# Location Ranking

I am delighted to share with you a small glimpse of the data science magic under the Polaris hood. In this post, I will shed some light on our machine learning tools and Ubimo’s pursuit for guaranteeing the highest quality of location data. I will do so by presenting an algorithm that tags and verifies the raw location signals in a self-learning way based just on coordinates, signal count and time stamps. In this manner, we enable decision making and media buying based on the best location signals.

We will start our journey with the tagging of location data which automates detection of fakes and outliers in the system. For the sake of simplification, our basic assumption is that most devices will send their true physical locations and occasionally will send fake location. The fake location will be an outlier, and will be far from the location most other signals came from.

Let us put this assumption to the test by taking all the devices that sent signals from a specific location (AKA: Anchor Location), and looking at all other locations those devices have sent signals from, during the period of a single hour. Then, let us calculate the weighted sum of distances to every location by the number of signals. The output is a value, which can be interpreted as a probabilistic radius around the anchor location, where the devices might be.

In the image above, Anchor Location generated 30 signals. Conjugate Location 1, located 7mi northwest to Anchor generated 10 and Conjugate Location 2, located 1.5mi north generated 8. Probabilistic radius therefore is:

(30 · 0 + 10 · 7 + 8 · 1.5 +….) / (30 + 8 + 10 +…) The first term in the numerator is 30 · 0 since distance from Anchor to itself is zero.

Bear with me, it’s worth it! Next, let us present this data on a visual chart, in order to build a **Probabilistic Radius**:

Each line on the “location distance” chart represents a single day of data, and describes cumulative distribution function of probabilistic radii. This means that for most location points the device did not move more than 60 – 100 miles during an hour. The hypothesis is that locations with an extremely high radius generate noise in the system. Those who have a consistently high radius are considered “Bad”.

OK, but how do we define “consistency”? Consistency, for the sake of our discussion, is an event having a high probability to happen in any given time frame.

Another thing we need to define is “high radius”, or threshold above which probabilistic radius is said to be high. We shall not give this threshold a numerical value at the moment, and rather just denote it as . Later we shall show, that it is more a continuous interval than just a number.

Lets call a location which has radius above on a specific day as “Sparse”, and so we are able to formulate our goal in a probabilistic fashion:

The days when we observe signals from the location, are called “observations”, and those days when the location is Sparse, are called “successes”. Once the proportion of such “successes” reaches some threshold, the location is called “Bad”. This is clearly a Binomial process with probability – a probability that we shall try to estimate using Bayesian methods. Indeed, for every location the probability of location being Sparse times out of , given is Binomial:

In a nutshell, Bayesian learning is about having some prior probabilities for events which are updated as new information becomes available. The updated probabilities are called “posterior”. It is reasonable, that a location which has a probabilistic radius of 300 miles should probably contribute more to the posterior probability, than the one having 70 miles, on any given day. Using statistical modelling (Beta-Binomial fitting) we’ve managed to establish the functional relationship between probabilistic radius and “learning rate”. That relationship is defined through coefficients of function. So, for every threshold radius , we say there is

The higher Probabilistic Radius is, the less “successes” we need to establish that the location is a “Bad” one.

Indeed, we can describe and as function of , call them and respectively:

We then consider location we observed times (days) in the period which had radius over 100 miles at least once. Define the following:

For every observation where the radius was over 100 miles, is the respective . Then calculate average where is the number of times location had radius over 100km. In the same fashion we get .

Now, according to Bayes, the posterior mean for probability of a location being Sparse:

, where is number of times the location was observed with radius > 100, and is total number of observations of location in period

Where

So, we have now some locations tagged as “high quality” and others as “low quality”. Using this tagging, we can calculate for each mobile app, the proportion of signals coming from each location quality type, and rank the data vendor (e.g.: apps and bidstream providing the data) according this metric.

Voila! To conclude, we have seen how by leveraging machine learning, we put in place a mechanism that ensures that we use only the highest quality of data for generating actionable insights. The algorithm “cleans” the location stream of data in a self learning way, taking almost no initial inputs, and by that refrains from placing bids on bad locations and works as a metric for the quality of location data.

Data Scientist at Ubimo

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