XO Vendor Record Linkage (part 1 of 3)
XO Vendor Record Linkage (part 1 of 3)
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Kris Pickrell, XO Group Inc.
In any system where a primary goal is to acquire more of a certain kind of data, there is a certain risk of introducing duplicates. This is especially the case where a variety of loosely controlled processes generate data, or where uncoordinated human action generates data, such as is the case with user entry via web forms. In the first of this three-part series, we will discuss the origin and cost of duplicates, assume their inevitability, and will show both how they can be detected, and how to leverage them to improve the quality of our data.
A duplicate is a pair of records in a single namespace whose content may differ slightly, however, they ultimately refer to the same entity. For example, your insurance agency probably has a record somewhere of your automobile:
Let's say the local sheriff's office had an eerily similar entry:
Whereas these would be duplicates in the global scheme, they wouldn't technically be problematic duplicates because they would exist in different databases. If, however, the databases were merged into the same namespace, there might be a problem. Consider what would happen, for example, if the car were sold. The owner field would need to be updated, but the potential exists to only update one of the records. This means there exists a real possibility of the law harassing an innocent owner, or of an insurance claim being denied until proper ownership could be proven. Note also that it is not entirely straightforward to link the duplicate records without a common and very specific key, a VIN for example. One must rely on inferential knowledge like Orange and Orange/Black are basically the same thing, Luke Duke is one of the Duke Cousins, Dodge is owned by Chrysler Corporation, and so on. In the next section, we will begin to look at techniques to detect, with a high degree of certainty, that these refer to the same entity, namely The General Lee. We will show how this determination can be made in spite of the absence of a single, uniquely identifying feature, and allowing for the fact that the field values are different, whether intentionally or accidentally.
Perhaps the most straightforward approach to duplicate detection relies on the fact that duplicates tend to have high string similarity. For example, in the above case, Orange and Orange/Black have the first 6 characters in common. Based on this single fact alone, there is some nominal probability (keep that in mind for a bit) that these records refer to the same vehicle. Intuitively, by the law of compound probability, we might dismiss two vehicle records as being duplicates based on the coincidental similarity of only one field, but we would be less and less inclined to do so if two fields were similar, three fields were similar, and so on. In fact, we can show that by measuring the string similarities over multiple fields, we can model this compound probability to within a high degree of accuracy. One subtle but important thing to remember is that we are using string similarity as a proxy for semantic similarity, which is really what we are concerned with. It is usually, but not always the case, that string similarity proxies semantic similarity: Robert~Bob, Abbey Road~Abbey RD, 5125551212x400~(512) 555-1212. But Dodge<>Chrysler, as in our above example. We will see that, since our concern is with probability, our model will allow for some significant dissimilarity as long as the right amount of information is similar enough.
Now that we've made the leap that string similarity over a combination of fields will track with the probability that two records are duplicates, our task becomes pretty simple...well, maybe not simple, but tractable. This may seem like an odd statement, as this is the part where some math enters into the equation, but that's the essence of what mathematical modeling is: simplifying the world around us in some reasonable way so we can have more than a reasonable chance of tackling tough problems.
As we are trying to determine the probability that two records are either duplicates or non-duplicates, we need a model that can give us this probability with respect to a combination of input measurements. For this, we can use a technique called logistic regression. Logistic regression (LR) estimates the log of the odds as a linear combination of inputs. In not so many words:
is the probability that a record is a duplicate, and each
is the measurement of the predictor we choose:
multiplied by the strength of it's corresponding contribution to the log-odds:
. Our concern with odds in terms of probability is instructive. Recall that odds give the relative magnitude of hits and misses. If we want to roll a 3 on a fair, six-sided die, the probability of hitting a 3 is 1 in 6, or 1 / 6 ~ 0.1666... But the probability of hitting something other than a 3 is 5 in 6, or 5 / 6 ~ 0.8333... So we say the odds are "1 to 5". Or 0.166../0.833.. ~ 0.2.
This model allows us to set up the right side as a linear equation of our inputs, which we will define in a second, and estimate the odds that our prediction "It's a duplicate" is true. Remember where we wanted to combine similarity among various fields into an overall compound probability that the records are duplicates? If we set up our
's to be some sort of measure of similarity, we then need to determine the appropriate
's that reflect the real predictive power of the similarities in the respective fields. For example, a high similarity in the make field increases the probability that two records are duplicates by some amount, but this amount is most likely different from the increase provided by the similarity in the color field. We then have a two-fold task: 1. Find measures of similarity 2. Estimate the appropriate
's. We actually have a pretty significant task to accomplish in (1). Not only do we need to find the right way to measure similarity, we need to find the right fields to put into our model. Intuitively, we would want to select fields whose data tends to be correlated: for example, "name". We wouldn't want to put something like a GUID in our model, as the similarity would be very low for all records (google maximum-entropy models), both dupe and non-dupe, and there is probably zero correlation between two records' GUIDs and their contents. This is one really nice thing about using a statistical model like LR that preserves the marginal probabilities of the data we use to train it in the coefficients. We can see how the coefficients (
's) behave in order to make some judgments about each of the predictors (
's). If the coefficients are independent, it means there is little covariance between the inputs.
Several techniques exist for measuring the similarity between two strings. These are nominally string metrics or string distance functions. The idea is to compute some numeric distance between two strings so that the shorter the distance, the more similar the string. For example: the strings "Sam" and "Samuel" should be closer than "Sam" and "Bob". This is, however, somewhat of a philosophical question; with respect to shorter versions of full names, "Sam" and "Bob" are more similar than "Sam" and "Samuel" whereas when referring to the same named individual, the former is closer. That is the majority case for what we are concerned with, but it's nice to keep in mind the assumptions behind what we mean by similar. We'll also leave aside the mathematical foundation of what a metric is. Just remember that when discussing linear classification like logistic regression, it's important that our distance functions be mathematical metrics. That is, they obey certain properties that make them behave like true distances. It's not terribly important exactly which metric we use or what it's natural range of values is. That's another nice thing about using LR is that it's the relative magnitude of the coefficients that determines probabilities and not the exact magnitude.
Many string metrics have been devised over the years. Perhaps the most recognizable is the Levenshtein distance. The Levenshtein distance is the minimum number of single-character edits required to transform one string into another, where edit is either substitution, insertion or deletion. For example: Levenshtein( Sam, Samuel ) = 3 because we can perform 3 single-character operations to Sam (add u, add e, add l). Levenshtein ( Sam, Bob ) is also three because we can substitute each of the three characters in "Bob" for each character in Sam. Note how in this case, Levenshtein fails to capture the semantic similarities: Sam is close to Samuel as referring to the same name, but closer to Bob in that they are both abbreviations. But for most purposes this will do.
Now that we have some way to generate our
's, we need some way to find the
's. For this we will use representative samples (examples) of our data that we have labeled as being either a match or a non-match. Once we have done that, we can use an iterative learning technique to estimate the
's. The general algorithm is the followingA:
Recall what we are doing here. We are first taking a labeled (match/non-match or 1/0) pair of records and we are generating a set of measurements of this pair. We then use these measurements along with the corresponding label to determine, or learn, the coefficients of our model. In other words, with the right coefficients, by simply plugging our measurements into the logistic equation, we will get a probability that those measurements correspond to one of our labels. If we call match 1, and non-match 0, a value of 0.97 represents a 97% probability that the measurements correspond to a match. We call the set of labeled pairs we use to determine the coefficients the training data. As long as our training data is drawn from the distribution of records we will eventually be deduplicating, we can be somewhat confident that the ratios we learn from our training data will also apply to duplicates in our record set in general.
This is far too thin a treatment for such a thick concept but hopefully you have a feel for how (or some terms to google) we can tackle the problem of intelligently modeling and comparing any two records to determine the probability they are duplicates based on a review of examples in our training data. A problem of scale exists, however, when we attempt to find all duplicates in any large set of records. As we must compare each record to each other record, for N records, each record will be compared to N-1 records. But since comparing A-B is the equivalent of comparing B-A, take half of this, and we have (N*(N-1))/2 comparisons. For a database of 100,000 records, this comes out to about 5 billion comparisons. If we can model and compare 5,000 records/second, we are looking at 9 months to complete this operation. In the next article, we will see how we can reduce the number of comparisons using indexing and clustering techniques that will provide a reasonable trade-off between runtime and overall recall.
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