Catch Me if You Can: Outlier Detection

Predicting Uber demand by means of historic evaluation (Taxi Trajectory Streams)

Taxis | Beijing Picture revealed on

Outlier detection is an fascinating information mining job that’s used fairly extensively to detect anomalies in information. Outliers are factors that exhibit considerably completely different properties than the vast majority of the factors. To this finish, outlier detection has very fascinating functions resembling bank card fraud detection (suspicious transactions), visitors administration (drunk/rash driving) or Community Intrusions (hacks) and many others. Because of the time-critical nature of those functions, there’s a want for scalable outlier detection strategies.

On this undertaking, we are going to purpose to detect outlier in a Taxi Dataset (Beijing), utilizing a way that solely makes use of spatio-temporal traits to detect outliers in very giant datasets. We might be utilizing the geo-coordinates and the timestamps collected by the GPS on these taxis.

For this undertaking, we might be utilizing the T-Drive dataset. This dataset has 15 million factors, covers a complete distance of 9 million kilometers from a complete of 10,357 taxis in Beijing. This an excellent pattern dataset as a result of it accommodates a really giant variety of factors, mimicking our real-life situations mentioned above. Every row on this dataset corresponds to the geo-coodinates of the taxi and the timestamp.

The algorithm that we’ll be utilizing for this drawback is the Outlier Detection Over Huge Trajectory Stream. To implement the algorithm, we’re gonna want some background data on the technical phrases.


A trajectory of a transferring object O, is outlined as a sequence of trajectory factors produced at time-bins t1, t2… denoted as Tri = P1i , P2i , …..Pji

Level Neighbor

If two trajectory factors, Pij , Pik , in the identical timebin Ti are inside a distance of d of one another, the place d is a distance threshold, then these two factors are thought-about level neighbors of one another.

Trajectory Neighbor

In a selected window Wc, a trajectory known as a neighbor trajectory if and provided that for not less than thr timebins, the trajectories share level neighbors in every of those timebins.

Trajectory Outlier

A Trajectory Tri is taken into account an outlier in window Wc, if in not less than thr time-bins, there are lower than ok variety of factors which can be level neighbors, the place ok is the neighbor depend threshold.

This definition is attempting to seize the concept if a trajectory is regular, it ought to have comparable factors in shut proximity each in area and throughout time-bins. In different phrases, these trajectories have to be behaving very equally and constantly for it to be categorized as an inlier within the explicit window.

Instance Trajectories | Tr4 is an outlier

To clarify the algorithm, let’s check out the instance above. We might be analyzing Trajectory Tr3 & Tr4. The dashed circles denote level neighbors for the trajectories. Let’s take thr=2 and Okay=three:

Tr4 has not less than thr (2) variety of level neighbors with Tr1 (t2,t4) & Tr3 (t2,t4) solely. Since, it solely has thr level neighbors for lower than Okay trajectories (on this case solely 2 trajectories), it’s an outlier.

Tr3 has not less than thr (2) variety of level neighbors with Tr1 (t1,t2,t3,t4), Tr2 (t1,t2,t3) & Tr4 (t2,t4). Because it has thr level neighbors for not less than Okay=three trajectories (Tr1,Tr2,Tr4), it’s not an outlier. For extra data, you’ll be able to learn the instance within the paper.

Loading the info

Step one entails loading the dataset (*.txt). For the reason that dataset is split into .txt recordsdata for every taxi, we have to learn all of the recordsdata within the T-Drive folder.

We additionally have to extract the values of timestamps (Month, Day, Hour, Minutes), Latitude and Longitude. Break up() is the quickest strategy to break the person values in every row

Information Preparation

The subsequent step, as in any information job, is cleansing the info. A fast have a look at the dataset reveals inconsistent sampling charges for the taxis within the dataset. Some taxi document location each min, whereas others skip a few minutes. To deal with this, we are going to use linear interpolation to fill the lacking values. The instance beneath exhibits a lacking worth for timestamp (T2). The lacking worth is calculated by taking the imply distinction between T1 and T3 and including it to T1.

Distance Perform

As , the placement stamp for every pattern is in geo-coordinates. Nonetheless, we’d like additionally have to calculate the gap between two coordinates to verify whether or not the factors are neighbors (d threshold). To unravel this problem, we use the Haversine Approximation.

Outlier Detection

Wanting on the algorithm, it’s apparent the slowest a part of the algorithm is the search question. To realize optimized efficiency, we are going to use kd-trees which can be designed to cater multi-dimensional factors (lat/lengthy in our case). We will use the Scipy library to assemble the kd-tree with the geo-coordinates.

After the tree is constructed, we are going to use the query_ball_point() perform to search out the neighbors inside our d threshold.


The T-Drive dataset doesn’t present us with floor reality values. One strategy to visualize the outcomes is plotting them on a Google Map. I used the Python shopper library for Google Maps API Internet Companies to plot the trajectories as present beneath.

Trajectory Outliers in a single window. The purple strains symbolize trajectories that had been recognized as outliers the place as blue strains symbolize regular trajectories. Many of the remoted trajectories, as proven, are accurately recognized as outlying.

As you’ll be able to see from the plot, many of the congested trajectories have been accurately recognized as inliers. Trajectories that aren’t shut spatio-temporally have been recognized as outliers with some errors, as may be see within the map.

This algorithm will also be utilized in different situations resembling bank card fraud detection or shares monitoring. Similar to geo-coordinates, we will use inventory worth/quantity because the traits to find out whether or not a inventory would carry out higher or worse, as an illustration.

Different works embrace utilizing segmentation and partitioning to enhance outlier detection outcomes. In one other article, I’ll cowl utilizing a number of cores to divide the workload amongst CPUs to attain increased efficiency.

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