Data Science Bookcamp: Five Python Projects MEAP V04 by Leonard Apeltsin

Author:Leonard Apeltsin [Apeltsin, Leonard]
Language: eng
Format: epub, mobi, pdf
Publisher: Manning Publications Co.
Published: 0101-01-01T00:00:00+00:00

Figure 12.3. Mapped K-Means city clusters. K is set to 6. Africa’s clustered points are incorrectly split between the European and Asian continents.

Increasing the K improves clustering within the North and South American continents. South America now falls within its own searate cluster, and North America is split between two Western and Eastern cluster groups. However, on the other side of the Atlantic, the clustering quality remains low. Africa’s geolocations are incorrectly split between the European and Asian continents. K-mean’s sense of centrality is unable to properly distinguish between Africa, Europe and Asia. Perhaps the algorithm’s reliance on Euclidean distance is preventing it from capturing relationships between points distributed on our planet’s curved surface.

As an alternative approach, we can attempt to execute DBSCAN clustering. The DBSCAN algorithm takes as input any distance metric of our choosing, allowing us to cluster on the great-circle distance between points. We’ll start by coding a great-circle distance function whose inputs are a pair of NumPy arrays.

Listing 12.20. Defining a NumPy-based great-circle metric

def great_circle_distance(coord1, coord2, radius=3956): ❶ if np.array_equal(coord1, coord2): return 0.0 coord1, coord2 = np.radians(coord1), np.radians(coord2) delta_x, delta_y = coord2 - coord1 haversin = sin(delta_x / 2) ** 2 + np.product([cos(coord1[0]), cos(coord2[0]), sin(delta_y / 2) ** 2]) return 2 * radius * asin(haversin ** 0.5)

❶

radius is preset to the radius of the Earth, in miles.

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