 +1,853 @@
    +---
    +title: "SparkR - Practical Guide"
    +output:
    +  html_document:
    +    theme: united
    +    toc: true
    +    toc_depth: 4
    +    toc_float: true
    +    highlight: textmate
    +---
    +
    +## Overview
    +
    +SparkR is an R package that provides a light-weight frontend to use Apache 
Spark from R. In Spark 2.0.0, SparkR provides a distributed data frame 
implementation that supports data processing operations like selection, 
filtering, aggregation etc. and distributed machine learning using 
[MLlib](http://spark.apache.org/mllib/).
    +
    +## Getting Started
    +
    +We begin with an example running on the local machine and provide an 
overview of the use of SparkR: data ingestion, data processing and machine 
learning.
    +
    +First, let's load and attach the package.
    +```{r, message=FALSE}
    +library(SparkR)
    +```
    +
    +`SparkSession` is the entry point into SparkR which connects your R 
program to a Spark cluster. You can create a `SparkSession` using 
`sparkR.session` and pass in options such as the application name, any Spark 
packages depended on, etc.
    +
    +We use default settings in which it runs in local mode. It auto downloads 
Spark package in the background if no previous installation is found. For more 
details about setup, see [Spark Session](#SetupSparkSession).
    +
    +```{r, message=FALSE, warning=FALSE}
    +sparkR.session()
    +```
    +
    +The operations in SparkR are centered around an R class called 
`SparkDataFrame`. It is a distributed collection of data organized into named 
columns, which is conceptually equivalent to a table in a relational database 
or a data frame in R, but with richer optimizations under the hood.
    +
    +`SparkDataFrame` can be constructed from a wide array of sources such as: 
structured data files, tables in Hive, external databases, or existing local R 
data frames. For example, we create a `SparkDataFrame` from a local R data 
frame,
    +
    +```{r}
    +cars <- cbind(model = rownames(mtcars), mtcars)
    +carsDF <- createDataFrame(cars)
    +```
    +
    +We can view the first few rows of the `SparkDataFrame` by `showDF` or 
`head` function.
    +```{r}
    +showDF(carsDF)
    +```
    +
    +Common data processing operations such as `filter`, `select` are supported 
on the `SparkDataFrame`.
    +```{r}
    +carsSubDF <- select(carsDF, "model", "mpg", "hp")
    +carsSubDF <- filter(carsSubDF, carsSubDF$hp >= 200)
    +showDF(carsSubDF)
    +```
    +
    +SparkR can use many common aggregation functions after grouping.
    +
    +```{r}
    +carsGPDF <- summarize(groupBy(carsDF, carsDF$gear), count = n(carsDF$gear))
    +showDF(carsGPDF)
    +```
    +
    +The results `carsDF` and `carsSubDF` are `SparkDataFrame` objects. To 
convert back to R `data.frame`, we can use `collect`.
    +```{r}
    +carsGP <- collect(carsGPDF)
    +class(carsGP)
    +```
    +
    +SparkR supports a number of commonly used machine learning algorithms. 
Under the hood, SparkR uses MLlib to train the model. Users can call `summary` 
to print a summary of the fitted model, `predict` to make predictions on new 
data, and `write.ml`/`read.ml` to save/load fitted models.
    +
    +SparkR supports a subset of R formula operators for model fitting, 
including ‘~’, ‘.’, ‘:’, ‘+’, and ‘-‘. We use linear 
regression as an example.
    +```{r}
    +model <- spark.glm(carsDF, mpg ~ wt + cyl)
    +```
    +
    +```{r}
    +summary(model)
    +```
    +
    +The model can be saved by `write.ml` and loaded back using `read.ml`.
    +```{r, eval=FALSE}
    +write.ml(model, path = "/HOME/tmp/mlModel/glmModel")
    +```
    +
    +In the end, we can stop Spark Session by running
    +```{r, eval=FALSE}
    +sparkR.session.stop()
    +```
    +
    +## Setup
    +
    +### Installation
    +
    +Different from many other R packages, to use SparkR, you need an 
additional installation of Apache Spark. The Spark installation will be used to 
run a backend process that will compile and execute SparkR programs.
    +
    +If you don't have Spark installed on the computer, you may download it 
from [Apache Spark Website](http://spark.apache.org/downloads.html). 
Alternatively, we provide an easy-to-use function `install.spark` to complete 
this process.
    +
    +```{r, eval=FALSE}
    +install.spark()
    +```
    +
    +If you already have Spark installed, you don't have to install again and 
can pass the `sparkHome` argument to `sparkR.session` to let SparkR know where 
the Spark installation is.
    +
    +```{r, eval=FALSE}
    +sparkR.session(sparkHome = "/HOME/spark")
    +```
    +
    +### Spark Session {#SetupSparkSession}
    +
    +**For Windows users**: Due to different file prefixes across operating 
systems, to avoid the issue of potential wrong prefix, a current workaround is 
to specify `spark.sql.warehouse.dir` when starting the `SparkSession`.
    +
    +```{r, eval=FALSE}
    +spark_warehouse_path <- file.path(path.expand('~'), "spark-warehouse")
    +sparkR.session(spark.sql.warehouse.dir = spark_warehouse_path)
    +```
    +
    +In addition to `sparkHome`, many other options can be specified in 
`sparkR.session`. For a complete list, see the [SparkR API 
doc](http://spark.apache.org/docs/latest/api/R/sparkR.session.html).
    +
    +In particular, the following Spark driver properties can be set in 
`sparkConfig`.
    +
    +Property Name | Property group | spark-submit equivalent
    +---------------- | ------------------ | ----------------------
    +spark.driver.memory | Application Properties | --driver-memory
    +spark.driver.extraClassPath | Runtime Environment | --driver-class-path
    +spark.driver.extraJavaOptions | Runtime Environment | --driver-java-options
    +spark.driver.extraLibraryPath | Runtime Environment | --driver-library-path
    +
    +
    +
    +### Cluster Mode
    +SparkR can connect to remote Spark clusters. [Cluster Mode 
Overview](http://spark.apache.org/docs/latest/cluster-overview.html) is a good 
introduction to different Spark cluster modes.
    +
    +When connecting SparkR to a remote Spark cluster, make sure that the Spark 
version and Hadoop version on the machine match the corresponding versions on 
the cluster. Current SparkR package is compatible with
    +```{r, echo=FALSE, tidy = TRUE}
    +paste("Spark", packageVersion("SparkR"))
    +```
    +It should be used both on the local computer and on the remote cluster.
    +
    +To connect, pass the URL of the master node to `sparkR.session`. A 
complete list can be seen in [Spark Master 
URLs](http://spark.apache.org/docs/latest/submitting-applications.html#master-urls).
    +For example, to connect to a local standalone Spark master, we can call
    +
    +```{r, eval=FALSE}
    +sparkR.session(master = "spark://local:7077")
    +```
    +
    +For YARN cluster, SparkR supports the client mode with the master set as 
"yarn".
    +```{r, eval=FALSE}
    +sparkR.session(master = "yarn")
    +```
    +
    +
    +## Data Import
    +
    +### Local Data Frame
    +The simplest way is to convert a local R data frame into a 
`SparkDataFrame`. Specifically we can use `as.DataFrame` or `createDataFrame` 
and pass in the local R data frame to create a `SparkDataFrame`. As an example, 
the following creates a `SparkDataFrame` based using the `faithful` dataset 
from R.
    +```{r}
    +df <- as.DataFrame(faithful)
    +head(df)
    +```
    +
    +### Data Sources
    +SparkR supports operating on a variety of data sources through the 
`SparkDataFrame` interface. You can check the Spark SQL programming guide for 
more [specific 
options](https://spark.apache.org/docs/latest/sql-programming-guide.html#manually-specifying-options)
 that are available for the built-in data sources.
    +
    +The general method for creating `SparkDataFrame` from data sources is 
`read.df`. This method takes in the path for the file to load and the type of 
data source, and the currently active Spark Session will be used automatically. 
SparkR supports reading CSV, JSON and Parquet files natively and through Spark 
Packages you can find data source connectors for popular file formats like 
Avro. These packages can be added with `sparkPackages` parameter when 
initializing SparkSession using `sparkR.session'.`
    +
    +```{r, eval=FALSE}
    +sparkR.session(sparkPackages = "com.databricks:spark-avro_2.11:3.0.0")
    +```
    +
    +We can see how to use data sources using an example CSV input file. For 
more information please refer to SparkR 
[read.df](https://spark.apache.org/docs/latest/api/R/read.df.html) API 
documentation.
    +```{r, eval=FALSE}
    +df <- read.df(csvPath, "csv", header = "true", inferSchema = "true", 
na.strings = "NA")
    +```
    +
    +The data sources API natively supports JSON formatted input files. Note 
that the file that is used here is not a typical JSON file. Each line in the 
file must contain a separate, self-contained valid JSON object. As a 
consequence, a regular multi-line JSON file will most often fail.
    +
    +Let's take a look at the first two lines of the raw JSON file used here.
    +
    +```{r}
    +filePath <- paste0(sparkR.conf("spark.home"),
    +                         "/examples/src/main/resources/people.json")
    +readLines(filePath, n = 2L)
    +```
    +
    +We use `read.df` to read that into a `SparkDataFrame`.
    +
    +```{r}
    +people <- read.df(filePath, "json")
    +count(people)
    +head(people)
    +```
    +
    +SparkR automatically infers the schema from the JSON file.
    +```{r}
    +printSchema(people)
    +```
    +
    +If we want to read multiple JSON files, `read.json` can be used.
    +```{r}
    +people <- read.json(paste0(Sys.getenv("SPARK_HOME"),
    +                           c("/examples/src/main/resources/people.json",
    +                             "/examples/src/main/resources/people.json")))
    +count(people)
    +```
    +
    +The data sources API can also be used to save out `SparkDataFrames` into 
multiple file formats. For example we can save the `SparkDataFrame` from the 
previous example to a Parquet file using `write.df`.
    +```{r, eval=FALSE}
    +write.df(people, path = "people.parquet", source = "parquet", mode = 
"overwrite")
    +```
    +
    +### Hive Tables
    +You can also create SparkDataFrames from Hive tables. To do this we will 
need to create a SparkSession with Hive support which can access tables in the 
Hive MetaStore. Note that Spark should have been built with Hive support and 
more details can be found in the [SQL programming 
guide](https://spark.apache.org/docs/latest/sql-programming-guide.html). In 
SparkR, by default it will attempt to create a SparkSession with Hive support 
enabled (`enableHiveSupport = TRUE`).
    +
    +```{r, eval=FALSE}
    +sql("CREATE TABLE IF NOT EXISTS src (key INT, value STRING)")
    +
    +txtPath <- paste0(sparkR.conf("spark.home"), 
"/examples/src/main/resources/kv1.txt")
    +sqlCMD <- sprintf("LOAD DATA LOCAL INPATH '%s' INTO TABLE src", txtPath)
    +sql(sqlCMD)
    +
    +results <- sql("FROM src SELECT key, value")
    +
    +# results is now a SparkDataFrame
    +head(results)
    +```
    +
    +
    +## Data Processing
    +
    +**To dplyr users**: SparkR has similar interface as dplyr in data 
processing. However, some noticeable differences are worth mentioning in the 
first place. We use `df` to represent a `SparkDataFrame` and `col` to represent 
the name of column here.
    +
    +1. indicate columns. SparkR uses either a character string of the column 
name or a Column object constructed with `$` to indicate a column. For example, 
to select `col` in `df`, we can write `select(df, "col")` or `select(df, 
df$col)`.
    +
    +2. describe conditions. In SparkR, the Column object representation can be 
inserted into the condition directly, or we can use a character string to 
describe the condition, without referring to the `SparkDataFrame` used. For 
example, to select rows with value > 1, we can write `filter(df, df$col > 1)` 
or `filter(df, "col > 1")`.
    +
    +Here are more concrete examples.
    +
    +dplyr | SparkR
    +-------- | ---------
    +`select(mtcars, mpg, hp)` | `select(carsDF, "mpg", "hp")`
    +`filter(mtcars, mpg > 20, hp > 100)` | `filter(carsDF, carsDF$mpg > 20, 
carsDF$hp > 100)`
    +
    +Other differences will be mentioned in the specific methods.
    +
    +We use the `SparkDataFrame` `carsDF` created above. We can get basic 
information about the `SparkDataFrame`.
    +```{r}
    +carsDF
    +```
    +
    +Print out the schema in tree format.
    +```{r}
    +printSchema(carsDF)
    +```
    +
    +### SparkDataFrame Operations
    +
    +#### Selecting rows, columns
    +
    +SparkDataFrames support a number of functions to do structured data 
processing. Here we include some basic examples and a complete list can be 
found in the [API](https://spark.apache.org/docs/latest/api/R/index.html) docs:
    +
    +You can also pass in column name as strings.
    +```{r}
    +head(select(carsDF, "mpg"))
    +```
    +
    +Filter the SparkDataFrame to only retain rows with wait times shorter than 
50 mins.
    +```{r}
    +head(filter(carsDF, carsDF$mpg < 20))
    +```
    +
    +#### Grouping, Aggregation
    +
    +A common flow of grouping and aggregation is
    +
    +1. Use `groupBy` or `group_by` with respect to some grouping variables to 
create a `GroupedData` object
    +
    +2. Feed the `GroupedData` object to `agg` or `summarize` functions, with 
some provided aggregation functions to compute a number within each group.
    +
    +A number of widely used functions are supported to aggregate data after 
grouping, including `avg`, `countDistinct`, `count`, `first`, `kurtosis`, 
`last`, `max`, `mean`, `min`, `sd`, `skewness`, `stddev_pop`, `stddev_samp`, 
`sumDistinct`, `sum`, `var_pop`, `var_samp`, `var`.
    +
    +For example we can compute a histogram of the number of cylinders in the 
`mtcars` dataset as shown below.
    +
    +```{r}
    +numCyl <- summarize(groupBy(carsDF, carsDF$cyl), count = n(carsDF$cyl))
    +head(numCyl)
    +```
    +
    +#### Operating on Columns
    +
    +SparkR also provides a number of functions that can directly applied to 
columns for data processing and during aggregation. The example below shows the 
use of basic arithmetic functions.
    +
    +```{r}
    +carsDF_km <- carsDF
    +carsDF_km$kmpg <- carsDF_km$mpg * 1.61
    +head(select(carsDF_km, "model", "mpg", "kmpg"))
    +```
    +
    +
    +### Window Functions
    +A window function is a variation of aggregation function. In simple words,
    +
    +* aggregation function: `n` to `1` mapping - returns a single value for a 
group of entries. Examples include `sum`, `count`, `max`.
    +
    +* window function: `n` to `n` mapping - returns one value for each entry 
in the group, but the value may depend on all the entries of the *group*. 
Examples include `rank`, `lead`, `lag`.
    +
    +Formally, the *group* mentioned above is called the *frame*. Every input 
row can have a unique frame associated with it and the output of the window 
function on that row is based on the rows confined in that frame.
    +
    +Window functions are often used in conjunction with the following 
functions: `windowPartitionBy`, `windowOrderBy`, `partitionBy`, `orderBy`, 
`over`. To illustrate this we next look at an example.
    +
    +We still use the `mtcars` dataset. The corresponding `SparkDataFrame` is 
`carsDF`. Suppose for each number of cylinders, we want to calculate the rank 
of each car in `mpg` within the group.
    +```{r}
    +carsSubDF <- select(carsDF, "model", "mpg", "cyl")
    +ws <- orderBy(windowPartitionBy("cyl"), "mpg")
    +carsRank <- withColumn(carsSubDF, "rank", over(rank(), ws))
    +showDF(carsRank)
    +```
    +
    +We explain in detail the above steps.
    +
    +* `windowPartitionBy` creates a window specification object `WindowSpec` 
that defines the partition. It controls which rows will be in the same 
partition as the given row. In this case, rows with the same value in `cyl` 
will be put in the same partition. `orderBy` further defines the ordering - the 
position a given row is in the partition. The resulting `WindowSpec` is 
returned as `ws`.
    +
    +More window specification methods include `rangeBetween`, which can define 
boundaries of the frame by value, and `rowsBetween`, which can define the 
boundaries by row indices.
    +
    +* `withColumn` appends a Column called `"rank"` to the `SparkDataFrame`. 
`over` returns a windowing column. The first argument is usually a Column 
returned by window function(s) such as `rank()`, `lead(carsDF$wt)`. That 
calculates the corresponding values according to the partitioned-and-ordered 
table.
    +
    +### User-Defined Function
    +
    +In SparkR, we support several kinds of user-defined functions (UDFs).
    +
    +#### Apply by Partition
    +
    +`dapply` can apply a function to each partition of a `SparkDataFrame`. The 
function to be applied to each partition of the `SparkDataFrame` should have 
only one parameter, a `data.frame` corresponding to a partition, and the output 
should be a `data.frame` as well. Schema specifies the row format of the 
resulting a `SparkDataFrame`. It must match to data types of returned value. 
See [here](#DataTypes) for mapping between R and Spark.
    +
    +We convert `mpg` to `kmpg` (kilometers per gallon). `carsSubDF` is a 
`SparkDataFrame` with a subset of `carsDF` columns.
    +
    +```{r}
    +carsSubDF <- select(carsDF, "model", "mpg")
    +schema <- structType(structField("model", "string"), structField("mpg", 
"double"),
    +                     structField("kmpg", "double"))
    +out <- dapply(carsSubDF, function(x) { x <- cbind(x, x$mpg * 1.61) }, 
schema)
    +head(collect(out))
    +```
    +
    +Like `dapply`, apply a function to each partition of a `SparkDataFrame` 
and collect the result back. The output of function should be a `data.frame`, 
but no schema is required in this case. Note that `dapplyCollect` can fail if 
the output of UDF run on all the partition cannot be pulled to the driver and 
fit in driver memory.
    +
    +```{r}
    +out <- dapplyCollect(
    +         carsSubDF,
    +         function(x) {
    +           x <- cbind(x, "kmpg" = x$mpg * 1.61)
    +         })
    +head(out, 3)
    +```
    +
    +#### Apply by Group
    +`gapply` can apply a function to each group of a `SparkDataFrame`. The 
function is to be applied to each group of the `SparkDataFrame` and should have 
only two parameters: grouping key and R `data.frame` corresponding to that key. 
The groups are chosen from `SparkDataFrames` column(s). The output of function 
should be a `data.frame`. Schema specifies the row format of the resulting 
`SparkDataFrame`. It must represent R function’s output schema on the basis 
of Spark data types. The column names of the returned `data.frame` are set by 
user. See [here](#DataTypes) for mapping between R and Spark.
    +
    +```{r}
    +schema <- structType(structField("cyl", "double"), structField("max_mpg", 
"double"))
    +result <- gapply(
    +    carsDF,
    +    "cyl",
    +    function(key, x) {
    +        y <- data.frame(key, max(x$mpg))
    +    },
    +    schema)
    +head(arrange(result, "max_mpg", decreasing = TRUE))
    +```
    +
    +Like gapply, `gapplyCollect` applies a function to each partition of a 
`SparkDataFrame` and collect the result back to R `data.frame`. The output of 
the function should be a `data.frame` but no schema is required in this case. 
Note that `gapplyCollect` can fail if the output of UDF run on all the 
partition cannot be pulled to the driver and fit in driver memory.
    +
    +```{r}
    +result <- gapplyCollect(
    +    carsDF,
    +    "cyl",
    +    function(key, x) {
    +         y <- data.frame(key, max(x$mpg))
    +        colnames(y) <- c("cyl", "max_mpg")
    +        y
    +    })
    +head(result[order(result$max_mpg, decreasing = TRUE), ])
    +```
    +
    +#### Distribute Local Functions
    +
    +Similar to `lapply` in native R, `spark.lapply` runs a function over a 
list of elements and distributes the computations with Spark. `spark.lapply` 
works in a manner that is similar to `doParallel` or `lapply` to elements of a 
list. The results of all the computations should fit in a single machine. If 
that is not the case you can do something like `df <- createDataFrame(list)` 
and then use `dapply`.
    +
    +```{r}
    +families <- c("gaussian", "poisson")
    +train <- function(family) {
    +  model <- glm(mpg ~ hp, mtcars, family = family)
    +  summary(model)
    +}
    +```
    +
    +Return a list of model's summaries.
    +```{r}
    +model.summaries <- spark.lapply(families, train)
    +```
    +
    +Print the summary of each model.
    +```{r}
    +print(model.summaries)
    +```
    +
    +
    +### SQL Queries
    +A `SparkDataFrame` can also be registered as a temporary view in Spark SQL 
and that allows you to run SQL queries over its data. The sql function enables 
applications to run SQL queries programmatically and returns the result as a 
`SparkDataFrame`.
    +
    +```{r}
    +people <- read.df(paste0(sparkR.conf("spark.home"),
    +                         "/examples/src/main/resources/people.json"), 
"json")
    +```
    +
    +Register this SparkDataFrame as a temporary view.
    +
    +```{r}
    +createOrReplaceTempView(people, "people")
    +```
    +
    +SQL statements can be run by using the sql method.
    +```{r}
    +teenagers <- sql("SELECT name FROM people WHERE age >= 13 AND age <= 19")
    +head(teenagers)
    +```
    +
    +
    +## Machine Learning
    +
    +SparkR supports the following machine learning models and algorithms.
    +
    +* Generalized Linear Model (GLM)
    +
    +* Naive Bayes Model
    +
    +* $k$-means Clustering
    +
    +* Accelerated Failure Time (AFT) Survival Model
    +
    +* Gaussian Mixture Model (GMM)
    +
    +* Latent Dirichlet Allocation (LDA)
    +
    +* Multilayer Perceptron Model
    +
    +* Collaborative Filtering with Alternating Least Squares (ALS)
    +
    +* Isotonic Regression Model
    +
    +More will be added in the future.
    +
    +### R Formula
    +
    +For most above, SparkR supports **R formula operators**, including `~`, 
`.`, `:`, `+` and `-` for model fitting. This makes it a similar experience as 
using R functions.
    +
    +### Training and Test Sets
    +
    +We can easily split `SparkDataFrame` into random training and test sets by 
the `randomSplit` function. It returns a list of split `SparkDataFrames` with 
provided `weights`. We use `carsDF` as an example and want to have about $70%$ 
training data and $30%$ test data.
    +```{r}
    +splitDF_list <- randomSplit(carsDF, c(0.7, 0.3), seed = 0)
    +carsDF_train <- splitDF_list[[1]]
    +carsDF_test <- splitDF_list[[2]]
    +```
    +
    +```{r}
    +count(carsDF_train)
    +head(carsDF_train)
    +```
    +
    +```{r}
    +count(carsDF_test)
    +head(carsDF_test)
    +```
    +
    +
    +### Models and Algorithms
    +
    +#### Generalized Linear Model
    +
    +The main function is `spark.glm`. The following families and link 
functions are supported. The default is gaussian.
    +
    +Family | Link Function
    +------ | ---------
    +gaussian | identity, log, inverse
    +binomial | logit, probit, cloglog (complementary log-log)
    +poisson | log, identity, sqrt
    +gamma | inverse, identity, log
    +
    +There are three ways to specify the `family` argument.
    +
    +* Family name as a character string, e.g. `family = "gaussian"`.
    +
    +* Family function, e.g. `family = binomial`.
    +
    +* Result returned by a family function, e.g. `family = poisson(link = log)`
    +
    +For more information regarding the families and their link functions, see 
the Wikipedia page [Generalized Linear 
Model](https://en.wikipedia.org/wiki/Generalized_linear_model).
    +
    +We use the `mtcars` dataset as an illustration. The corresponding 
`SparkDataFrame` is `carsDF`. After fitting the model, we print out a summary 
and see the fitted values by making predictions on the original dataset. We can 
also pass into a new `SparkDataFrame` of same schema to predict on new data.
    +
    +```{r}
    +gaussianGLM <- spark.glm(carsDF, mpg ~ wt + hp)
    +summary(gaussianGLM)
    +```
    +When doing prediction, a new column called `prediction` will be appended. 
Let's look at only a subset of columns here.
    +```{r}
    +gaussianFitted <- predict(gaussianGLM, carsDF)
    +head(select(gaussianFitted, "model", "prediction", "mpg", "wt", "hp"))
    +```
    +
    +#### Naive Bayes Model
    +
    +Naive Bayes model assumes independence among the features. 
`spark.naiveBayes` fits a [Bernoulli naive Bayes 
model](https://en.wikipedia.org/wiki/Naive_Bayes_classifier#Bernoulli_naive_Bayes)
 against a SparkDataFrame. The data should be all categorical. These models are 
often used for document classification.
    +
    +```{r}
    +titanic <- as.data.frame(Titanic)
    +titanicDF <- createDataFrame(titanic[titanic$Freq > 0, -5])
    +naiveBayesModel <- spark.naiveBayes(titanicDF, Survived ~ Class + Sex + 
Age)
    +summary(naiveBayesModel)
    +naiveBayesPrediction <- predict(naiveBayesModel, titanicDF)
    +showDF(select(naiveBayesPrediction, "Class", "Sex", "Age", "Survived", 
"prediction"))
    +```
    +
    +#### k-Means Clustering
    +
    +`spark.kmeans` fits a $k$-means clustering model against a 
`SparkDataFrame`. As an unsupervised learning method, we don't need a response 
variable. Hence, the left hand side of the R formula should be left blank. The 
clustering is based only on the variables on the right hand side.
    +
    +```{r}
    +kmeansModel <- spark.kmeans(carsDF, ~ mpg + hp + wt, k = 3)
    +summary(kmeansModel)
    +kmeansPredictions <- predict(kmeansModel, carsDF)
    +showDF(select(kmeansPredictions, "model", "mpg", "hp", "wt", "prediction"))
    +```
    +
    +#### AFT Survival Model
    +Survival analysis studies the expected duration of time until an event 
happens, and often the relationship with risk factors or treatment taken on the 
subject. In contrast to standard regression analysis, survival modeling has to 
deal with special characteristics in the data including non-negative survival 
time and censoring.
    +
    +Accelerated Failure Time (AFT) model is a parametric survival model for 
censored data that assumes the effect of a covariate is to accelerate or 
decelerate the life course of an event by some constant. For more information, 
refer to the Wikipedia page [AFT 
Model](https://en.wikipedia.org/wiki/Accelerated_failure_time_model) and the 
references there. Different from a [Proportional Hazards 
Model](https://en.wikipedia.org/wiki/Proportional_hazards_model) designed for 
the same purpose, the AFT model is easier to parallelize because each instance 
contributes to the objective function independently.
    +```{r}
    +library(survival)
    +ovarianDF <- createDataFrame(ovarian)
    +aftModel <- spark.survreg(ovarianDF, Surv(futime, fustat) ~ ecog_ps + rx)
    +summary(aftModel)
    +aftPredictions <- predict(aftModel, ovarianDF)
    +head(aftPredictions)
    +```
    +
    +#### Gaussian Mixture Model
    +
    +(Coming in 2.1.0)
    +
    +`spark.gaussianMixture` fits multivariate [Gaussian Mixture 
Model](https://en.wikipedia.org/wiki/Mixture_model#Multivariate_Gaussian_mixture_model)
 (GMM) against a `SparkDataFrame`. 
[Expectation-Maximization](https://en.wikipedia.org/wiki/Expectation%E2%80%93maximization_algorithm)
 (EM) is used to approximate the maximum likelihood estimator (MLE) of the 
model.
    +
    +We use a simulated example to demostrate the usage.
    +```{r}
    +X1 <- data.frame(V1 = rnorm(4), V2 = rnorm(4))
    +X2 <- data.frame(V1 = rnorm(6, 3), V2 = rnorm(6, 4))
    +data <- rbind(X1, X2)
    +df <- createDataFrame(data)
    +gmmModel <- spark.gaussianMixture(df, ~ V1 + V2, k = 2)
    +summary(gmmModel)
    +gmmFitted <- predict(gmmModel, df)
    +showDF(select(gmmFitted, "V1", "V2", "prediction"))
    +```
    +
    +
    +#### Latent Dirichlet Allocation
    +
    +(Coming in 2.1.0)
    +
    +`spark.lda` fits a [Latent Dirichlet 
Allocation](https://en.wikipedia.org/wiki/Latent_Dirichlet_allocation) model on 
a `SparkDataFrame`. It is often used in topic modeling in which topics are 
inferred from a collection of text documents. LDA can be thought of as a 
clustering algorithm as follows:
    +
    +* Topics correspond to cluster centers, and documents correspond to 
examples (rows) in a dataset.
    +
    +* Topics and documents both exist in a feature space, where feature 
vectors are vectors of word counts (bag of words).
    +
    +* Rather than estimating a clustering using a traditional distance, LDA 
uses a function based on a statistical model of how text documents are 
generated.
    +
    +To use LDA, we need to specify a `features` column in `data` where each 
entry represents a document. There are two type options for the column:
    +
    +* character string: This can be a string of the whole document. It will be 
parsed automatically. Additional stop words can be added in 
`customizedStopWords`.
    +
    +* libSVM: Each entry is a collection of words and will be processed 
directly.
    +
    +There are several parameters LDA takes for fitting the model.
    +
    +* `k`: number of topics (default 10).
    +
    +* `maxIter`: maximum iterations (default 20).
    +
    +* `optimizer`: optimizer to train an LDA model, "online" (default) uses 
[online variational 
inference](https://www.cs.princeton.edu/~blei/papers/HoffmanBleiBach2010b.pdf). 
"em" uses 
[expectation-maximization](https://en.wikipedia.org/wiki/Expectation%E2%80%93maximization_algorithm).
    +
    +* `subsamplingRate`: For `optimizer = "online"`. Fraction of the corpus to 
be sampled and used in each iteration of mini-batch gradient descent, in range 
(0, 1] (default 0.05).
    +
    +* `topicConcentration`: concentration parameter (commonly named beta or 
eta) for the prior placed on topic distributions over terms, default -1 to set 
automatically on the Spark side. Use `summary` to retrieve the effective 
topicConcentration. Only 1-size numeric is accepted.
    +
    +* `docConcentration`: concentration parameter (commonly named alpha) for 
the prior placed on documents distributions over topics (theta), default -1 to 
set automatically on the Spark side. Use `summary` to retrieve the effective 
docConcentration. Only 1-size or k-size numeric is accepted.
    +
    +* `maxVocabSize`: maximum vocabulary size, default 1 << 18.
    +
    +Two more functions are provided for the fitted model.
    +
    +* `spark.posterior` returns a `SparkDataFrame` containing a column of 
posterior probabilities vectors named "topicDistribution".
    +
    +* `spark.perplexity` returns the log perplexity of given `SparkDataFrame`, 
or the log perplexity of the training data if missing argument `data`.
    +
    +For more information, see the help document `?spark.lda`.
    +
    +Let's look an artificial example.
    +```{r}
    +corpus <- data.frame(features = c(
    +  "1 2 6 0 2 3 1 1 0 0 3",
    +  "1 3 0 1 3 0 0 2 0 0 1",
    +  "1 4 1 0 0 4 9 0 1 2 0",
    +  "2 1 0 3 0 0 5 0 2 3 9",
    +  "3 1 1 9 3 0 2 0 0 1 3",
    +  "4 2 0 3 4 5 1 1 1 4 0",
    +  "2 1 0 3 0 0 5 0 2 2 9",
    +  "1 1 1 9 2 1 2 0 0 1 3",
    +  "4 4 0 3 4 2 1 3 0 0 0",
    +  "2 8 2 0 3 0 2 0 2 7 2",
    +  "1 1 1 9 0 2 2 0 0 3 3",
    +  "4 1 0 0 4 5 1 3 0 1 0"))
    +corpusDF <- createDataFrame(corpus)
    +model <- spark.lda(data = corpusDF, k = 5, optimizer = "em")
    +summary(model)
    +```
    +
    +```{r}
    +posterior <- spark.posterior(model, corpusDF)
    +head(posterior)
    +```
    +
    +```{r}
    +perplexity <- spark.perplexity(model, corpusDF)
    +perplexity
    +```
    +
    +
    +#### Multilayer Perceptron
    +
    +(Coming in 2.1.0)
    +
    +Multilayer perceptron classifier (MLPC) is a classifier based on the 
[feedforward artificial neural 
network](https://en.wikipedia.org/wiki/Feedforward_neural_network). MLPC 
consists of multiple layers of nodes. Each layer is fully connected to the next 
layer in the network. Nodes in the input layer represent the input data. All 
other nodes map inputs to outputs by a linear combination of the inputs with 
the node’s weights $w$ and bias $b$ and applying an activation function. This 
can be written in matrix form for MLPC with $K+1$ layers as follows:
    +$$
    +y(x)=f_K(\ldots f_2(w_2^T f_1(w_1^T x + b_1) + b_2) \ldots + b_K).
    +$$
    +
    +Nodes in intermediate layers use sigmoid (logistic) function:
    +$$
    +f(z_i) = \frac{1}{1+e^{-z_i}}.
    +$$
    +
    +Nodes in the output layer use softmax function:
    +$$
    +f(z_i) = \frac{e^{z_i}}{\sum_{k=1}^N e^{z_k}}.
    +$$
    +
    +The number of nodes $N$ in the output layer corresponds to the number of 
classes.
    +
    +MLPC employs backpropagation for learning the model. We use the logistic 
loss function for optimization and L-BFGS as an optimization routine.
    +
    +`spark.mlp` requires at least two columns in `data`: one named `"label"` 
and the other one `"features"`. The `"features"` column should be in 
libSVM-format. According to the description above, there are several additional 
parameters that can be set:
    +
    +* `layers`: integer vector containing the number of nodes for each layer.
    +
    +* `solver`: solver parameter, supported options: `"gd"` (minibatch 
gradient descent) or `"l-bfgs"`.
    +
    +* `maxIter`: maximum iteration number.
    +
    +* `tol`: convergence tolerance of iterations.
    +
    +* `stepSize`: step size for `"gd"`.        
    +
    +* `seed`: seed parameter for weights initialization.
    +
    +#### Collaborative Filtering
    +
    +(Coming in 2.1.0)
    +
    +`spark.als` learns latent factors in [collaborative 
filtering](https://en.wikipedia.org/wiki/Recommender_system#Collaborative_filtering)
 via [alternating least squares](http://dl.acm.org/citation.cfm?id=1608614).
    +
    +There are multiple options that can be configured in `spark.als`, 
including `rank`, `reg`, `nonnegative`. For a complete list, refer to the help 
file.
    +
    +```{r}
    +ratings <- list(list(0, 0, 4.0), list(0, 1, 2.0), list(1, 1, 3.0), list(1, 
2, 4.0),
    +                list(2, 1, 1.0), list(2, 2, 5.0))
    +df <- createDataFrame(ratings, c("user", "item", "rating"))
    +model <- spark.als(df, "rating", "user", "item", rank = 10, reg = 0.1, 
nonnegative = TRUE)
    +```
    +
    +Extract latent factors.
    +```{r}
    +stats <- summary(model)
    +userFactors <- stats$userFactors
    +itemFactors <- stats$itemFactors
    +head(userFactors)
    +head(itemFactors)
    +```
    +
    +Make predictions.
    +
    +```{r}
    +predicted <- predict(model, df)
    +showDF(predicted)
    +```
    +
    +#### Isotonic Regression Model
    +
    +(Coming in 2.1.0)
    +
    +`spark.isoreg` fits an [Isotonic 
Regression](https://en.wikipedia.org/wiki/Isotonic_regression) model against a 
`SparkDataFrame`. It solves a weighted univariate a regression problem under a 
complete order constraint. Specifically, given a set of real observed responses 
$y_1, \ldots, y_n$, corresponding real features $x_1, \ldots, x_n$, and 
optionally positive weights $w_1, \ldots, w_n$, we want to find a monotone 
(piecewise linear) function $f$ to  minimize
    +$$
    +\ell(f) = \sum_{i=1}^n w_i (y_i - f(x_i))^2.
    +$$
    +
    +There are a few more arguments that may be useful.
    +
    +* `weightCol`: a character string specifying the weight column.
    +
    +* `isotonic`: logical value indicating whether the output sequence should 
be isotonic/increasing (`TRUE`) or antitonic/decreasing (`FALSE`).
    +
    +* `featureIndex`: the index of the feature on the right hand side of the 
formula if it is a vector column (default: 0), no effect otherwise.
    +
    +We use an artificial example to show the use.
    +
    +```{r}
    +y <- c(3.0, 6.0, 8.0, 5.0, 7.0)
    +x <- c(1.0, 2.0, 3.5, 3.0, 4.0)
    +w <- rep(1.0, 5)
    +data <- data.frame(y = y, x = x, w = w)
    +df <- createDataFrame(data)
    +isoregModel <- spark.isoreg(df, y ~ x, weightCol = "w")
    +isoregFitted <- predict(isoregModel, df)
    +head(select(isoregFitted, "x", "y", "prediction"))
    +```
    +
    +In the prediction stage, based on the fitted monotone piecewise function, 
the rules are:
    +
    +* If the prediction input exactly matches a training feature then 
associated prediction is returned. In case there are multiple predictions with 
the same feature then one of them is returned. Which one is undefined.
    +
    +* If the prediction input is lower or higher than all training features 
then prediction with lowest or highest feature is returned respectively. In 
case there are multiple predictions with the same feature then the lowest or 
highest is returned respectively.
    +
    +* If the prediction input falls between two training features then 
prediction is treated as piecewise linear function and interpolated value is 
calculated from the predictions of the two closest features. In case there are 
multiple values with the same feature then the same rules as in previous point 
are used.
    +
    +For example, when the input is $3.2$, the two closest feature values are 
$3.0$ and $3.5$, then predicted value would be a linear interpolation between 
the predicted values at $3.0$ and $3.5$.
    +
    +```{r}
    +newDF <- createDataFrame(data.frame(x = c(1.5, 3.2)))
    +head(predict(isoregModel, newDF))
    +```
    +
    +#### What's More?
    +We also expect Decision Tree, Random Forest, Kolmogorov-Smirnov Test 
coming in the next version 2.1.0.
    +
    +### Model Persistence
    +The following example shows how to save/load an ML model by SparkR.
    +```{r}
    +irisDF <- suppressWarnings(createDataFrame(iris))
    +gaussianGLM <- spark.glm(irisDF, Sepal_Length ~ Sepal_Width + Species, 
family = "gaussian")
    +
    +# Save and then load a fitted MLlib model
    +modelPath <- tempfile(pattern = "ml", fileext = ".tmp")
    +write.ml(gaussianGLM, modelPath)
    +gaussianGLM2 <- read.ml(modelPath)
    +
    +# Check model summary
    +summary(gaussianGLM2)
    +
    +# Check model prediction
    +gaussianPredictions <- predict(gaussianGLM2, irisDF)
    +showDF(gaussianPredictions)
    +
    +unlink(modelPath)
    +```
    +
    +
    +## Advanced Topics
    +
    +### SparkR Object Classes
    +
    +There are three main object classes in SparkR you may be working with.
    +
    +* `SparkDataFrame`: the central component of SparkR. It is an S4 class 
representing distributed collection of data organized into named columns, which 
is conceptually equivalent to a table in a relational database or a data frame 
in R. It has two slots `sdf` and `env`.
    +    + `sdf` stores a reference to the corresponding Spark Dataset in the 
Spark JVM backend.
    +    + `env` saves the meta-information of the object such as `isCached`.
    +
    +It can be created by data import methods or by transforming an existing 
`SparkDataFrame`. We can manipulate `SparkDataFrame` by numerous data 
processing functions and feed that into machine learning algorithms.
    +
    +* `Column`: an S4 class representing column of `SparkDataFrame`. The slot 
`jc` saves a reference to the corresponding Column object in the Spark JVM 
backend.
    +
    +It can be obtained from a `SparkDataFrame` by `$` operator, `df$col`. More 
often, it is used together with other functions, for example, with `select` to 
select particular columns, with `filter` and constructed conditions to select 
rows, with aggregation functions to compute aggregate statistics for each group.
    +
    +* `GroupedData`: an S4 class representing grouped data created by 
`groupBy` or by transforming other `GroupedData`. Its `sgd` slot saves a 
reference to a RelationalGroupedDataset object in the backend.
    +
    +This is often an intermediate object with group information and followed 
up by aggregation operations.
    +
    +### Architecture
    +
    +A complete description of architecture can be seen in paper [SparkR: 
Scaling R Programs with 
Spark](https://people.csail.mit.edu/matei/papers/2016/sigmod_sparkr.pdf), 
Shivaram Venkataraman, Zongheng Yang, Davies Liu, Eric Liang, Hossein Falaki, 
Xiangrui Meng, Reynold Xin, Ali Ghodsi, Michael Franklin, Ion Stoica, and Matei 
Zaharia. SIGMOD 2016. June 2016.
    +
    +Under the hood of SparkR is Spark SQL engine. This avoids the overheads of 
running interpreted R code, and the optimized SQL execution engine in Spark 
uses structural information about data and computation flow to perform a bunch 
of optimizations to speed up the computation.
    +
    +The main method calls of actual computation happen in the Spark JVM of the 
driver. We have a socket-based SparkR API that allows us to invoke functions on 
the JVM from R. We use a SparkR JVM backend that listens on a Netty-based 
socket server.
    +
    +Two kinds of RPCs are supported in the SparkR JVM backend: method 
invocation and creating new objects. Method invocation can be done in two ways.
    +
    +* `invokeJMethod` takes a reference to an existing Java object and a list 
of arguments to be passed on to the method.
    +
    +* `invokeJStatic` takes a class name for static method and a list of 
arguments to be passed on to the method.
    +
    +The arguments are serialized using our custom wire format which is then 
deserialized on the JVM side. We then use Java reflection to invoke the 
appropriate method.
    +
    +To create objects, a special method name `init` is used and then similarly 
the appropriate constructor is invoked with provided arguments.
    +
    +Finally, we use a new R class `jobj` that refers to a Java object existing 
in the backend. These references are tracked on the Java side and are 
automatically garbage collected when they go out of scope on the R side.
    +
    +## Appendix
    +
    +### R and Spark Data Types {#DataTypes}
    +
    +R | Spark
    --- End diff --
    
    it's not clear to me the best way to do this but isn't this sort of 
duplicating the SparkR programming guide? Should this link to that instead?


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