weighted quantile summaries, energy iteration clustering, spark_write_rds(), and extra

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Sparklyr 1.6 is now out there on CRAN!

To put in sparklyr 1.6 from CRAN, run

On this weblog submit, we will spotlight the next options and enhancements
from sparklyr 1.6:

Weighted quantile summaries

Apache Spark is well-known for supporting
approximate algorithms that commerce off marginal quantities of accuracy for higher
pace and parallelism.
Such algorithms are significantly useful for performing preliminary information
explorations at scale, as they allow customers to shortly question sure estimated
statistics inside a predefined error margin, whereas avoiding the excessive price of
actual computations.
One instance is the Greenwald-Khanna algorithm for on-line computation of quantile
summaries, as described in Greenwald and Khanna (2001).
This algorithm was initially designed for environment friendly (epsilon)
approximation of quantiles inside a big dataset with out the notion of information
factors carrying completely different weights, and the unweighted model of it has been
applied as
approxQuantile()
since Spark 2.0.
Nonetheless, the identical algorithm will be generalized to deal with weighted
inputs, and as sparklyr consumer @Zhuk66 talked about
in this concern, a
weighted model
of this algorithm makes for a helpful sparklyr characteristic.

To correctly clarify what weighted-quantile means, we should make clear what the
weight of every information level signifies. For instance, if we’ve a sequence of
observations ((1, 1, 1, 1, 0, 2, -1, -1)), and wish to approximate the
median of all information factors, then we’ve the next two choices:

  • Both run the unweighted model of approxQuantile() in Spark to scan
    by means of all 8 information factors

  • Or alternatively, “compress” the information into 4 tuples of (worth, weight):
    ((1, 0.5), (0, 0.125), (2, 0.125), (-1, 0.25)), the place the second part of
    every tuple represents how usually a worth happens relative to the remainder of the
    noticed values, after which discover the median by scanning by means of the 4 tuples
    utilizing the weighted model of the Greenwald-Khanna algorithm

We will additionally run by means of a contrived instance involving the usual regular
distribution for instance the facility of weighted quantile estimation in
sparklyr 1.6. Suppose we can not merely run qnorm() in R to judge the
quantile perform
of the usual regular distribution at (p = 0.25) and (p = 0.75), how can
we get some obscure thought in regards to the 1st and third quantiles of this distribution?
A method is to pattern numerous information factors from this distribution, and
then apply the Greenwald-Khanna algorithm to our unweighted samples, as proven
beneath:

library(sparklyr)

sc <- spark_connect(grasp = "native")

num_samples <- 1e6
samples <- information.body(x = rnorm(num_samples))

samples_sdf <- copy_to(sc, samples, identify = random_string())

samples_sdf %>%
  sdf_quantile(
    column = "x",
    possibilities = c(0.25, 0.75),
    relative.error = 0.01
  ) %>%
  print()
##        25%        75%
## -0.6629242  0.6874939

Discover that as a result of we’re working with an approximate algorithm, and have specified
relative.error = 0.01, the estimated worth of (-0.6629242) from above
could possibly be anyplace between the twenty fourth and the twenty sixth percentile of all samples.
In truth, it falls within the (25.36896)-th percentile:

## [1] 0.2536896

Now how can we make use of weighted quantile estimation from sparklyr 1.6 to
acquire comparable outcomes? Easy! We will pattern numerous (x) values
uniformly randomly from ((-infty, infty)) (or alternatively, simply choose a
giant variety of values evenly spaced between ((-M, M)) the place (M) is
roughly (infty)), and assign every (x) worth a weight of
(displaystyle frac{1}{sqrt{2 pi}}e^{-frac{x^2}{2}}), the usual regular
distribution’s likelihood density at (x). Lastly, we run the weighted model
of sdf_quantile() from sparklyr 1.6, as proven beneath:

library(sparklyr)

sc <- spark_connect(grasp = "native")

num_samples <- 1e6
M <- 1000
samples <- tibble::tibble(
  x = M * seq(-num_samples / 2 + 1, num_samples / 2) / num_samples,
  weight = dnorm(x)
)

samples_sdf <- copy_to(sc, samples, identify = random_string())

samples_sdf %>%
  sdf_quantile(
    column = "x",
    weight.column = "weight",
    possibilities = c(0.25, 0.75),
    relative.error = 0.01
  ) %>%
  print()
##    25%    75%
## -0.696  0.662

Voilà! The estimates should not too far off from the twenty fifth and seventy fifth percentiles (in
relation to our abovementioned most permissible error of (0.01)):

## [1] 0.2432144
## [1] 0.7460144

Energy iteration clustering

Energy iteration clustering (PIC), a easy and scalable graph clustering methodology
offered in Lin and Cohen (2010), first finds a low-dimensional embedding of a dataset, utilizing
truncated energy iteration on a normalized pairwise-similarity matrix of all information
factors, after which makes use of this embedding because the “cluster indicator,” an intermediate
illustration of the dataset that results in quick convergence when used as enter
to k-means clustering. This course of could be very effectively illustrated in determine 1
of Lin and Cohen (2010) (reproduced beneath)

during which the leftmost picture is the visualization of a dataset consisting of three
circles, with factors coloured in crimson, inexperienced, and blue indicating clustering
outcomes, and the next photographs present the facility iteration course of step by step
reworking the unique set of factors into what seems to be three disjoint line
segments, an intermediate illustration that may be quickly separated into 3
clusters utilizing k-means clustering with (ok = 3).

In sparklyr 1.6, ml_power_iteration() was applied to make the
PIC performance
in Spark accessible from R. It expects as enter a 3-column Spark dataframe that
represents a pairwise-similarity matrix of all information factors. Two of
the columns on this dataframe ought to comprise 0-based row and column indices, and
the third column ought to maintain the corresponding similarity measure.
Within the instance beneath, we are going to see a dataset consisting of two circles being
simply separated into two clusters by ml_power_iteration(), with the Gaussian
kernel getting used because the similarity measure between any 2 factors:

gen_similarity_matrix <- perform() {
  # Guassian similarity measure
  guassian_similarity <- perform(pt1, pt2) {
    exp(-sum((pt2 - pt1) ^ 2) / 2)
  }
  # generate evenly distributed factors on a circle centered on the origin
  gen_circle <- perform(radius, num_pts) {
    seq(0, num_pts - 1) %>%
      purrr::map_dfr(
        perform(idx) {
          theta <- 2 * pi * idx / num_pts
          radius * c(x = cos(theta), y = sin(theta))
        })
  }
  # generate factors on each circles
  pts <- rbind(
    gen_circle(radius = 1, num_pts = 80),
    gen_circle(radius = 4, num_pts = 80)
  )
  # populate the pairwise similarity matrix (saved as a 3-column dataframe)
  similarity_matrix <- information.body()
  for (i in seq(2, nrow(pts)))
    similarity_matrix <- similarity_matrix %>%
      rbind(seq(i - 1L) %>%
        purrr::map_dfr(~ listing(
          src = i - 1L, dst = .x - 1L,
          similarity = guassian_similarity(pts[i,], pts[.x,])
        ))
      )

  similarity_matrix
}

library(sparklyr)

sc <- spark_connect(grasp = "native")
sdf <- copy_to(sc, gen_similarity_matrix())
clusters <- ml_power_iteration(
  sdf, ok = 2, max_iter = 10, init_mode = "diploma",
  src_col = "src", dst_col = "dst", weight_col = "similarity"
)

clusters %>% print(n = 160)
## # A tibble: 160 x 2
##        id cluster
##     <dbl>   <int>
##   1     0       1
##   2     1       1
##   3     2       1
##   4     3       1
##   5     4       1
##   ...
##   157   156       0
##   158   157       0
##   159   158       0
##   160   159       0

The output exhibits factors from the 2 circles being assigned to separate clusters,
as anticipated, after solely a small variety of PIC iterations.

spark_write_rds() + collect_from_rds()

spark_write_rds() and collect_from_rds() are applied as a much less memory-
consuming various to accumulate(). Not like accumulate(), which retrieves all
components of a Spark dataframe by means of the Spark driver node, therefore doubtlessly
inflicting slowness or out-of-memory failures when gathering giant quantities of information,
spark_write_rds(), when used at the side of collect_from_rds(), can
retrieve all partitions of a Spark dataframe immediately from Spark staff,
relatively than by means of the Spark driver node.
First, spark_write_rds() will
distribute the duties of serializing Spark dataframe partitions in RDS model
2 format amongst Spark staff. Spark staff can then course of a number of partitions
in parallel, every dealing with one partition at a time and persisting the RDS output
on to disk, relatively than sending dataframe partitions to the Spark driver
node. Lastly, the RDS outputs will be re-assembled to R dataframes utilizing
collect_from_rds().

Proven beneath is an instance of spark_write_rds() + collect_from_rds() utilization,
the place RDS outputs are first saved to HDFS, then downloaded to the native
filesystem with hadoop fs -get, and eventually, post-processed with
collect_from_rds():

library(sparklyr)
library(nycflights13)

num_partitions <- 10L
sc <- spark_connect(grasp = "yarn", spark_home = "/usr/lib/spark")
flights_sdf <- copy_to(sc, flights, repartition = num_partitions)

# Spark staff serialize all partition in RDS format in parallel and write RDS
# outputs to HDFS
spark_write_rds(
  flights_sdf,
  dest_uri = "hdfs://<namenode>:8020/flights-part-{partitionId}.rds"
)

# Run `hadoop fs -get` to obtain RDS information from HDFS to native file system
for (partition in seq(num_partitions) - 1)
  system2(
    "hadoop",
    c("fs", "-get", sprintf("hdfs://<namenode>:8020/flights-part-%d.rds", partition))
  )

# Put up-process RDS outputs
partitions <- seq(num_partitions) - 1 %>%
  lapply(perform(partition) collect_from_rds(sprintf("flights-part-%d.rds", partition)))

# Optionally, name `rbind()` to mix information from all partitions right into a single R dataframe
flights_df <- do.name(rbind, partitions)

Just like different latest sparklyr releases, sparklyr 1.6 comes with a
variety of dplyr-related enhancements, reminiscent of

  • Help for the place() predicate inside choose() and summarize(throughout(...))
    operations on Spark dataframes
  • Addition of if_all() and if_any() features
  • Full compatibility with dbplyr 2.0 backend API

choose(the place(...)) and summarize(throughout(the place(...)))

The dplyr the place(...) assemble is helpful for making use of a range or
aggregation perform to a number of columns that fulfill some boolean predicate.
For instance,

returns all numeric columns from the iris dataset, and

computes the common of every numeric column.

In sparklyr 1.6, each sorts of operations will be utilized to Spark dataframes, e.g.,

if_all() and if_any()

if_all() and if_any() are two comfort features from dplyr 1.0.4 (see
right here for extra particulars)
that successfully
mix the outcomes of making use of a boolean predicate to a tidy number of columns
utilizing the logical and/or operators.

Ranging from sparklyr 1.6, if_all() and if_any() can be utilized to
Spark dataframes, .e.g.,

Compatibility with dbplyr 2.0 backend API

Sparklyr 1.6 is absolutely appropriate with the newer dbplyr 2.0 backend API (by
implementing all interface adjustments really helpful in
right here), whereas nonetheless
sustaining backward compatibility with the earlier version of dbplyr API, so
that sparklyr customers is not going to be pressured to modify to any specific model of
dbplyr.

This must be a principally non-user-visible change as of now. In truth, the one
discernible conduct change would be the following code

outputting

[1] 2

if sparklyr is working with dbplyr 2.0+, and

[1] 1

if in any other case.

Acknowledgements

In chronological order, we wish to thank the next contributors for
making sparklyr 1.6 superior:

We might additionally like to present an enormous shout-out to the fantastic open-source group
behind sparklyr, with out whom we’d not have benefitted from quite a few
sparklyr-related bug studies and have recommendations.

Lastly, the creator of this weblog submit additionally very a lot appreciates the extremely
beneficial editorial recommendations from @skeydan.

In the event you want to study extra about sparklyr, we advocate testing
sparklyr.ai, spark.rstudio.com,
and in addition some earlier sparklyr launch posts reminiscent of
sparklyr 1.5
and sparklyr 1.4.

That’s all. Thanks for studying!

Greenwald, Michael, and Sanjeev Khanna. 2001. “Area-Environment friendly On-line Computation of Quantile Summaries.” SIGMOD Rec. 30 (2): 58–66. https://doi.org/10.1145/376284.375670.

Lin, Frank, and William Cohen. 2010. “Energy Iteration Clustering.” In, 655–62.

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