Posts Tagged how-to
Gaps and islands problems involve finding a range of missing values (gaps) or a range of consecutive values (islands) in a sequence of numbers or dates.
Recently, I had to produce a dataset which showed how our interest rates varied over time, by product; for example, products A to E started at 10% through to 50%, but have been adjusted periodically to where they are today, a few points different. Practically, most of the changes have been made at or around the same time — but not exactly. For technical reasons, the specified rates aren’t stored in the database, so there’s no InterestRate table, or a parent table called InterestRateSet that links them together. However, the final result of an application is stored, so we know that a product has been sold, and what the corresponding interest rate was on that day.
The challenge was to work out how many sets of interest rates we’ve had since day 1; but because not every product is purchased every day, if we group by product/day, then it looks like our rates change more often than they do. This is where the ‘gaps and islands’ concept comes in, and luckily I remembered the lecture from a few years before. I found and tweaked some of Itzik’s code from a 2012 article Solving Gaps and Islands with Enhanced Window Functions (SQL Server Pro website) to accept a UDT (in this case, a list of dates). [See previous post, Passing structured data to stored procedures.]
Here it is:
-- Drop/Create our UDT: IF EXISTS (SELECT * FROM sys.types WHERE is_table_type = 1 AND name = 'DateListType') DROP TYPE DateListType GO CREATE TYPE DateListType AS TABLE ([Date] DATE) GO -- Drop/Create our function: IF OBJECT_ID('dbo.fn_GetIslandsFromDateList') IS NOT NULL DROP FUNCTION dbo.fn_GetIslandsFromDateList GO CREATE FUNCTION dbo.fn_GetIslandsFromDateList ( @dateListType DateListType READONLY ,@GapSize INT ) RETURNS TABLE AS RETURN ( WITH cte_Distinct AS ( SELECT [Date] FROM @dateListType GROUP BY [Date] ), cte_Part1 AS ( SELECT [Date] ,CASE WHEN DATEDIFF(day, LAG([Date]) OVER(ORDER BY [Date]), [Date]) <= @GapSize THEN 0 ELSE 1 END AS IsStart ,CASE WHEN DATEDIFF(day, [Date], LEAD([Date]) OVER(ORDER BY [Date])) <= @GapSize THEN 0 ELSE 1 END AS IsEnd FROM cte_Distinct ) , cte_Part2 AS ( SELECT [Date] AS RangeStart ,CASE WHEN IsEnd = 1 THEN [Date] ELSE LEAD([Date], 1) OVER(ORDER BY [Date]) END AS RangeEnd ,IsStart FROM cte_Part1 WHERE IsStart = 1 OR IsEnd = 1 ) SELECT ROW_NUMBER() OVER (ORDER BY RangeStart) AS ID ,RangeStart ,RangeEnd FROM cte_Part2 WHERE IsStart = 1 ) GO
Some things to note:
- dbo.fn_GetIslandsFromDateList is an inline function, which you can almost think of as ‘a view that takes parameters’ (a parameterised view).
- You can use CTEs (Common Table Expressions) in inline functions. I love using CTEs, they can make the code very readable. Often, the parser turns them into standard sub-queries, so there’s no performance hit.
- The @GapSize parameter controls how far apart our islands can be — see the examples below.
- If you follow the code through, and break it down in to its component parts, you can see how it works — like all the best code, it’s very neat and compact.
- To re-emphasise, this isn’t my algorithm, it’s Itzik Ben-Gan’s; I’ve done little more than re-format it for my own use.
Let’s feed some dates into our function:
DECLARE @myList DateListType INSERT @myList([Date]) VALUES('2017Feb01'),('2017Feb02'),('2017Feb03') ,('2017Feb06'),('2017Mar01'),('2017Mar02') SELECT * FROM dbo.fn_GetIslandsFromDateList(@myList, 2) GO ID RangeStart RangeEnd ---- ---------- ---------- 1 2017-02-01 2017-02-03 2 2017-02-06 2017-02-06 3 2017-03-01 2017-03-02
With a @GapSize of 2, we get 3 ranges (islands). With a @GapSize of 3:
SELECT * FROM dbo.fn_GetIslandsFromDateList(@myList, 2) GO ID RangeStart RangeEnd ---- ---------- ---------- 1 2017-02-01 2017-02-06 2 2017-03-01 2017-03-02
, we get 2 ranges, because the difference in days between 2017-02-06 and 2017-02-03 is less than or equal to 3.
So this code did the trick, and allowed us to work out exactly how many different sets of rates we’d actually had live. Yes, we could’ve worked it out by hand; but now we’ve got some reproducible code that can drive various different reports, that’ll show us exactly how our changes have affected the business.
A final thought: Quite often, solving a problem comes down to just knowing the right phrase to google!
Following on from the previous post, here’s my own recipe for a people-matching system. I don’t go into all the gory technical details – the post would be five times the length – but I hope there’s enough here to get the theme across.
Let’s assume a few things:
- We have a large number of Person records (millions?), all from the UK.
- We believe that a significant proportion of these records are duplicates or redundant, as they represent the same people; but the details may differ.
- We only want to identify the records that match; we’re not looking to build a single all-encompassing representation of a person, wherein data from one record ‘enriches’ another. (More to come on that subject in a future post.)
- The quality of data in each Person record varies, maybe markedly; some records may be customers we have a long-standing relationship with, and are very confident of their details. But other records might come from less trusted or unverified sources, e.g. a survey on the website that promises a voucher in return for answering some questions and entering a few personal details; these details would clearly be less reliable.
- Our records have the following details (‘data points’):
- First name
- Last name
- Date of birth
- Mobile phone number
- Email address
, plus a unique PersonID. We might have other data points available, e.g. home telephone number, employment details, bank account number / sort code, and we could absolutely use them for matching. For now, we’ll concentrate on the six above.
- Every Person record only has one set of details, that is, just the six pieces of information that we’ll use for matching. This restriction isn’t that realistic – people can have more than one mobile number or email address, and they move house, and occasionally change their names. Taking this into account in a system doesn’t significantly alter the structure of what’s being proposed here.
For each one of these data points, we want to generate and store what is known as the canonical version: that is, the version that is as standard as we can possibly make it. For names, the simplest thing to do is remove spaces, hyphens and apostrophes, which will help us match “Peter O’Toole” against “Peter Otoole”, or “Andrew Lloyd Webber” against “Andrew Lloyd-Webber”. Dates of birth don’t need changing, as long as they’re being stored in a sensible format (so in SQL we should be using DATE, and not VARCHAR). Phone numbers might be accepted in our system as “+442077319333” or “020 7731 9333”, but we need to translate them into one format – I’d go for the former.
Email addresses: As mentioned in the the previous post, email domains can be synonyms of each other, e.g. gmail.com and googlemail.com. Depending on your data, making domains canonical might be too much effort. Also, with some providers (including gmail) the local part of the address (the left-hand side of the @ symbol) can contain labels, so you’ll need to strip those out to make the canonical version.
Addresses: Making canonical versions of bricks-and-mortar addresses can be the biggest headache, which is why you’ll need an address validator: a piece of software that takes an unformatted address, and turns it into a formatted address. Examples of address validators include PCA Predict (formerly Postcode Anywhere) and Experian Data Quality (formerly QAS). The way they work is that if we present, e.g.
10 SW1A 2AA
10 Downing Street City Of Westminster LONDON
to the validator, then we’ll get the same result back:
10 Downing Street LONDON SW1A 2AA
If you pay for the extra data, then you can get the UDPRN (Unique Delivery Point Reference Number), which maps every postal address into an 8-digit code. If not, you can make your own loose version of it by hashing the text of the validated address, which you can then use for comparing.
From this point on, I’ll assume (a) that all our data points are canonical, and (b) there are no known ‘test’ people within our data – if there are, we should remove them from any matching process.
Excluding common data points
Next, we’ll need to consider generating lists of common and/or dummy data. For example, what are the most popular mobile numbers in the data?
In SQL, our query would look something like this:
SELECT TOP 20 Mobile, COUNT(1) AS Total FROM dbo.Person WHERE Mobile IS NOT NULL GROUP BY Mobile HAVING COUNT(1) > 1 ORDER BY COUNT(1) DESC
If your data comes to you via third parties (e.g. affiliates, introducers, brokers), I should imagine you’ll see something like:
+447000000000 +447777777777 +447123456789 +447111111111 ...
with some surprisingly large counts against each. You clearly can’t use these mobile numbers for matching; in fact, you should look at all the associated Person records, to see if it’s worth excluding everyone with obvious dummy numbers like these. But you’ll probably just want to exclude this data point from the match, not exclude the entire Person record.
Similarly, you’ll need to do the same for email addresses, e.g. email@example.com, firstname.lastname@example.org, etc.; and home telephone numbers, if you capture them. (As mentioned previously, when faced with a home telephone number field, some people like to enter phone numbers for their local Chinese restaurants, taxi firms and pubs.)
It’s not as necessary to identify common names and addresses, although you might see a few Joe Bloggs, John Smiths and David Camerons. [Brief aside: it’s always useful to have a table containing the headline details of famous people, so you can stop them getting into your system at the point of entry. It’s unlikely you’ll end up with the Prime Minister’s mobile number or email address in your database – but his name and address are no secret!]
We’re at the point where our data is as standard (canonical) as we can make it, and we have lists (tables) of data points we know we’re NOT going to be matching.
The next step is to ask: Given two sets of details, by what criteria would we confidently say “yes, these two people are the same”? A complete match would be:
First name, Last name, Date of birth, Address*, Mobile, Email, Home phone
, i.e. every single piece of information – but that’s the most obvious case, and there are certainly subsets of these details that we’d be happy to accept.
(* Address meaning either a UDPRN or a hashed version of the text data returned from the validator.)
If the details of Person A matched those of Person B, for any set of the following details, I’d consider the match to be a hard match:
- Set 1: First name, Last name, Postcode, Mobile, Email
- Set 2: First name, Last name, Address, Mobile
- Set 3: First name, Last name, Address, Email
- Set 4: Last name, Date of birth, Postcode, Mobile, Email
- Set 5: First name, Last name, Date of birth, Address
- Set 6: Date of birth, Address, Mobile
- Set 7: Date of birth, Address, Email
where Set 1 is the best, and Set 7 the ‘least best’. (You, and your data, of course may disagree.) So, every single piece of information in a set has to be identical between person A and person B for us to consider it a match.
Note that no set of details is a subset of any other; the larger set of details would be redundant.
Remember that, if at all possible, our criteria shouldn’t match the following people:
- Parents and children with the exact same name
- Older relatives borrowing mobile numbers and email addresses from other family members
For each Person record, we’ll make (up to) 7 separate hashes, one for each set of details, and store them in a new table. An MD5 hash takes up 16 bytes, so if we had a million records, it’s a maximum of 150MB in space (if we include numeric IDs for the Person and for the set of details).
Finding hard matches between Person records then becomes as simple as finding hashes with more than one PersonID entry in our table – a simple GROUP BY, which if indexed properly, will be lightning quick.
(NB: If we’ve decided that a piece of information in a Person record isn’t suitable for matching, due to being too common or an obvious dummy, then we can’t generate any hashes that include that piece of information; we can’t just put a blank in, the match would be too loose. That’s why it’s “(up to) 7” – not “7” – hashes.)
What about the rest of our data? We’ve three options:
- Do nothing. Depending on our requirements, this might be ok; in the grand scheme of things, what’s a handful of duplicate emails / letters / phone calls?
- Manual matching. Again, depending on our situation, this might be perfectly feasible. If there’s any human intervention (for example, a phone call) in our end-to-end process, then it could be straightforward to give your customer-facing employees a screen that says “We’ve found these sets of details that might be the same person, do you agree?”, then let them approve or reject the match.
- Scoring. Give various amounts of points to each part of the match criteria, depending on the strength of match between data points. If you like, you can consider this a soft match (cf. the hard matching above).
The second and third options require that you’ve some reason to believe a match might exist in the first place, e.g. an email address or mobile number in common; or a combination of date of birth and postcode. With the right indexes on the data, it’s trivial to generate these candidate lists quickly. (Of course, you don’t need to attempt to match Person records you’ve already matched against each other.)
The goal is to come up with a scoring mechanism such that likely matches get more ‘points’ than unlikely ones. Outside of some Very Hard Computer Science (probably involving neural networks), I don’t know of any standard ways of generating scorecards where the outcome is unknown – if the outcome is known, then standard methods apply (Google: Building a scorecard.) However, for this particular application, common sense should get us where we want to go.
For string data like names (first or last), we can make an educated guess at a scoring mechanism, e.g.
- Full match: 10 points
- One letter out: 9 points
- Name A is contained within B (or vice-versa), e.g. “Carter” would match “Knowles-Carter”: 7 points
- First n letters of A = First n letters of B, where 1 ≤ n ≤ 4: n points
- Last n letters of A = Last n letters of B, where 2 ≤ n ≤ 5: n-1 points
- Both names are longer than 5 letters, and have 2 letters incorrect: 2 points
I don’t know that the above is optimal, but it feels like a good starting point.
How do we assess how far apart strings are? We need a function that, given two strings, calculates some notion of ‘distance’ between them. Such functions already exist, and the Levenshtein distance (the number of insert/replace edits needed to turn one string into another) is a popular choice.
For non-string data like dates of birth, we’d start with something like:
- Full match: 8 points
- One day out: 7 points
- Month / day swapped: 6 points
- One month out: 5 points
- One year out : 4 points
- Day and month correct: 3 points
etc. I’m sure you get the idea: the point is we have lots of options!
Hence, we build up a scorecard that takes two sets of details and returns a single number, a score. We can apply this scoring function to every pair of details in our candidate list, and generate a score for all matches. Inspecting these matches by eye, it becomes fairly obvious what a good threshold for acceptance would be, and what changes to our scorecard are needed. Within a few iterations, we should have a scorecard and threshold that give us the balance we need between matching correct sets of details (where correctness is assessed by eye, by manually checking a sample), and not matching incorrect sets of details.
The scorecards can get as complicated as you like: you can award extra points for an uncommon domain in the email addresses, or for having the same post town, or the same home phone number area code; you can subtract points for too many repeated digits in the mobile numbers, or having 1st January as the date of birth, or having a common name (‘John Smith’). The law of diminishing returns applies in spades – you have to determine whether the extra effort is warranted.
One very important thought: you MUST record exactly how a match between two sets of details was made. Was it a hard match? If so, which one? If the match was via a scorecard, which scorecard was it? (You’ll end up with more than one.) What was the score? What was the threshold that it passed? If you don’t record this information, you can’t hope to reliably improve on the matching process in future.
I’ve not finished on this subject yet, but hopefully this article gives you some ideas about building your own person-matching system, should you require one. I’ve yet to cover:
- Generating single person objects from matches
- How you practically use such objects within your applications
I’ll come back to these topics soon.
As ever, if you’ve any comments, I’d love to hear them!