String grouper contains functions to do string matching using TF-IDF and the cossine similarity. Based on https://bergvca.github.io/2017/10/14/super-fast-string-matching.html

# String Grouper

Click to see image
<center></center>

The image displayed above is a visualization of the graph-structure of one of the groups of strings found by string_grouper. Each circle (node) represents a string, and each connecting arc (edge) represents a match between a pair of strings with a similarity score above a given threshold score (here 0.8).

The centroid of the group, as determined by string_grouper (see tutorials/group_representatives.md for an explanation), is the largest node, also with the most edges originating from it. A thick line in the image denotes a strong similarity between the nodes at its ends, while a faint thin line denotes weak similarity.

The power of string_grouper is discernible from this image: in large datasets, string_grouper is often able to resolve indirect associations between strings even when, say, due to memory-resource-limitations, direct matches between those strings cannot be computed using conventional methods with a lower threshold similarity score.

———

This image was designed using the graph-visualization software Gephi 0.9.2 with data generated by string_grouper operating on the sec__edgar_company_info.csv sample data file.

string_grouper is a library that makes finding groups of similar strings within a single, or multiple, lists of strings easy — and fast. string_grouper uses tf-idf to calculate cosine similarities within a single list or between two lists of strings. The full process is described in the blog Super Fast String Matching in Python.

## Installing

pip install string-grouper

## Usage

import pandas as pd
from string_grouper import match_strings, match_most_similar, \
group_similar_strings, compute_pairwise_similarities, \
StringGrouper


As shown above, the library may be used together with pandas, and contains four high level functions (match_strings, match_most_similar, group_similar_strings, and compute_pairwise_similarities) that can be used directly, and one class (StringGrouper) that allows for a more interactive approach.

The permitted calling patterns of the four functions, and their return types, are:

Function Parameters pandas Return Type
match_strings (master, **kwargs) DataFrame
match_strings (master, duplicates, **kwargs) DataFrame
match_strings (master, master_id=id_series, **kwargs) DataFrame
match_strings (master, duplicates, master_id, duplicates_id, **kwargs) DataFrame
match_most_similar (master, duplicates, **kwargs) Series (if kwarg ignore_index=True) otherwise DataFrame (default)
match_most_similar (master, duplicates, master_id, duplicates_id, **kwargs) DataFrame
group_similar_strings (strings_to_group, **kwargs) Series (if kwarg ignore_index=True) otherwise DataFrame (default)
group_similar_strings (strings_to_group, strings_id, **kwargs) DataFrame
compute_pairwise_similarities (string_series_1, string_series_2, **kwargs) Series

In the rest of this document the names, Series and DataFrame, refer to the familiar pandas object types.

#### Parameters:

Name Description
master A Series of strings to be matched with themselves (or with those in duplicates).
duplicates A Series of strings to be matched with those of master.
master_id (or id_series) A Series of IDs corresponding to the strings in master.
duplicates_id A Series of IDs corresponding to the strings in duplicates.
strings_to_group A Series of strings to be grouped.
strings_id A Series of IDs corresponding to the strings in strings_to_group.
string_series_1(_2) A Series of strings each of which is to be compared with its corresponding string in string_series_2(_1).
**kwargs Keyword arguments (see below).

New in version 0.6.0: each of the high-level functions listed above also has a StringGrouper method counterpart of the same name and parameters. Calling such a method of any instance of StringGrouper will not rebuild the instance's underlying corpus to make string-comparisons but rather use it to perform the string-comparisons. The input Series to the method (master, duplicates, and so on) will thus be encoded, or transformed, into tf-idf matrices, using this corpus. For example:

# Build a corpus using strings in the pandas Series master:
sg = StringGrouper(master)
# The following method-calls will compare strings first in
# pandas Series new_master_1 and next in new_master_2
# using the corpus already built above without rebuilding or
# changing it in any way:
matches1 = sg.match_strings(new_master_1)
matches2 = sg.match_strings(new_master_2)


• #### match_strings

Returns a DataFrame containing similarity-scores of all matching pairs of highly similar strings from master (and duplicates if given). Each matching pair in the output appears in its own row/record consisting of

1. its "left" part: a string (with/without its index-label) from master,
2. its similarity score, and
3. its "right" part: a string (with/without its index-label) from duplicates (or master if duplicates is not given),

in that order. Thus the column-names of the output are a collection of three groups:

1. The name of master and the name(s) of its index (or index-levels) all prefixed by the string 'left_',
2. 'similarity' whose column has the similarity-scores as values, and
3. The name of duplicates (or master if duplicates is not given) and the name(s) of its index (or index-levels) prefixed by the string 'right_'.

Indexes (or their levels) only appear when the keyword argument ignore_index=False (the default). (See tutorials/ignore_index_and_replace_na.md for a demonstration.)

If either master or duplicates has no name, it assumes the name 'side' which is then prefixed as described above. Similarly, if any of the indexes (or index-levels) has no name it assumes its pandas default name ('index', 'level_0', and so on) and is then prefixed as described above.

In other words, if only parameter master is given, the function will return pairs of highly similar strings within master. This can be seen as a self-join where both 'left_' and 'right_' prefixed columns come from master. If both parameters master and duplicates are given, it will return pairs of highly similar strings between master and duplicates. This can be seen as an inner-join where 'left_' and 'right_' prefixed columns come from master and duplicates respectively.

The function also supports optionally inputting IDs (master_id and duplicates_id) corresponding to the strings being matched. In which case, the output includes two additional columns whose names are the names of these optional Series prefixed by 'left_' and 'right_' accordingly, and containing the IDs corresponding to the strings in the output. If any of these Series has no name, then it assumes the name 'id' and is then prefixed as described above.

• #### match_most_similar

If ignore_index=True, returns a Series of strings, where for each string in duplicates the most similar string in master is returned. If there are no similar strings in master for a given string in duplicates (because there is no potential match where the cosine similarity is above the threshold [default: 0.8]) then the original string in duplicates is returned. The output Series thus has the same length and index as duplicates.

For example, if an input Series with the values $'foooo', 'bar', 'baz'$ is passed as the argument master, and $'foooob', 'bar', 'new'$ as the values of the argument duplicates, the function will return a Series with values: $'foooo', 'bar', 'new'$.

The name of the output Series is the same as that of master prefixed with the string 'most_similar_'. If master has no name, it is assumed to have the name 'master' before being prefixed.

If ignore_index=False (the default), match_most_similar returns a DataFrame containing the same Series described above as one of its columns. So it inherits the same index and length as duplicates. The rest of its columns correspond to the index (or index-levels) of master and thus contain the index-labels of the most similar strings being output as values. If there are no similar strings in master for a given string in duplicates then the value(s) assigned to this index-column(s) for that string is NaN by default. However, if the keyword argument replace_na=True, then these NaN values are replaced with the index-label(s) of that string in duplicates. Note that such replacements can only occur if the indexes of master and duplicates have the same number of levels. (See tutorials/ignore_index_and_replace_na.md for a demonstration.)

Each column-name of the output DataFrame has the same name as its corresponding column, index, or index-level of master prefixed with the string 'most_similar_'.

If both parameters master_id and duplicates_id are also given, then a DataFrame is always returned with the same column(s) as described above, but with an additional column containing those IDs from these input Series corresponding to the output strings. This column's name is the same as that of master_id prefixed in the same way as described above. If master_id has no name, it is assumed to have the name 'master_id' before being prefixed.

• #### group_similar_strings

Takes a single Series of strings (strings_to_group) and groups them by assigning to each string one string from strings_to_group chosen as the group-representative for each group of similar strings found. (See tutorials/group_representatives.md for details on how the the group-representatives are chosen.)

If ignore_index=True, the output is a Series (with the same name as strings_to_group prefixed by the string 'group_rep_') of the same length and index as strings_to_group containing the group-representative strings. If strings_to_group has no name then the name of the returned Series is 'group_rep'.

For example, an input Series with values: $'foooo', 'foooob', 'bar'$ will return $'foooo', 'foooo', 'bar'$. Here 'foooo' and 'foooob' are grouped together into group 'foooo' because they are found to be similar. Another example can be found below.

If ignore_index=False, the output is a DataFrame containing the above output Series as one of its columns with the same name. The remaining column(s) correspond to the index (or index-levels) of strings_to_group and contain the index-labels of the group-representatives as values. These columns have the same names as their counterparts prefixed by the string 'group_rep_'.

If strings_id is also given, then the IDs from strings_id corresponding to the group-representatives are also returned in an additional column (with the same name as strings_id prefixed as described above). If strings_id has no name, it is assumed to have the name 'id' before being prefixed.

• #### compute_pairwise_similarities

Returns a Series of cosine similarity scores the same length and index as string_series_1. Each score is the cosine similarity between the pair of strings in the same position (row) in the two input Series, string_series_1 and string_series_2, as the position of the score in the output Series. This can be seen as an element-wise comparison between the two input Series.

All functions are built using a class StringGrouper. This class can be used through pre-defined functions, for example the four high level functions above, as well as using a more interactive approach where matches can be added or removed if needed by calling the StringGrouper class directly.

• #### kwargs

All keyword arguments not mentioned in the function definitions above are used to update the default settings. The following optional arguments can be used:

• ngram_size: The amount of characters in each n-gram. Default is 3.
• regex: The regex string used to clean-up the input string. Default is r"[,-./]|\s".
• ignore_case: Determines whether or not letter case in strings should be ignored. Defaults to True.
• tfidf_matrix_dtype: The datatype for the tf-idf values of the matrix components. Allowed values are numpy.float32 and numpy.float64. Default is numpy.float32. (Note: numpy.float32 often leads to faster processing and a smaller memory footprint albeit less numerical precision than numpy.float64.)
• max_n_matches: The maximum number of matching strings in master allowed per string in duplicates. Default is the total number of strings in master.
• min_similarity: The minimum cosine similarity for two strings to be considered a match. Defaults to 0.8
• number_of_processes: The number of processes used by the cosine similarity calculation. Defaults to number of cores on a machine - 1.
• ignore_index: Determines whether indexes are ignored or not. If False (the default), index-columns will appear in the output, otherwise not. (See tutorials/ignore_index_and_replace_na.md for a demonstration.)
• replace_na: For function match_most_similar, determines whether NaN values in index-columns are replaced or not by index-labels from duplicates. Defaults to False. (See tutorials/ignore_index_and_replace_na.md for a demonstration.)
• include_zeroes: When min_similarity ≤ 0, determines whether zero-similarity matches appear in the output. Defaults to True. (See tutorials/zero_similarity.md.) Note: If include_zeroes is True and the kwarg max_n_matches is set then it must be sufficiently high to capture all nonzero-similarity-matches, otherwise an error is raised and string_grouper suggests an alternative value for max_n_matches. To allow string_grouper to automatically use the appropriate value for max_n_matches then do not set this kwarg at all.
• group_rep: For function group_similar_strings, determines how group-representatives are chosen. Allowed values are 'centroid' (the default) and 'first'. See tutorials/group_representatives.md for an explanation.
• force_symmetries: In cases where duplicates is None, specifies whether corrections should be made to the results to account for symmetry, thus compensating for those losses of numerical significance which violate the symmetries. Defaults to True.
• n_blocks: This parameter is a tuple of two ints provided to help boost performance, if possible, of processing large DataFrames (see Subsection Performance), by splitting the DataFrames into n_blocks[0] blocks for the left operand (of the underlying matrix multiplication) and into n_blocks[1] blocks for the right operand before performing the string-comparisons block-wise. Defaults to 'guess', in which case the numbers of blocks are estimated based on previous empirical results. If n_blocks = 'auto', then splitting is done automatically in the event of an OverflowError.

## Examples

In this section we will cover a few use cases for which string_grouper may be used. We will use the same data set of company names as used in: Super Fast String Matching in Python.

### Find all matches within a single data set

import pandas as pd
import numpy as np
from string_grouper import match_strings, match_most_similar, \
group_similar_strings, compute_pairwise_similarities, \
StringGrouper

company_names = '/media/chris/data/dev/name_matching/data/sec_edgar_company_info.csv'
# We only look at the first 50k as an example:
# Create all matches:
matches = match_strings(companies['Company Name'])
# Look at only the non-exact matches:

left_index left_Company Name similarity right_Company Name right_index
15 14 0210, LLC 0.870291 90210 LLC 4211
167 165 1 800 MUTUALS ADVISOR SERIES 0.931615 1 800 MUTUALS ADVISORS SERIES 166
168 166 1 800 MUTUALS ADVISORS SERIES 0.931615 1 800 MUTUALS ADVISOR SERIES 165
172 168 1 800 RADIATOR FRANCHISE INC 1.000000 1-800-RADIATOR FRANCHISE INC. 201
178 173 1 FINANCIAL MARKETPLACE SECURITIES LLC ... 0.949364 1 FINANCIAL MARKETPLACE SECURITIES, LLC 174

### Find all matches in between two data sets.

The match_strings function finds similar items between two data sets as well. This can be seen as an inner join between two data sets:

# Create a small set of artificial company names:
duplicates = pd.Series(['S MEDIA GROUP', '012 SMILE.COMMUNICATIONS', 'foo bar', 'B4UTRADE COM CORP'])
# Create all matches:
matches = match_strings(companies['Company Name'], duplicates)
matches

left_index left_Company Name similarity right_side right_index
0 12 012 SMILE.COMMUNICATIONS LTD 0.944092 012 SMILE.COMMUNICATIONS 1
1 49777 B.A.S. MEDIA GROUP 0.854383 S MEDIA GROUP 0

Out of the four company names in duplicates, three companies are found in the original company data set. One company is found three times.

### Finding duplicates from a (database extract to) DataFrame where IDs for rows are supplied.

A very common scenario is the case where duplicate records for an entity have been entered into a database. That is, there are two or more records where a name field has slightly different spelling. For example, "A.B. Corporation" and "AB Corporation". Using the optional 'ID' parameter in the match_strings function duplicates can be found easily. A tutorial that steps though the process with an example data set is available.

### For a second data set, find only the most similar match

In the example above, it's possible that multiple matches are found for a single string. Sometimes we just want a string to match with a single most similar string. If there are no similar strings found, the original string should be returned:

# Create a small set of artificial company names:
new_companies = pd.Series(['S MEDIA GROUP', '012 SMILE.COMMUNICATIONS', 'foo bar', 'B4UTRADE COM CORP'],\
name='New Company')
# Create all matches:
matches = match_most_similar(companies['Company Name'], new_companies, ignore_index=True)
# Display the results:
pd.concat([new_companies, matches], axis=1)

New Company most_similar_Company Name
0 S MEDIA GROUP B.A.S. MEDIA GROUP
1 012 SMILE.COMMUNICATIONS 012 SMILE.COMMUNICATIONS LTD
2 foo bar foo bar

### Deduplicate a single data set and show items with most duplicates

The group_similar_strings function groups strings that are similar using a single linkage clustering algorithm. That is, if item A and item B are similar; and item B and item C are similar; but the similarity between A and C is below the threshold; then all three items are grouped together.

# Add the grouped strings:
companies['deduplicated_name'] = group_similar_strings(companies['Company Name'],
ignore_index=True)
# Show items with most duplicates:

deduplicated_name
AGL LIFE ASSURANCE CO SEPARATE ACCOUNT                           183
ANGELLIST-ART-FUND, A SERIES OF ANGELLIST-FG-FUNDS, LLC          116
AMERICREDIT AUTOMOBILE RECEIVABLES TRUST 2001-1                   87
ACE SECURITIES CORP. HOME EQUITY LOAN TRUST, SERIES 2006-HE2      57
ASSET-BACKED PASS-THROUGH CERTIFICATES SERIES 2004-W1             40
ALLSTATE LIFE GLOBAL FUNDING TRUST 2005-3                         39
ALLY AUTO RECEIVABLES TRUST 2014-1                                33
ANDERSON ROBERT E /                                               28
ADVENT INTERNATIONAL GPE VIII LIMITED PARTNERSHIP                 28
Name: Line Number, dtype: int64


The group_similar_strings function also works with IDs: imagine a DataFrame (customers_df) with the following content:

# Create a small set of artificial customer names:
customers_df = pd.DataFrame(
[
('BB016741P', 'Mega Enterprises Corporation'),
('CC082744L', 'Hyper Startup Incorporated'),
('AA098762D', 'Hyper Startup Inc.'),
('BB099931J', 'Hyper-Startup Inc.'),
('HH072982K', 'Hyper Hyper Inc.')
],
columns=('Customer ID', 'Customer Name')
).set_index('Customer ID')
# Display the data:
customers_df

Customer Name
Customer ID
BB016741P Mega Enterprises Corporation
CC082744L Hyper Startup Incorporated
AA098762D Hyper Startup Inc.
BB099931J Hyper-Startup Inc.
HH072982K Hyper Hyper Inc.

The output of group_similar_strings can be directly used as a mapping table:

# Group customers with similar names:
customers_df[["group-id", "name_deduped"]]  = \
group_similar_strings(customers_df["Customer Name"])
# Display the mapping table:
customers_df

Customer Name group-id name_deduped
Customer ID
BB016741P Mega Enterprises Corporation BB016741P Mega Enterprises Corporation
CC082744L Hyper Startup Incorporated CC082744L Hyper Startup Incorporated
AA098762D Hyper Startup Inc. AA098762D Hyper Startup Inc.
BB099931J Hyper-Startup Inc. AA098762D Hyper Startup Inc.
HH072982K Hyper Hyper Inc. HH072982K Hyper Hyper Inc.

Note that here customers_df initially had only one column "Customer Name" (before the group_similar_strings function call); and it acquired two more columns "group-id" (the index-column) and "name_deduped" after the call through a "setting with enlargement" (a pandas feature).

### Simply compute the cosine similarities of pairs of strings

Sometimes we have pairs of strings that have already been matched but whose similarity scores need to be computed. For this purpose we provide the function compute_pairwise_similarities:

# Create a small DataFrame of pairs of strings:
pair_s = pd.DataFrame(
[
('Mega Enterprises Corporation', 'Mega Enterprises Corporation'),
('Hyper Startup Inc.', 'Hyper Startup Incorporated'),
('Hyper Startup Inc.', 'Hyper Startup Inc.'),
('Hyper Startup Inc.', 'Hyper-Startup Inc.'),
('Hyper Hyper Inc.', 'Hyper Hyper Inc.'),
('Mega Enterprises Corporation', 'Mega Enterprises Corp.')
],
columns=('left', 'right')
)
# Display the data:
pair_s

left right
0 Mega Enterprises Corporation Mega Enterprises Corporation
1 Hyper Startup Inc. Hyper Startup Incorporated
2 Hyper Startup Inc. Hyper Startup Inc.
3 Hyper Startup Inc. Hyper-Startup Inc.
4 Hyper Hyper Inc. Hyper Hyper Inc.
5 Mega Enterprises Corporation Mega Enterprises Corp.
# Compute their cosine similarities and display them:
pair_s['similarity'] = compute_pairwise_similarities(pair_s['left'], pair_s['right'])
pair_s

left right similarity
0 Mega Enterprises Corporation Mega Enterprises Corporation 1.000000
1 Hyper Startup Inc. Hyper Startup Incorporated 0.633620
2 Hyper Startup Inc. Hyper Startup Inc. 1.000000
3 Hyper Startup Inc. Hyper-Startup Inc. 1.000000
4 Hyper Hyper Inc. Hyper Hyper Inc. 1.000000
5 Mega Enterprises Corporation Mega Enterprises Corp. 0.826463

## The StringGrouper class

The four functions mentioned above all create a StringGrouper object behind the scenes and call different functions on it. The StringGrouper class keeps track of all tuples of similar strings and creates the groups out of these. Since matches are often not perfect, a common workflow is to:

1. Create matches
2. Manually inspect the results
3. Add and remove matches where necessary
4. Create groups of similar strings

The StringGrouper class allows for this without having to re-calculate the cosine similarity matrix. See below for an example.

company_names = '/media/chris/data/dev/name_matching/data/sec_edgar_company_info.csv'

1. Create matches
# Create a new StringGrouper
string_grouper = StringGrouper(companies['Company Name'], ignore_index=True)
# Check if the ngram function does what we expect:
string_grouper.n_grams('McDonalds')

['McD', 'cDo', 'Don', 'ona', 'nal', 'ald', 'lds']

# Now fit the StringGrouper - this will take a while since we are calculating cosine similarities on 600k strings
string_grouper = string_grouper.fit()

# Add the grouped strings
companies['deduplicated_name'] = string_grouper.get_groups()


Suppose we know that PWC HOLDING CORP and PRICEWATERHOUSECOOPERS LLP are the same company. StringGrouper will not match these since they are not similar enough.

companies[companies.deduplicated_name.str.contains('PRICEWATERHOUSECOOPERS LLP')]

Line Number Company Name Company CIK Key deduplicated_name
478441 478442 PRICEWATERHOUSECOOPERS LLP /TA 1064284 PRICEWATERHOUSECOOPERS LLP /TA
478442 478443 PRICEWATERHOUSECOOPERS LLP 1186612 PRICEWATERHOUSECOOPERS LLP /TA
478443 478444 PRICEWATERHOUSECOOPERS SECURITIES LLC 1018444 PRICEWATERHOUSECOOPERS LLP /TA
companies[companies.deduplicated_name.str.contains('PWC')]

Line Number Company Name Company CIK Key deduplicated_name
485535 485536 PWC CAPITAL INC. 1690640 PWC CAPITAL INC.
485536 485537 PWC HOLDING CORP 1456450 PWC HOLDING CORP
485537 485538 PWC INVESTORS, LLC 1480311 PWC INVESTORS, LLC
485538 485539 PWC REAL ESTATE VALUE FUND I LLC 1668928 PWC REAL ESTATE VALUE FUND I LLC
485539 485540 PWC SECURITIES CORP /BD 1023989 PWC SECURITIES CORP /BD
485540 485541 PWC SECURITIES CORPORATION 1023989 PWC SECURITIES CORPORATION
485541 485542 PWCC LTD 1172241 PWCC LTD
485542 485543 PWCG BROKERAGE, INC. 67301 PWCG BROKERAGE, INC.

string_grouper = string_grouper.add_match('PRICEWATERHOUSECOOPERS LLP', 'PWC HOLDING CORP')
companies['deduplicated_name'] = string_grouper.get_groups()
# Now lets check again:

companies[companies.deduplicated_name.str.contains('PRICEWATERHOUSECOOPERS LLP')]

Line Number Company Name Company CIK Key deduplicated_name
478441 478442 PRICEWATERHOUSECOOPERS LLP /TA 1064284 PRICEWATERHOUSECOOPERS LLP /TA
478442 478443 PRICEWATERHOUSECOOPERS LLP 1186612 PRICEWATERHOUSECOOPERS LLP /TA
478443 478444 PRICEWATERHOUSECOOPERS SECURITIES LLC 1018444 PRICEWATERHOUSECOOPERS LLP /TA
485536 485537 PWC HOLDING CORP 1456450 PRICEWATERHOUSECOOPERS LLP /TA

This can also be used to merge two groups:

string_grouper = string_grouper.add_match('PRICEWATERHOUSECOOPERS LLP', 'ZUCKER MICHAEL')
companies['deduplicated_name'] = string_grouper.get_groups()

# Now lets check again:
companies[companies.deduplicated_name.str.contains('PRICEWATERHOUSECOOPERS LLP')]

Line Number Company Name Company CIK Key deduplicated_name
478441 478442 PRICEWATERHOUSECOOPERS LLP /TA 1064284 PRICEWATERHOUSECOOPERS LLP /TA
478442 478443 PRICEWATERHOUSECOOPERS LLP 1186612 PRICEWATERHOUSECOOPERS LLP /TA
478443 478444 PRICEWATERHOUSECOOPERS SECURITIES LLC 1018444 PRICEWATERHOUSECOOPERS LLP /TA
485536 485537 PWC HOLDING CORP 1456450 PRICEWATERHOUSECOOPERS LLP /TA
662585 662586 ZUCKER MICHAEL 1629018 PRICEWATERHOUSECOOPERS LLP /TA
662604 662605 ZUCKERMAN MICHAEL 1303321 PRICEWATERHOUSECOOPERS LLP /TA
662605 662606 ZUCKERMAN MICHAEL 1496366 PRICEWATERHOUSECOOPERS LLP /TA

We can remove strings from groups in the same way:

string_grouper = string_grouper.remove_match('PRICEWATERHOUSECOOPERS LLP', 'ZUCKER MICHAEL')
companies['deduplicated_name'] = string_grouper.get_groups()

# Now lets check again:
companies[companies.deduplicated_name.str.contains('PRICEWATERHOUSECOOPERS LLP')]

Line Number Company Name Company CIK Key deduplicated_name
478441 478442 PRICEWATERHOUSECOOPERS LLP /TA 1064284 PRICEWATERHOUSECOOPERS LLP /TA
478442 478443 PRICEWATERHOUSECOOPERS LLP 1186612 PRICEWATERHOUSECOOPERS LLP /TA
478443 478444 PRICEWATERHOUSECOOPERS SECURITIES LLC 1018444 PRICEWATERHOUSECOOPERS LLP /TA
485536 485537 PWC HOLDING CORP 1456450 PRICEWATERHOUSECOOPERS LLP /TA

# Performance

### Semilogx plots of run-times of match_strings() vs the number of blocks (n_blocks[1]) into which the right matrix-operand of the dataset (663 000 strings from sec__edgar_company_info.csv) was split before performing the string comparison. As shown in the legend, each plot corresponds to the number n_blocks[0] of blocks into which the left matrix-operand was split.

String comparison, as implemented by string_grouper, is essentially matrix multiplication. A pandas Series of strings is converted (tokenized) into a matrix. Then that matrix is multiplied by itself (or another) transposed.

Here is an illustration of multiplication of two matrices D and MT:

It turns out that when the matrix (or Series) is very large, the computer proceeds quite slowly with the multiplication (apparently due to the RAM being too full). Some computers give up with an OverflowError.

To circumvent this issue, string_grouper now allows the division of the Series into smaller chunks (or blocks) and multiplies the chunks one pair at a time instead to get the same result:

But surprise ... the run-time of the process is sometimes drastically reduced as a result. For example, the speed-up of the following call is about 500% (here, the Series is divided into 200 blocks on the right operand, that is, 1 block on the left × 200 on the right) compared to the same call with no splitting [n_blocks=(1, 1), the default, which is what previous versions (0.5.0 and earlier) of string_grouper did]:

# A DataFrame of 668 000 records:

# The following call is more than 6 times faster than earlier versions of
# match_strings() (that is, when n_blocks=(1, 1))!
match_strings(companies['Company Name')], n_blocks=(1, 200))


Further exploration of the block number space (see plot above) has revealed that for any fixed number of right blocks, the run-time gets longer the larger the number of left blocks specified. For this reason, it is recommended not to split the left matrix.

In general,

total runtime = n_blocks[0] × n_blocks[1] × mean runtime per block-pair

= Left Operand Size × Right Operand Size ×

mean runtime per block-pair / (Left Block Size × Right Block Size)

So for given left and right operands, minimizing the total runtime is the same as minimizing the

runtime per string-pair comparison
mean runtime per block-pair / (Left Block Size × Right Block Size)

Below is a log-log-log contour plot of the runtime per string-pair comparison scaled by its value at Left Block Size = Right Block Size = 5000. Here, Block Size is the number of strings in that block, and mean runtime per block-pair is the time taken for the following call to run:

# note the parameter order!
match_strings(right_Series, left_Series, n_blocks=(1, 1))


where left_Series and right_Series, corresponding to Left Block and Right Block respectively, are random subsets of the Series companies['Company Name')] from the sec__edgar_company_info.csv sample data file.

It can be seen that when right_Series is roughly the size of 80 000 (denoted by the white dashed line in the contour plot above), the runtime per string-pair comparison is at its lowest for any fixed left_Series size. Above Right Block Size = 80 000, the matrix-multiplication routine begins to feel the limits of the computer's available memory space and thus its performance deteriorates, as evidenced by the increase in runtime per string-pair comparison there (above the white dashed line). This knowledge could serve as a guide for estimating the optimum block numbers — namely those that divide the Series into blocks of size roughly equal to 80 000 for the right operand (or right_Series).

So what are the optimum block number values for any given Series? That is anyone's guess, and may likely depend on the data itself. Furthermore, as hinted above, the answer may vary from computer to computer.

We however encourage the user to make judicious use of the n_blocks parameter to boost performance of string_grouper whenever possible.

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