# Spark ML -- Latent Dirichlet Allocation

Latent Dirichlet Allocation (LDA), a topic model designed for text documents.

```
ml_lda(x, formula = NULL, k = 10, max_iter = 20,
doc_concentration = NULL, topic_concentration = NULL,
subsampling_rate = 0.05, optimizer = "online",
checkpoint_interval = 10, keep_last_checkpoint = TRUE,
learning_decay = 0.51, learning_offset = 1024,
optimize_doc_concentration = TRUE, seed = NULL,
features_col = "features",
topic_distribution_col = "topicDistribution",
uid = random_string("lda_"), ...)
ml_describe_topics(model, max_terms_per_topic = 10)
ml_log_likelihood(model, dataset)
ml_log_perplexity(model, dataset)
ml_topics_matrix(model)
```

## Arguments

x | A |

formula | Used when |

k | The number of clusters to create |

max_iter | The maximum number of iterations to use. |

doc_concentration | Concentration parameter (commonly named "alpha") for the prior placed on documents' distributions over topics ("theta"). See details. |

topic_concentration | Concentration parameter (commonly named "beta" or "eta") for the prior placed on topics' distributions over terms. |

subsampling_rate | (For Online optimizer only) Fraction of the corpus to be sampled and used in each iteration of mini-batch gradient descent, in range (0, 1]. Note that this should be adjusted in synch with |

optimizer | Optimizer or inference algorithm used to estimate the LDA model. Supported: "online" for Online Variational Bayes (default) and "em" for Expectation-Maximization. |

checkpoint_interval | Set checkpoint interval (>= 1) or disable checkpoint (-1). E.g. 10 means that the cache will get checkpointed every 10 iterations, defaults to 10. |

keep_last_checkpoint | (Spark 2.0.0+) (For EM optimizer only) If using checkpointing, this indicates whether to keep the last checkpoint. If |

learning_decay | (For Online optimizer only) Learning rate, set as an exponential decay rate. This should be between (0.5, 1.0] to guarantee asymptotic convergence. This is called "kappa" in the Online LDA paper (Hoffman et al., 2010). Default: 0.51, based on Hoffman et al. |

learning_offset | (For Online optimizer only) A (positive) learning parameter that downweights early iterations. Larger values make early iterations count less. This is called "tau0" in the Online LDA paper (Hoffman et al., 2010) Default: 1024, following Hoffman et al. |

optimize_doc_concentration | (For Online optimizer only) Indicates whether the |

seed | A random seed. Set this value if you need your results to be reproducible across repeated calls. |

features_col | Features column name, as a length-one character vector. The column should be single vector column of numeric values. Usually this column is output by |

topic_distribution_col | Output column with estimates of the topic mixture distribution for each document (often called "theta" in the literature). Returns a vector of zeros for an empty document. |

uid | A character string used to uniquely identify the ML estimator. |

... | Optional arguments, see Details. |

model | A fitted LDA model returned by |

max_terms_per_topic | Maximum number of terms to collect for each topic. Default value of 10. |

dataset | test corpus to use for calculating log likelihood or log perplexity |

## Value

The object returned depends on the class of `x`

.

`spark_connection`

: When`x`

is a`spark_connection`

, the function returns an instance of a`ml_estimator`

object. The object contains a pointer to a Spark`Estimator`

object and can be used to compose`Pipeline`

objects.`ml_pipeline`

: When`x`

is a`ml_pipeline`

, the function returns a`ml_pipeline`

with the clustering estimator appended to the pipeline.`tbl_spark`

: When`x`

is a`tbl_spark`

, an estimator is constructed then immediately fit with the input`tbl_spark`

, returning a clustering model.`tbl_spark`

, with`formula`

or`features`

specified: When`formula`

is specified, the input`tbl_spark`

is first transformed using a`RFormula`

transformer before being fit by the estimator. The object returned in this case is a`ml_model`

which is a wrapper of a`ml_pipeline_model`

. This signature does not apply to`ml_lda()`

.

`ml_describe_topics`

returns a DataFrame with topics and their top-weighted terms.

`ml_log_likelihood`

calculates a lower bound on the log likelihood of
the entire corpus

## Details

For `ml_lda.tbl_spark` with the formula interface, you can specify named arguments in `...` that will be passed `ft_regex_tokenizer()`, `ft_stop_words_remover()`, and `ft_count_vectorizer()`. For example, to increase the default `min_token_length`, you can use `ml_lda(dataset, ~ text, min_token_length = 4)`.

Terminology for LDA:

"term" = "word": an element of the vocabulary

"token": instance of a term appearing in a document

"topic": multinomial distribution over terms representing some concept

"document": one piece of text, corresponding to one row in the input data

Original LDA paper (journal version): Blei, Ng, and Jordan. "Latent Dirichlet Allocation." JMLR, 2003.

Input data (`features_col`

): LDA is given a collection of documents as input data, via the `features_col`

parameter. Each document is specified as a Vector of length `vocab_size`

, where each entry is the count for the corresponding term (word) in the document. Feature transformers such as `ft_tokenizer`

and `ft_count_vectorizer`

can be useful for converting text to word count vectors

## Parameter details

`doc_concentration`

This is the parameter to a Dirichlet distribution, where larger values mean more smoothing (more regularization). If not set by the user, then `doc_concentration`

is set automatically. If set to singleton vector [alpha], then alpha is replicated to a vector of length k in fitting. Otherwise, the `doc_concentration`

vector must be length k. (default = automatic)

Optimizer-specific parameter settings:

EM

Currently only supports symmetric distributions, so all values in the vector should be the same.

Values should be greater than 1.0

default = uniformly (50 / k) + 1, where 50/k is common in LDA libraries and +1 follows from Asuncion et al. (2009), who recommend a +1 adjustment for EM.

Online

Values should be greater than or equal to 0

default = uniformly (1.0 / k), following the implementation from here

`topic_concentration`

This is the parameter to a symmetric Dirichlet distribution.

Note: The topics' distributions over terms are called "beta" in the original LDA paper by Blei et al., but are called "phi" in many later papers such as Asuncion et al., 2009.

If not set by the user, then `topic_concentration`

is set automatically. (default = automatic)

Optimizer-specific parameter settings:

EM

Value should be greater than 1.0

default = 0.1 + 1, where 0.1 gives a small amount of smoothing and +1 follows Asuncion et al. (2009), who recommend a +1 adjustment for EM.

Online

Value should be greater than or equal to 0

default = (1.0 / k), following the implementation from here.

`topic_distribution_col`

This uses a variational approximation following Hoffman et al. (2010), where the approximate distribution is called "gamma." Technically, this method returns this approximation "gamma" for each document.

## See also

See http://spark.apache.org/docs/latest/ml-clustering.html for more information on the set of clustering algorithms.

Other ml clustering algorithms: `ml_bisecting_kmeans`

,
`ml_gaussian_mixture`

,
`ml_kmeans`

## Examples

```
if (FALSE) {
library(janeaustenr)
library(dplyr)
sc <- spark_connect(master = "local")
lines_tbl <- sdf_copy_to(sc,
austen_books()[c(1:30), ],
name = "lines_tbl",
overwrite = TRUE
)
# transform the data in a tidy form
lines_tbl_tidy <- lines_tbl %>%
ft_tokenizer(
input_col = "text",
output_col = "word_list"
) %>%
ft_stop_words_remover(
input_col = "word_list",
output_col = "wo_stop_words"
) %>%
mutate(text = explode(wo_stop_words)) %>%
filter(text != "") %>%
select(text, book)
lda_model <- lines_tbl_tidy %>%
ml_lda(~text, k = 4)
# vocabulary and topics
tidy(lda_model)
}
```