# Fuzzy Matching

library(fedmatch)

# Intro

Fuzzy matching is an essential part of the matching process. After trying all the name cleaning that you can with clean_strings, you have gotten the ‘low hanging fruit’ of your match, and now you need to move on to non-exact matches. merge_plus has a built-in setting for this called ‘fuzzy’ matching. It lets you match on strings that are similar, but not exactly the same.

# Fuzzy matching theory

The basic idea behind fuzzy matching is to compute a numerical ‘distance’ between every potential string comparison, and then for each string in data set 1, pick the ‘closest’ string in data set 2. One can also specify a threshold such that every match is of a certain quality. The concept of ‘distance’ can be defined in several methods, explained below. Each method will define a similarity $$s$$, $$0 \leq s \leq 1$$ , such that higher values will mean the strings are more similar, and a corresponding distance $$d = 1 - s$$.

## Jaro-Winkler

The most common method of matching strings with fedmatch uses the Jaro-Winkler string distance. The Jaro similarity is defined as

$s_j = \begin{cases} 0 & \text{if } m = 0 \\ \frac{1}{3} \left(\frac{m}{|s_1|} + \frac{m}{|s_2|} + \frac{m - t}{m} \right) & \text{otherwise} \end{cases}$

where $$|s_i|$$ is the length of the $$i$$th string, $$m$$ is the number of characters that match, and $$t$$ is the number of transpositions (the number of letters to be interchanged to place them in the proper order.) For example, if $$s_1$$ is “abcd” and $$s_2$$ is “acbd”, then the number of transpositions is 1, the matching characters are 4, and the similarity is $$\frac{1}{3}\left( 1 + 1 + \frac{3}{4} \right) \approx .917$$.

Winkler’s modification to this similarity is to weight the start of the strings more heavily. Thus, if the strings share a common prefix, the similarity will be higher. The Jaro-Winkler similarity is

$s_w = s_j + l p (1-s_j),$

where $$l$$ is the shared prefix length (up to four characters, so $$0 \leq l \leq 4$$ ), and $$p$$ is just user-defined constant, $$0 < p \leq .25$$, that defines how heavily to weight the shared prefix. $$p=.1$$ is the default used by fedmatch.

## Weighted Jaccard Similarity

Another string distance metric is called the Jaccard Similarity. If $$A$$ is the set of letters in one string, and $$B$$ is the set of letters in another string, then the Jaccard similarity $$J$$ is defined as

$J = \frac{A \bigcap B}{A \bigcup B}.$

Thus, if the two strings share all of the same letters, then the distance is 0, or the similarity is 1.

We take one step further and innovate to create a new measure of string distance, which we call the Weighted Jaccard distance. Rather than looking at the sets of letters in each string, we look at the set of words in each string. Then, we construct a corpus of all of the words in the two columns to be matched and compute the term frequency-inverse document frequency (TF-IDF) for each word. TF-IDF is a measure of word importance that accounts for how frequently a word appears in a corpus. For example, the word ‘Corporation’ appears frequently in the names of companies in common data sets, and so its TF-IDF would be low. But, the word ‘Apple’ probably only appears in a few company names out of the many thousands in the data, so its TF-IDF score would be high.

Once we have the TF-IDF score for every word, we take the log of these scores to help attenuate the influence of outliers. If these logged scores are called $$w_i$$, where $$i$$ denotes a given word, then the Weighted Jaccard similarity is computed as

$J_w = \frac{ \sum w_i, \forall i \text{ in } A \bigcap B}{ \sum w_i, \forall i \text{ in } A \bigcup B}$ Thus, if the two strings share many words that are uniquely identifying in the corpus, the Weighted Jaccard similarity will be higher. We have found this method of matching is able to pick up many more matches when used in conjunction with the Jaro-Winkler distance. To our knowledge, such a Weighted Jaccard method has never been used before, and is one of the key innovations that makes fedmatch unique.

## Other similarity metrics

Because fedmatch uses stringdist::amatch for all other options, one can use any of the similarity metrics listed in the documentation for that function in fedmatch.

# Using fuzzy matching in fedmatch

## Basic Syntax

As shown in the ‘Intro to fedmatch’ vignette, the basic syntax of using fuzzy match is just the same as exact matching, but changing the ‘match_type’ argument in merge_plus:

fuzzy_result <- merge_plus(data1 = corp_data1,
data2 = corp_data2,
by.x = "Company",
by.y = "Name", match_type = "fuzzy",
unique_key_1 = "unique_key_1",
unique_key_2 = "unique_key_2")
print(fuzzy_result$matches) #> unique_key_2 unique_key_1 Country State SIC Revenue Company #> 1: 1 1 USA OH 3300 485 Walmart #> 2: 2 2 USA 2222 223 Bershire Hataway #> 3: 6 6 USA MA NA 184 UnitedHealth Group #> Name country state_code SIC_code earnings tier #> 1: Walmart USA OH 3380 490,000 all #> 2: Bershire Hathaway USA NE 2220 220,000 all #> 3: UnitedHealth Group USA MA 1130 180,000 all Note that ‘Bershire Hathaway’ matched to ‘Bershire Hataway,’ which makes sense - the names are only off by one character. All of the settings of fuzzy matching are controlled in the ‘fuzzy_settings’ argument of merge_plus, and these settings can be easily modified with the function build_fuzzy_settings. build_fuzzy_settings returns a list that is properly formatted for merge_plus.The options and their defaults are: • method , default “jw”, determines the string distance metric to use. • p , default 0.1, is a numeric vector of length 1, that determines the factor $$p$$ in the Jaro-Winkler string distance. Only used if method == "jw". • maxDist, default 0.05, is a numeric vector of length 1 that determines the maximum allowable string distance that qualifies as a match. • matchNA, default FALSE, is a boolean to determine whether to count NAs as a match (see stringdist::amatch for details.) • nthread, number of threads to use in the underlying C code. If using any method besides “wgt_jaccard”, uses `stringdist::amatch’ to parallelize. If using “wgt_jaccard”, instead uses built in C++ code to parallelize. ## An example - weighted Jaccard match ### Weighted Jaccard Match wgt_jaccard_match <- merge_plus(data1 = corp_data1, data2 = corp_data2, by.x = "Company", by.y = "Name", match_type = "fuzzy", fuzzy_settings = build_fuzzy_settings(method = "wgt_jaccard", maxDist = .5), unique_key_1 = "unique_key_1", unique_key_2 = "unique_key_2") print(wgt_jaccard_match) #>$matches
#>    unique_key_2 unique_key_1 Country State  SIC Revenue            Company
#> 1:            1            1     USA    OH 3300     485            Walmart
#> 2:            4            4     USA    TX 2222     205       Exxon Mobile
#> 3:            6            6     USA    MA   NA     184 UnitedHealth Group
#> 4:           10           10     USA    MI   NA     151 Ford Motor Company
#>                  Name wgt_jaccard_sim country state_code SIC_code earnings tier
#> 1:            Walmart             1.0     USA         OH     3380  490,000  all
#> 2: Exxon Mobile Inc.              0.5     USA         TX     2222  210,000  all
#> 3: UnitedHealth Group             1.0     USA         MA     1130  180,000  all
#> 4:         Ford Motor             0.5     USA         MI     2222  150,000  all
#>
#> $matches_filter #> Null data.table (0 rows and 0 cols) #> #>$data1_nomatch
#>             Company Country State  SIC Revenue unique_key_1
#> 1: Bershire Hataway     USA       2222     223            2
#> 2:            Apple     USA    CA 3384     215            3
#> 3:        McKesson  Germany    MA  222     192            5
#> 4:       CVS Health     USA    RI 1112     177            7
#> 5:   General Motors     USA    MI 2222     166            8
#> 6:             AT&T     USA    TN 4000     163            9
#>
#> $data2_nomatch #> Name country state_code SIC_code earnings unique_key_2 #> 1: Bershire Hathaway USA NE 2220 220,000 2 #> 2: Apple Computer USA CA NA 220,000 3 #> 3: McKesson Corp. MA 2222 190,000 5 #> 4: CVS RI 1122 180,000 7 #> 5: GM MI 2222 170,000 8 #> 6: AT & T USA TN 4000 160,000 9 #> #>$match_evaluation
#>    tier matches in_tier_unique_1 in_tier_unique_2 pct_matched_1 pct_matched_2
#> 1:  all       4                4                4           0.4           0.4
#>    new_unique_1 new_unique_2
#> 1:            4            4

Note that we have an extra column, ‘wgt_jaccard_sim’, that shows the similarity score for the weighted Jaccard method.