# Implementing K-means clustering to find an optimal location to open an exclusive gym in Manhattan

This post is part of IBM Data Science Capstone Project.

**Table of Contents**

- Introduction
- Data
- Methodology
- Results
- Conclusion

**Introduction:**

While exciting, starting a new business can also be very risky. There are many factors that need to be taken into consideration for the success of a new business, such as location, competition, safety. The purpose of this project is to find an optimal location for opening an exclusive gym at Manhattan, NY. To answer this question for a client who is seeking the best area to open a new exclusive gym, we first have to determine which neighborhoods are considered safe, find which neighborhoods have high income, and look into the nearby competition since we want an area that is not very competitive to increase the chances of a successful business.

**Data:**

The following datasets were used in this project:

· NYC census to determine neighborhoods with high income

· NYPD arrests to determine the safest neighborhoods

· NYC borough and neighborhood data with Latitude and Longitude

· Venues data was obtained from Foursquare API

**Methodology:**

The first step of is to find Manhattan neighborhoods with high income using the Census dataset. To accomplish this, we are going to merge the census track and census block datasets, and filter to only keep data that contains Manhattan income information. Since we need to extract neighborhood information from the latitude and longitude data, we are going to use reverse Geocoding to extract neighborhoods from the address and create two new columns in data frame: Neighborhood and Suburb. The reason we need Suburb information is because we notice that some of the rows were missing neighborhood information but had suburb data, and we will use that to filter data only to Manhattan.Figure 1. shows merged census data that contains 41 columns and over 18 thousands rows.

Once we have all neighborhoods, next we focus on income. Figure 2. represents distribution of income.We are looking for neighborhoods with high income, so the data is filtered on neighborhoods with more than 10 occurrences of an annual income higher than $100k per neighborhood. As a result, we have a list of 16 neighborhoods(Figure 3. )

The next step is to find neighborhoods with low crime rates. For this, we will be using the NYPD arrest dataset. This dataset contains a lot of information on the date and time of the crime, the type of crime, the perpetrator’s sex, age, etc. For our purpose we narrowed down attributes to date, type of crime, arrest borough, and latitude and longitude.Figure 4. presents crime frequency, we can see that petit larceny, assault and burglary are top 3 crimes in Manhattan. As with the previous dataset, we are going to use reverse Geocoder to extract information about the neighborhoods where the crimes occurred.

Once we did that, we took a closer look into the frequency of crimes that occurred in Manhattan neighborhoods, setting the threshold to less than 300 occurrences. Our result was list of more than 30 neighborhoods with low crime Figure.5

As a final result we got the intersection between the list of neighborhoods with low crime and neighborhoods with high income and we had total of 7 neighborhoods that will be used for further analyses: *Battery Park City, Financial District, Hudson Square, Midtown East, Morningside Heights, Upper East Side* and *Yorkville*. In order to segment the neighborhoods and explore them, we need a dataset that contains NYC’s 5 boroughs and their neighborhoods, with latitude and longitude information for each of them. We created a dataset that contains common neighborhoods and their geographical locations. Next, we utilized the Foursquare API to obtain information about venues that are found in our neighborhoods and we sorted them by frequency to get only the top 10 most frequent ones.

All the work above was done to prepare our data for the next step which was applying the K-Means machine learning algorithm to cluster our data. The measure of centrality of data can be used to analyze the difference between the means of different groups of observations. We can utilize this difference to determine if observations belong to the same group. All data points within a single group should cluster around their central value. We used two methods to determine what would be optimal K value. First, we used The Elbow method which depends on a calculated value called inertia, which is the sum of the squared distances between each point and its closest K-means center. If K is 1, then the inertia will equal the sum of all squared distances to the dataset’s mean. Figure 6. represents Elbow Plot

Second, we used the Silhouette score which captures the distance of each point to neighboring clusters. It can be used to study the separation distance between the resulting clusters. The silhouette plot displays a measure of how close each point in one cluster is to points in the neighboring clusters and thus provides a way to assess parameters like number of clusters visually. This measure has a range of -1, 1. A higher Silhouette score would indicate optimal K value. We concluded that 3 is an optimal number for K value based on results we obtained fro Elbow method and Silhouette score.

## Results and Discussion:

After applying the K-Means clustering algorithm to our dataset, we had each neighborhood assigned to one of the 3 clusters. We used the Folium map to visualize clusters on map of Manhattan( Figure 7.)

Next, we carefully examined each cluster and its neighborhood venues

*From the first cluster we could see that neighborhoods *Midtown *and *Battery Park City* are clustered together. Looking closer into venues we can see that both of them have a Gym listed in top 10 venues.

*Neighborhoods *Upper East, Yorkville, Financial District* and *Hudson Yards* were clustered together in second cluster. We also notice that all of them contains Gym in top 10 venues.

* In the third cluster we have only one Neighborhood: *Morningside Heights.* Taking a closer look into venues we can see that this is the only cluster that does not have a Gym in 10 most common venues.

**Conclusion:**

In this project, we looked to find an optimal location to open an exclusive gym. To answer this question for our client, we had to take a few steps. Our approach was to evaluate Manhattan neighborhoods based on income, crime rate, and nearby competition. Once we had neighborhoods with high income and low crime rate, we used the Foursquare API to get most common venues in those areas. We applied K-Means to cluster neighborhoods and used the Folium map to visualize them on a map of Manhattan. Analyzing each cluster, we concluded that the third cluster, containing the neighborhood *Morningside Heights*, would be an optimal location to open a gym.

Jupyter Notebook with detailed code can be found here: https://github.com/sivosevic/Coursera_Capstone/blob/master/IBM_capstone_Notebook.ipynb

Thanks for reading!