, Katelyn Queen [aut]
| Title: | Agglomerative Partitioning Framework for Dimension Reduction |
|---|---|
| Description: | A fast and flexible framework for agglomerative partitioning. 'partition' uses an approach called Direct-Measure-Reduce to create new variables that maintain the user-specified minimum level of information. Each reduced variable is also interpretable: the original variables map to one and only one variable in the reduced data set. 'partition' is flexible, as well: how variables are selected to reduce, how information loss is measured, and the way data is reduced can all be customized. 'partition' is based on the Partition framework discussed in Millstein et al. (2020) <doi:10.1093/bioinformatics/btz661>. |
| Authors: | Joshua Millstein [aut], Malcolm Barrett [aut, cre]
, Katelyn Queen [aut]
|
| Maintainer: | Malcolm Barrett <[email protected]> |
| License: | MIT + file LICENSE |
| Version: | 0.2.2 |
| Built: | 2024-11-09 06:12:32 UTC |
| Source: | CRAN |
Directors are functions that tell the partition algorithm what
to try to reduce. as_director() is a helper function to create new
directors to be used in partitioners. partitioners can be created with
as_partitioner().
as_director(.pairs, .target, ...)as_director(.pairs, .target, ...)
.pairs |
a function that returns a matrix of targets (e.g. a distance matrix of variables) |
.target |
a function that returns a vector of targets (e.g. the minimum pair) |
... |
Extra arguments passed to |
a function to use in as_partitioner()
Other directors:
direct_distance(),
direct_k_cluster()
# use euclidean distance to calculate distances euc_dist <- function(.data) as.matrix(dist(t(.data))) # find the pair with the minimum distance min_dist <- function(.x) { indices <- arrayInd(which.min(.x), dim(as.matrix(.x))) # get variable names with minimum distance c( colnames(.x)[indices[1]], colnames(.x)[indices[2]] ) } as_director(euc_dist, min_dist)# use euclidean distance to calculate distances euc_dist <- function(.data) as.matrix(dist(t(.data))) # find the pair with the minimum distance min_dist <- function(.x) { indices <- arrayInd(which.min(.x), dim(as.matrix(.x))) # get variable names with minimum distance c( colnames(.x)[indices[1]], colnames(.x)[indices[2]] ) } as_director(euc_dist, min_dist)
Metrics are functions that tell how much information would be
lost for a given reduction in the data. reduce. as_measure() is a
helper function to create new metrics to be used in partitioners.
partitioners can be created with as_partitioner().
as_measure(.f, ...)as_measure(.f, ...)
.f |
a function that returns either a numeric vector or a |
... |
Extra arguments passed to |
a function to use in as_partitioner()
Other metrics:
measure_icc(),
measure_min_icc(),
measure_min_r2(),
measure_std_mutualinfo(),
measure_variance_explained()
Other metrics:
measure_icc(),
measure_min_icc(),
measure_min_r2(),
measure_std_mutualinfo(),
measure_variance_explained()
inter_item_reliability <- function(mat) { corrs <- corr(mat) corrs[lower.tri(corrs, diag = TRUE)] <- NA corrs %>% colMeans(na.rm = TRUE) %>% mean(na.rm = TRUE) } measure_iir <- as_measure(inter_item_reliability) measure_iirinter_item_reliability <- function(mat) { corrs <- corr(mat) corrs[lower.tri(corrs, diag = TRUE)] <- NA corrs %>% colMeans(na.rm = TRUE) %>% mean(na.rm = TRUE) } measure_iir <- as_measure(inter_item_reliability) measure_iir
as_partition_step() creates a partition_step object. partition_steps
are used while iterating through the partition algorithm: it stores necessary
information about how to proceed in the partitioning, such as the information
threshold. as_partition_step() is primarily called internally by
partition() but can be helpful while developing partitioners.
as_partition_step( .x, threshold = NA, reduced_data = NA, target = NA, metric = NA, tolerance = 0.01, var_prefix = NA, partitioner = NA, ... )as_partition_step( .x, threshold = NA, reduced_data = NA, target = NA, metric = NA, tolerance = 0.01, var_prefix = NA, partitioner = NA, ... )
.x |
a |
threshold |
The minimum information loss allowable |
reduced_data |
A data set with reduced variables |
target |
A character or integer vector: the variables to reduce |
metric |
A measure of information |
tolerance |
A tolerance around the threshold to accept a reduction |
var_prefix |
Variable name for reduced variables |
partitioner |
A |
... |
Other objects to store during the partition step |
a partition_step object
.df <- data.frame(x = rnorm(100), y = rnorm(100)) as_partition_step(.df, threshold = .6).df <- data.frame(x = rnorm(100), y = rnorm(100)) as_partition_step(.df, threshold = .6)
Partitioners are functions that tell the partition algorithm 1)
what to try to reduce 2) how to measure how much information is lost from
the reduction and 3) how to reduce the data. In partition, functions that
handle 1) are called directors, functions that handle 2) are called
metrics, and functions that handle 3) are called reducers. partition has a
number of pre-specified partitioners for agglomerative data reduction.
Custom partitioners can be created with as_partitioner().
Pass partitioner objects to the partitioner argument of partition().
as_partitioner(direct, measure, reduce)as_partitioner(direct, measure, reduce)
direct |
a function that directs, possibly created by |
measure |
a function that measures, possibly created by |
reduce |
a function that reduces, possibly created by |
a partitioner
Other partitioners:
part_icc(),
part_kmeans(),
part_minr2(),
part_pc1(),
part_stdmi(),
replace_partitioner()
as_partitioner( direct = direct_distance_pearson, measure = measure_icc, reduce = reduce_scaled_mean )as_partitioner( direct = direct_distance_pearson, measure = measure_icc, reduce = reduce_scaled_mean )
Reducers are functions that tell the partition algorithm how
to reduce the data. as_reducer() is a helper function to create new
reducers to be used in partitioners. partitioners can be created with
as_partitioner().
as_reducer(.f, ..., returns_vector = TRUE, first_match = NULL)as_reducer(.f, ..., returns_vector = TRUE, first_match = NULL)
.f |
a function that returns either a numeric vector or a |
... |
Extra arguments passed to |
returns_vector |
logical. Does |
first_match |
logical. Should the partition algorithm stop when it finds
a reduction that is equal to the threshold? Default is |
a function to use in as_partitioner()
Other reducers:
reduce_first_component(),
reduce_kmeans(),
reduce_scaled_mean()
Other reducers:
reduce_first_component(),
reduce_kmeans(),
reduce_scaled_mean()
reduce_row_means <- as_reducer(rowMeans) reduce_row_meansreduce_row_means <- as_reducer(rowMeans) reduce_row_means
Clinical and microbiome data derived from "Microbiota-based model improves
the sensitivity of fecal immunochemical test for detecting colonic lesions"
by Baxter et al. (2016). These data represent a subset of 172 health
participants. baxter_clinical contains 8 clinical variables for each of the
participants: sample_name, id, age, bmi, gender, height,
total_reads, and disease_state (all H for healthy). baxter_otu has
1,234 columns, where each columns represent an Operational Taxonomic Unit
(OTU). OTUs are species-like relationships among bacteria determined by
analyzing their RNA. The cells are logged counts for how often the OTU was
detected in a participant's stool sample. Each column name is a shorthand
name, e.g. otu1; you can find the true name of the OTU mapped in
baxter_data_dictionary. baxter_family and baxter_genus are also logged
counts but instead group OTUs at the family and genus level, respectively, a
common approach to reducing microbiome data. Likewise, the column names are
shorthands, which you can find mapped in baxter_data_dictionary.
baxter_clinical baxter_otu baxter_family baxter_genus baxter_data_dictionarybaxter_clinical baxter_otu baxter_family baxter_genus baxter_data_dictionary
5 data frames
An object of class tbl_df (inherits from tbl, data.frame) with 172 rows and 1234 columns.
An object of class tbl_df (inherits from tbl, data.frame) with 172 rows and 35 columns.
An object of class tbl_df (inherits from tbl, data.frame) with 172 rows and 82 columns.
An object of class tbl_df (inherits from tbl, data.frame) with 1351 rows and 3 columns.
Baxter et al. (2016) doi:10.1186/s13073-016-0290-3
Efficiently fit correlation coefficient for matrix or two vectors
corr(x, y = NULL, spearman = FALSE)corr(x, y = NULL, spearman = FALSE)
x |
a matrix or vector |
y |
a vector. Optional. |
spearman |
Logical. Use Spearman's correlation? |
a numeric vector, the correlation coefficient
library(dplyr) # fit for entire data set iris %>% select_if(is.numeric) %>% corr() # just fit for two vectors corr(iris$Sepal.Length, iris$Sepal.Width)library(dplyr) # fit for entire data set iris %>% select_if(is.numeric) %>% corr() # just fit for two vectors corr(iris$Sepal.Length, iris$Sepal.Width)
Directors are functions that tell the partition algorithm what
to try to reduce. as_director() is a helper function to create new
directors to be used in partitioners. partitioners can be created with
as_partitioner().
direct_distance() fits a distance matrix using either Pearson's or
Spearman's correlation and finds the pair with the smallest distance to
target. If the distance matrix already exists, direct_distance() only
fits the distances for any new reduced variables.
direct_distance_pearson() and direct_distance_spearman() are
convenience functions that directly call the type of distance matrix.
direct_distance(.partition_step, spearman = FALSE) direct_distance_pearson(.partition_step) direct_distance_spearman(.partition_step)direct_distance(.partition_step, spearman = FALSE) direct_distance_pearson(.partition_step) direct_distance_spearman(.partition_step)
.partition_step |
a |
spearman |
Logical. Use Spearman's correlation? |
a partition_step object
Other directors:
as_director(),
direct_k_cluster()
Directors are functions that tell the partition algorithm what
to try to reduce. as_director() is a helper function to create new
directors to be used in partitioners. partitioners can be created with
as_partitioner().
direct_k_cluster() assigns each variable to a cluster using
K-means. As the partition looks for the best reduction,
direct_k_cluster() iterates through values of k to assign clusters.
This search is handled by the binary search method by default and thus
does not necessarily need to fit every value of k.
direct_k_cluster( .partition_step, algorithm = c("armadillo", "Hartigan-Wong", "Lloyd", "Forgy", "MacQueen"), search = c("binary", "linear"), init_k = NULL, seed = 1L )direct_k_cluster( .partition_step, algorithm = c("armadillo", "Hartigan-Wong", "Lloyd", "Forgy", "MacQueen"), search = c("binary", "linear"), init_k = NULL, seed = 1L )
.partition_step |
a |
algorithm |
The K-Means algorithm to use. The default is a fast version
of the LLoyd algorithm written in armadillo. The rest are options in
|
search |
The search method. Binary search is generally more efficient but linear search can be faster in very low dimensions. |
init_k |
The initial k to test. If |
seed |
The seed to set for reproducibility |
a partition_step object
Other directors:
as_director(),
direct_distance()
filter_reduced() and unnest_reduced() are convenience functions to
quickly retrieve the mappings for only the reduced variables.
filter_reduced() returns a nested tibble while unnest_reduced() unnests
it.
filter_reduced(.partition) unnest_reduced(.partition)filter_reduced(.partition) unnest_reduced(.partition)
.partition |
a |
a tibble with mapping key
set.seed(123) df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100) # fit partition prt <- partition(df, threshold = .6) # A tibble: 3 x 4 filter_reduced(prt) # A tibble: 9 x 4 unnest_reduced(prt)set.seed(123) df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100) # fit partition prt <- partition(df, threshold = .6) # A tibble: 3 x 4 filter_reduced(prt) # A tibble: 9 x 4 unnest_reduced(prt)
icc() efficiently calculates the ICC for a numeric data set.
icc(.x, method = c("r", "c"))icc(.x, method = c("r", "c"))
.x |
a data set |
method |
The method source: both the pure R and C++ versions are efficient |
a numeric vector of length 1
library(dplyr) iris %>% select_if(is.numeric) %>% icc()library(dplyr) iris %>% select_if(is.numeric) %>% icc()
Is this object a partition?
is_partition(x)is_partition(x)
x |
an object to be tested |
logical: TRUE or FALSE
partition_step?Is this object a partition_step?
is_partition_step(x)is_partition_step(x)
x |
an object to be tested |
logical: TRUE or FALSE
Is this object a partitioner?
is_partitioner(x)is_partitioner(x)
x |
an object to be tested |
logical: TRUE or FALSE
map_partition() fits partition() across a range of minimum information
values, specified in the information argument. The output is a tibble with
a row for each value of information, a summary of the partition, and a
list-col containing the partition object.
map_partition( .data, partitioner = part_icc(), ..., information = seq(0.1, 0.5, by = 0.1) )map_partition( .data, partitioner = part_icc(), ..., information = seq(0.1, 0.5, by = 0.1) )
.data |
a data set to partition |
partitioner |
the partitioner to use. The default is |
... |
arguments passed to |
information |
a vector of minimum information to fit in |
a tibble
set.seed(123) df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100) map_partition(df, partitioner = part_pc1())set.seed(123) df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100) map_partition(df, partitioner = part_pc1())
mapping_key() returns a data frame with each reduced variable and its
mapping and information loss; the mapping and indices are represented as
list-cols (so there is one row per variable in the reduced data set).
unnest_mappings() unnests the list columns to return a tidy data frame.
mapping_groups() returns a list of mappings (either the variable names or
their column position).
mapping_key(.partition) unnest_mappings(.partition) mapping_groups(.partition, indices = FALSE)mapping_key(.partition) unnest_mappings(.partition) mapping_groups(.partition, indices = FALSE)
.partition |
a |
indices |
logical. Return just the indices instead of the names? Default is |
a tibble
set.seed(123) df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100) # fit partition prt <- partition(df, threshold = .6) # tibble: 6 x 4 mapping_key(prt) # tibble: 12 x 4 unnest_mappings(prt) # list: length 6 mapping_groups(prt)set.seed(123) df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100) # fit partition prt <- partition(df, threshold = .6) # tibble: 6 x 4 mapping_key(prt) # tibble: 12 x 4 unnest_mappings(prt) # list: length 6 mapping_groups(prt)
Metrics are functions that tell how much information would be
lost for a given reduction in the data. reduce. as_measure() is a
helper function to create new metrics to be used in partitioners.
partitioners can be created with as_partitioner().
measure_icc() assesses information loss by calculating the
intraclass correlation coefficient for the target variables.
measure_icc(.partition_step)measure_icc(.partition_step)
.partition_step |
a |
a partition_step object
Other metrics:
as_measure(),
measure_min_icc(),
measure_min_r2(),
measure_std_mutualinfo(),
measure_variance_explained()
Metrics are functions that tell how much information would be
lost for a given reduction in the data. reduce. as_measure() is a
helper function to create new metrics to be used in partitioners.
partitioners can be created with as_partitioner().
measure_min_icc() assesses information loss by calculating the
intraclass correlation coefficient for each set of the target variables and
finding their minimum.
measure_min_icc(.partition_step, search_method = c("binary", "linear"))measure_min_icc(.partition_step, search_method = c("binary", "linear"))
.partition_step |
a |
search_method |
The search method. Binary search is generally more efficient but linear search can be faster in very low dimensions. |
a partition_step object
Other metrics:
as_measure(),
measure_icc(),
measure_min_r2(),
measure_std_mutualinfo(),
measure_variance_explained()
Metrics are functions that tell how much information would be
lost for a given reduction in the data. reduce. as_measure() is a
helper function to create new metrics to be used in partitioners.
partitioners can be created with as_partitioner().
measure_min_r2() assesses information loss by
calculating the minimum R-squared for the target variables.
measure_min_r2(.partition_step)measure_min_r2(.partition_step)
.partition_step |
a |
a partition_step object
Other metrics:
as_measure(),
measure_icc(),
measure_min_icc(),
measure_std_mutualinfo(),
measure_variance_explained()
Metrics are functions that tell how much information would be
lost for a given reduction in the data. reduce. as_measure() is a
helper function to create new metrics to be used in partitioners.
partitioners can be created with as_partitioner().
measure_std_mutualinfo() assesses information loss by
calculating the standardized mutual information for the target variables.
See mutual_information().
measure_std_mutualinfo(.partition_step)measure_std_mutualinfo(.partition_step)
.partition_step |
a |
a partition_step object
Other metrics:
as_measure(),
measure_icc(),
measure_min_icc(),
measure_min_r2(),
measure_variance_explained()
Metrics are functions that tell how much information would be
lost for a given reduction in the data. reduce. as_measure() is a
helper function to create new metrics to be used in partitioners.
partitioners can be created with as_partitioner().
measure_variance_explained() assesses information loss by
calculating the variance explained by the first component of a principal
components analysis. Because the PCA calculates the components and the
variance explained at the same time, if the reducer is
reduce_first_component(), then measure_variance_explained() will store
the first component for later use to avoid recalculation.
measure_variance_explained(.partition_step)measure_variance_explained(.partition_step)
.partition_step |
a |
a partition_step object
Other metrics:
as_measure(),
measure_icc(),
measure_min_icc(),
measure_min_r2(),
measure_std_mutualinfo()
mutual_information calculate the standardized mutual information of a data
set using the infotheo package.
mutual_information(.data)mutual_information(.data)
.data |
a dataframe of numeric values |
a list containing the standardized MI and the scaled row means
library(dplyr) iris %>% select_if(is.numeric) %>% mutual_information()library(dplyr) iris %>% select_if(is.numeric) %>% mutual_information()
Partitioners are functions that tell the partition algorithm 1)
what to try to reduce 2) how to measure how much information is lost from
the reduction and 3) how to reduce the data. In partition, functions that
handle 1) are called directors, functions that handle 2) are called
metrics, and functions that handle 3) are called reducers. partition has a
number of pre-specified partitioners for agglomerative data reduction.
Custom partitioners can be created with as_partitioner().
Pass partitioner objects to the partitioner argument of partition().
part_icc() uses the following direct-measure-reduce approach:
direct: direct_distance(), Minimum Distance
measure: measure_icc(), Intraclass Correlation
reduce: reduce_scaled_mean(), Scaled Row Means
part_icc(spearman = FALSE)part_icc(spearman = FALSE)
spearman |
logical. Use Spearman's correlation for distance matrix? |
a partitioner
Other partitioners:
as_partitioner(),
part_kmeans(),
part_minr2(),
part_pc1(),
part_stdmi(),
replace_partitioner()
set.seed(123) df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100) # fit partition using part_icc() partition(df, threshold = .6, partitioner = part_icc())set.seed(123) df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100) # fit partition using part_icc() partition(df, threshold = .6, partitioner = part_icc())
Partitioners are functions that tell the partition algorithm 1)
what to try to reduce 2) how to measure how much information is lost from
the reduction and 3) how to reduce the data. In partition, functions that
handle 1) are called directors, functions that handle 2) are called
metrics, and functions that handle 3) are called reducers. partition has a
number of pre-specified partitioners for agglomerative data reduction.
Custom partitioners can be created with as_partitioner().
Pass partitioner objects to the partitioner argument of partition().
part_kmeans() uses the following direct-measure-reduce approach:
direct: direct_k_cluster(), K-Means Clusters
measure: measure_min_icc(), Minimum Intraclass Correlation
reduce: reduce_kmeans(), Scaled Row Means
part_kmeans( algorithm = c("armadillo", "Hartigan-Wong", "Lloyd", "Forgy", "MacQueen"), search = c("binary", "linear"), init_k = NULL, n_hits = 4 )part_kmeans( algorithm = c("armadillo", "Hartigan-Wong", "Lloyd", "Forgy", "MacQueen"), search = c("binary", "linear"), init_k = NULL, n_hits = 4 )
algorithm |
The K-Means algorithm to use. The default is a fast version
of the LLoyd algorithm written in armadillo. The rest are options in
|
search |
The search method. Binary search is generally more efficient but linear search can be faster in very low dimensions. |
init_k |
The initial k to test. If |
n_hits |
In linear search method, the number of iterations that should be under the threshold before reducing; useful for preventing false positives. |
a partitioner
Other partitioners:
as_partitioner(),
part_icc(),
part_minr2(),
part_pc1(),
part_stdmi(),
replace_partitioner()
set.seed(123) df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100) # fit partition using part_kmeans() partition(df, threshold = .6, partitioner = part_kmeans())set.seed(123) df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100) # fit partition using part_kmeans() partition(df, threshold = .6, partitioner = part_kmeans())
Partitioners are functions that tell the partition algorithm 1)
what to try to reduce 2) how to measure how much information is lost from
the reduction and 3) how to reduce the data. In partition, functions that
handle 1) are called directors, functions that handle 2) are called
metrics, and functions that handle 3) are called reducers. partition has a
number of pre-specified partitioners for agglomerative data reduction.
Custom partitioners can be created with as_partitioner().
Pass partitioner objects to the partitioner argument of partition().
part_minr2() uses the following direct-measure-reduce approach:
direct: direct_distance(), Minimum Distance
measure: measure_min_r2(), Minimum R-Squared
reduce: reduce_scaled_mean(), Scaled Row Means
part_minr2(spearman = FALSE)part_minr2(spearman = FALSE)
spearman |
logical. Use Spearman's correlation for distance matrix? |
a partitioner
Other partitioners:
as_partitioner(),
part_icc(),
part_kmeans(),
part_pc1(),
part_stdmi(),
replace_partitioner()
set.seed(123) df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100) # fit partition using part_minr2() partition(df, threshold = .6, partitioner = part_minr2())set.seed(123) df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100) # fit partition using part_minr2() partition(df, threshold = .6, partitioner = part_minr2())
Partitioners are functions that tell the partition algorithm 1)
what to try to reduce 2) how to measure how much information is lost from
the reduction and 3) how to reduce the data. In partition, functions that
handle 1) are called directors, functions that handle 2) are called
metrics, and functions that handle 3) are called reducers. partition has a
number of pre-specified partitioners for agglomerative data reduction.
Custom partitioners can be created with as_partitioner().
Pass partitioner objects to the partitioner argument of partition().
part_pc1() uses the following direct-measure-reduce approach:
direct: direct_distance(), Minimum Distance
measure: measure_variance_explained(), Variance Explained (PCA)
reduce: reduce_first_component(), First Principal Component
part_pc1(spearman = FALSE)part_pc1(spearman = FALSE)
spearman |
logical. Use Spearman's correlation for distance matrix? |
a partitioner
Other partitioners:
as_partitioner(),
part_icc(),
part_kmeans(),
part_minr2(),
part_stdmi(),
replace_partitioner()
set.seed(123) df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100) # fit partition using part_pc1() partition(df, threshold = .6, partitioner = part_pc1())set.seed(123) df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100) # fit partition using part_pc1() partition(df, threshold = .6, partitioner = part_pc1())
Partitioners are functions that tell the partition algorithm 1)
what to try to reduce 2) how to measure how much information is lost from
the reduction and 3) how to reduce the data. In partition, functions that
handle 1) are called directors, functions that handle 2) are called
metrics, and functions that handle 3) are called reducers. partition has a
number of pre-specified partitioners for agglomerative data reduction.
Custom partitioners can be created with as_partitioner().
Pass partitioner objects to the partitioner argument of partition().
part_stdmi() uses the following direct-measure-reduce approach:
direct: direct_distance(), Minimum Distance
measure: measure_std_mutualinfo(), Standardized Mutual Information
reduce: reduce_scaled_mean(), Scaled Row Means
part_stdmi(spearman = FALSE)part_stdmi(spearman = FALSE)
spearman |
logical. Use Spearman's correlation for distance matrix? |
a partitioner
Other partitioners:
as_partitioner(),
part_icc(),
part_kmeans(),
part_minr2(),
part_pc1(),
replace_partitioner()
set.seed(123) df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100) # fit partition using part_stdmi() partition(df, threshold = .6, partitioner = part_stdmi())set.seed(123) df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100) # fit partition using part_stdmi() partition(df, threshold = .6, partitioner = part_stdmi())
partition() reduces data while minimizing information loss
using an agglomerative partitioning algorithm. The partition algorithm is
fast and flexible: at every iteration, partition() uses an approach
called Direct-Measure-Reduce (see Details) to create new variables that
maintain the user-specified minimum level of information. Each reduced
variable is also interpretable: the original variables map to one and only
one variable in the reduced data set.
partition( .data, threshold, partitioner = part_icc(), tolerance = 1e-04, niter = NULL, x = "reduced_var", .sep = "_" )partition( .data, threshold, partitioner = part_icc(), tolerance = 1e-04, niter = NULL, x = "reduced_var", .sep = "_" )
.data |
a data.frame to partition |
threshold |
the minimum proportion of information explained by a reduced
variable; |
partitioner |
a |
tolerance |
a small tolerance within the threshold; if a reduction is within the threshold plus/minus the tolerance, it will reduce. |
niter |
the number of iterations. By default, it is calculated as 20% of the number of variables or 10, whichever is larger. |
x |
the prefix of the new variable names |
.sep |
a character vector that separates |
partition() uses an approach called Direct-Measure-Reduce.
Directors tell the partition algorithm what to reduce, metrics tell it
whether or not there will be enough information left after the reduction,
and reducers tell it how to reduce the data. Together these are called a
partitioner. The default partitioner for partition() is part_icc():
it finds pairs of variables to reduce by finding the pair with the minimum
distance between them, it measures information loss through ICC, and it
reduces data using scaled row means. There are several other partitioners
available (part_*() functions), and you can create custom partitioners
with as_partitioner() and replace_partitioner().
a partition object
Millstein, Joshua, Francesca Battaglin, Malcolm Barrett, Shu Cao, Wu Zhang, Sebastian Stintzing, Volker Heinemann, and Heinz-Josef Lenz. 2020. “Partition: A Surjective Mapping Approach for Dimensionality Reduction.” Bioinformatics 36 (3): https://doi.org/676–81.10.1093/bioinformatics/btz661.
Barrett, Malcolm and Joshua Millstein (2020). partition: A fast and flexible framework for data reduction in R. Journal of Open Source Software, 5(47), 1991, https://doi.org/10.21105/joss.01991
part_icc(), part_kmeans(), part_minr2(), part_pc1(),
part_stdmi(), as_partitioner(), replace_partitioner()
set.seed(123) df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100) # don't accept reductions where information < .6 prt <- partition(df, threshold = .6) prt # return reduced data partition_scores(prt) # access mapping keys mapping_key(prt) unnest_mappings(prt) # use a lower threshold of information loss partition(df, threshold = .5, partitioner = part_kmeans()) # use a custom partitioner part_icc_rowmeans <- replace_partitioner(part_icc, reduce = as_reducer(rowMeans)) partition(df, threshold = .6, partitioner = part_icc_rowmeans)set.seed(123) df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100) # don't accept reductions where information < .6 prt <- partition(df, threshold = .6) prt # return reduced data partition_scores(prt) # access mapping keys mapping_key(prt) unnest_mappings(prt) # use a lower threshold of information loss partition(df, threshold = .5, partitioner = part_kmeans()) # use a custom partitioner part_icc_rowmeans <- replace_partitioner(part_icc, reduce = as_reducer(rowMeans)) partition(df, threshold = .6, partitioner = part_icc_rowmeans)
The reduced data is stored as reduced_data in the partition object and can
thus be returned by subsetting object$reduced_data. Alternatively, the
functions partition_score() and fitted() also return the reduced data.
partition_scores(object, ...) ## S3 method for class 'partition' fitted(object, ...)partition_scores(object, ...) ## S3 method for class 'partition' fitted(object, ...)
object |
a |
... |
not currently used (for S3 consistency with |
a tibble containing the reduced data for the partition
set.seed(123) df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100) # fit partition prt <- partition(df, threshold = .6) # three ways to retrieve reduced data partition_scores(prt) fitted(prt) prt$reduced_dataset.seed(123) df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100) # fit partition prt <- partition(df, threshold = .6) # three ways to retrieve reduced data partition_scores(prt) fitted(prt) prt$reduced_data
permute_df() permutes a data set: it randomizes the order within each
variable, which breaks any association between them. Permutation is useful
for testing against null statistics.
permute_df(.data)permute_df(.data)
.data |
a |
a permuted data.frame
permute_df(iris)permute_df(iris)
plot_stacked_area_clusters() and plot_area_clusters() plot the partition
against a permuted partition. plot_ncluster() plots the number of
variables per cluster. If .partition is the result of map_partition() or
test_permutation(), plot_ncluster() facets the plot by each partition.
plot_information() plots a histogram or density plot of the information of
each variable in the partition. If .partition is the result of
map_partition() or test_permutation(), plot_information() plots a
scatterplot of the targeted vs. observed information with a 45 degree line
indicating perfect alignment.
plot_area_clusters( .data, partitioner = part_icc(), information = seq(0.1, 0.5, length.out = 25), ..., obs_color = "#E69F00", perm_color = "#56B4E9" ) plot_stacked_area_clusters( .data, partitioner = part_icc(), information = seq(0.1, 0.5, length.out = 25), ..., stack_colors = c("#E69F00", "#56B4E9", "#009E73", "#F0E442", "#0072B2", "#D55E00") ) plot_ncluster( .partition, show_n = 100, fill = "#0172B1", color = NA, labeller = "target information:" ) plot_information( .partition, fill = "#0172B1", color = NA, geom = ggplot2::geom_density )plot_area_clusters( .data, partitioner = part_icc(), information = seq(0.1, 0.5, length.out = 25), ..., obs_color = "#E69F00", perm_color = "#56B4E9" ) plot_stacked_area_clusters( .data, partitioner = part_icc(), information = seq(0.1, 0.5, length.out = 25), ..., stack_colors = c("#E69F00", "#56B4E9", "#009E73", "#F0E442", "#0072B2", "#D55E00") ) plot_ncluster( .partition, show_n = 100, fill = "#0172B1", color = NA, labeller = "target information:" ) plot_information( .partition, fill = "#0172B1", color = NA, geom = ggplot2::geom_density )
.data |
a data.frame to partition |
partitioner |
a |
information |
a vector of minimum information to fit in |
... |
arguments passed to |
obs_color |
the color of the observed partition |
perm_color |
the color of the permuted partition |
stack_colors |
the colors of the cluster sizes |
.partition |
either a |
show_n |
the number of reduced variables to plot |
fill |
the color of the fill for |
color |
the color of the |
labeller |
the facet label |
geom |
the |
a ggplot
set.seed(123) df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100) df %>% partition(.6, partitioner = part_pc1()) %>% plot_ncluster()set.seed(123) df <- simulate_block_data(c(3, 4, 5), lower_corr = .4, upper_corr = .6, n = 100) df %>% partition(.6, partitioner = part_pc1()) %>% plot_ncluster()
plot_permutation() takes the results of test_permutation() and plots the
distribution of permuted partitions compared to the observed partition.
plot_permutation( permutations, .plot = c("information", "nclusters", "nreduced"), labeller = "target information:", perm_color = "#56B4EA", obs_color = "#CC78A8", geom = ggplot2::geom_density )plot_permutation( permutations, .plot = c("information", "nclusters", "nreduced"), labeller = "target information:", perm_color = "#56B4EA", obs_color = "#CC78A8", geom = ggplot2::geom_density )
permutations |
a |
.plot |
the variable to plot: observed information, the number of clusters created, or the number of observed variables reduced |
labeller |
the facet label |
perm_color |
the color of the permutation fill |
obs_color |
the color of the observed statistic line |
geom |
the |
a ggplot
reduce_cluster() and map_cluster() apply the data reduction to the targets
found in the director step. They only do so if the metric is above the
threshold, however. reduce_cluster() is for functions that return vectors
while map_cluster() is for functions that return data.frames. If you're
using as_reducer(), there's no need to call these functions directly.
reduce_cluster(.partition_step, .f, first_match = FALSE) map_cluster(.partition_step, .f, rewind = FALSE, first_match = FALSE)reduce_cluster(.partition_step, .f, first_match = FALSE) map_cluster(.partition_step, .f, rewind = FALSE, first_match = FALSE)
.partition_step |
a |
.f |
a function to reduce the data to either a vector or a data.frame |
first_match |
logical. Should the partition algorithm stop when it finds
a reduction that is equal to the threshold? Default is |
rewind |
logical. Should the last target be used instead of the current target? |
a partition_step object
reduce_row_means <- function(.partition_step, .data) { reduce_cluster(.partition_step, rowMeans) } replace_partitioner( part_icc, reduce = reduce_row_means )reduce_row_means <- function(.partition_step, .data) { reduce_cluster(.partition_step, rowMeans) } replace_partitioner( part_icc, reduce = reduce_row_means )
Reducers are functions that tell the partition algorithm how
to reduce the data. as_reducer() is a helper function to create new
reducers to be used in partitioners. partitioners can be created with
as_partitioner().
reduce_first_component() returns the first component from the
principal components analysis of the target variables. Because the PCA
calculates the components and the variance explained at the same time, if
the metric is measure_variance_explained(), that function will store the
first component for use in reduce_first_component() to avoid
recalculation. If the partitioner uses a different metric, the first
component will be calculated by reduce_first_component().
reduce_first_component(.partition_step)reduce_first_component(.partition_step)
.partition_step |
a |
a partition_step object
Other reducers:
as_reducer(),
reduce_kmeans(),
reduce_scaled_mean()
Reducers are functions that tell the partition algorithm how
to reduce the data. as_reducer() is a helper function to create new
reducers to be used in partitioners. partitioners can be created with
as_partitioner().
reduce_kmeans() is efficient in that it doesn't reduce until
the closest k to the information threshold is found.
reduce_kmeans(.partition_step, search = c("binary", "linear"), n_hits = 4)reduce_kmeans(.partition_step, search = c("binary", "linear"), n_hits = 4)
.partition_step |
a |
search |
The search method. Binary search is generally more efficient but linear search can be faster in very low dimensions. |
n_hits |
In linear search method, the number of iterations that should be under the threshold before reducing; useful for preventing false positives. |
a partition_step object
Other reducers:
as_reducer(),
reduce_first_component(),
reduce_scaled_mean()
Reducers are functions that tell the partition algorithm how
to reduce the data. as_reducer() is a helper function to create new
reducers to be used in partitioners. partitioners can be created with
as_partitioner().
reduce_scaled_mean() returns the scaled row means of the
target variables to reduce.
reduce_scaled_mean(.partition_step)reduce_scaled_mean(.partition_step)
.partition_step |
a |
a partition_step object
Other reducers:
as_reducer(),
reduce_first_component(),
reduce_kmeans()
Replace the director, metric, or reducer for a partitioner
replace_partitioner(partitioner, direct = NULL, measure = NULL, reduce = NULL)replace_partitioner(partitioner, direct = NULL, measure = NULL, reduce = NULL)
partitioner |
a |
direct |
a function that directs, possibly created by |
measure |
a function that measures, possibly created by |
reduce |
a function that reduces, possibly created by |
a partitioner
Other partitioners:
as_partitioner(),
part_icc(),
part_kmeans(),
part_minr2(),
part_pc1(),
part_stdmi()
replace_partitioner( part_icc, reduce = as_reducer(rowMeans) )replace_partitioner( part_icc, reduce = as_reducer(rowMeans) )
data.frame
scaled_mean() calculates scaled row means for a dataframe.
scaled_mean(.x, method = c("r", "c"))scaled_mean(.x, method = c("r", "c"))
.x |
a |
method |
The method source: both the pure R and C++ versions are efficient |
a numeric vector
library(dplyr) iris %>% select_if(is.numeric) %>% scaled_mean()library(dplyr) iris %>% select_if(is.numeric) %>% scaled_mean()
simulate_block_data() creates a dataset of blocks of data where variables
within each block are correlated. The correlation for each pair of variables
is sampled uniformly from lower_corr to upper_corr, and the values of
each are sampled using MASS::mvrnorm().
simulate_block_data( block_sizes, lower_corr, upper_corr, n, block_name = "block", sep = "_", var_name = "x" )simulate_block_data( block_sizes, lower_corr, upper_corr, n, block_name = "block", sep = "_", var_name = "x" )
block_sizes |
a vector of block sizes. The size of each block is the number of variables within it. |
lower_corr |
the lower bound of the correlation within each block |
upper_corr |
the upper bound of the correlation within each block |
n |
the number of observations or rows |
block_name |
description prepended to the variable to indicate the block it belongs to |
sep |
a character, what to separate the variable names with |
var_name |
the name of the variable within the block |
a tibble with sum(block_sizes) columns and n rows.
# create a 100 x 15 data set with 3 blocks simulate_block_data( block_sizes = rep(5, 3), lower_corr = .4, upper_corr = .6, n = 100 )# create a 100 x 15 data set with 3 blocks simulate_block_data( block_sizes = rep(5, 3), lower_corr = .4, upper_corr = .6, n = 100 )
super_partition implements the agglomerative, data reduction method Partition for datasets with large numbers of features by first 'super-partitioning' the data into smaller clusters to Partition.
super_partition( full_data, threshold = 0.5, cluster_size = 4000, partitioner = part_icc(), tolerance = 1e-04, niter = NULL, x = "reduced_var", .sep = "_", verbose = TRUE, progress_bar = TRUE )super_partition( full_data, threshold = 0.5, cluster_size = 4000, partitioner = part_icc(), tolerance = 1e-04, niter = NULL, x = "reduced_var", .sep = "_", verbose = TRUE, progress_bar = TRUE )
full_data |
sample by feature data frame or matrix |
threshold |
the minimum proportion of information explained by a reduced variable; |
cluster_size |
maximum size of any single cluster; default is 4000 |
partitioner |
a |
tolerance |
a small tolerance within the threshold; if a reduction is within the threshold plus/minus the tolerance, it will reduce. |
niter |
the number of iterations. By default, it is calculated as 20% of the number of variables or 10, whichever is larger. |
x |
the prefix of the new variable names; must not be contained in any existing data names |
.sep |
a character vector that separates |
verbose |
logical for whether or not to display information about super partition step; default is TRUE |
progress_bar |
logical for whether or not to show progress bar; default is TRUE |
super_partition scales up partition with an approximation, using Genie, a fast, hierarchical clustering algorithm with similar qualities of those to Partition, to first super-partition the data into ceiling(N/c) clusters, where N is the number of features in the full dataset and c is the user-defined maximum cluster size (default value = 4,000). Then, if any cluster from the super-partition has a size greater than c, use Genie again on that cluster until all cluster sizes are less than c. Finally, apply the Partition algorithm to each of the super-partitions.
It may be the case that large super-partitions cannot be easily broken with Genie due to high similarity between features. In this case, we use k-means to break the cluster.
Partition object
Katelyn Queen, [email protected]
Barrett, Malcolm and Joshua Millstein (2020). partition: A fast and flexible framework for data reduction in R. Journal of Open Source Software, 5(47), 1991, https://doi.org/10.21105/joss.01991Millstein J, Battaglin F, Barrett M, Cao S, Zhang W, Stintzing S, et al. Partition: a surjective mapping approach for dimensionality reduction. Bioinformatics 36 (2019) 676–681. doi:10.1093/bioinformatics/btz661.
Gagolewski, Marek, Maciej Bartoszuk, and Anna Cena. "Genie: A new, fast, and outlier-resistant hierarchical clustering algorithm." Information Sciences 363 (2016): 8-23.
Millstein, Joshua, Francesca Battaglin, Malcolm Barrett, Shu Cao, Wu Zhang, Sebastian Stintzing, Volker Heinemann, and Heinz-Josef Lenz. 2020. “Partition: A Surjective Mapping Approach for Dimensionality Reduction.” Bioinformatics 36 (3): https://doi.org/676–81.10.1093/bioinformatics/btz661.
set.seed(123) df <- simulate_block_data(c(15, 20, 10), lower_corr = .4, upper_corr = .6, n = 100) # don't accept reductions where information < .6 prt <- super_partition(df, threshold = .6, cluster_size = 30) prtset.seed(123) df <- simulate_block_data(c(15, 20, 10), lower_corr = .4, upper_corr = .6, n = 100) # don't accept reductions where information < .6 prt <- super_partition(df, threshold = .6, cluster_size = 30) prt
test_permutation() permutes data and partitions the results to generate a
distribution of null statistics for observed information, number of clusters,
and number of observed variables reduced to clusters. The result is a
tibble with a summary of the observed data results and the averages of the
permuted results. The partitions and and permutations are also available in
list-cols. test_permutation() tests across a range of target information
values, as specified in the information argument.
test_permutation( .data, information = seq(0.1, 0.6, by = 0.1), partitioner = part_icc(), ..., nperm = 100 )test_permutation( .data, information = seq(0.1, 0.6, by = 0.1), partitioner = part_icc(), ..., nperm = 100 )
.data |
a data set to partition |
information |
a vector of minimum information to fit in |
partitioner |
the partitioner to use. The default is |
... |
arguments passed to |
nperm |
Number of permuted data sets to test. Default is 100. |
a tibble with summaries on observed and permuted data (the means of the permuted summaries), as well as list-cols containing them