数学homework代写 Part 2: Clustering of Trajectories

Part 2: Clustering of Trajectories

数学homework代写 For each trajectory, we will take the first data point as the starting point, and the last data point as the ending point.

Question 7  数学homework代写

The dissimilarity measure

The dissimilarity measure I designed for trajectories are as follow:

For each trajectory, we will take the first data point as the starting point, and the last data point as the ending point. The distance function is the same Euclidean distance we used in Part 1.

Math property

The measure is symmetric because the Euclidean distance is symmetric:  数学homework代写

d = 0 if and only if X = Y

Reason for the design

People daily commute for different purposes, while the route they take everyday may be difference due to traffic and weather, the starting points and destinations should largely stay the same. Therefore we only need to measure the starting point and ending point. If two person travel from residential area to CBD offices, their dissimilarity measure will be very small.

Robust to error  数学homework代写

The error in the middle of the trip will not be counted in the dissimilarity measure.

Question 8  

Yes, my measure is a distance metric. Note that for any 3 points, we have:

The equality holds only if B is in the line between A and C. Therefore:

Question 9  数学homework代写

I will suggest DBScan clustering algorithm.

This is because with a dissimilarity measure, we only have pairwise distance measure between any two trips. And DBScan is ideal for such data input.

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