Google Colab Clustering Assignment Instructions

Objective: Perform unsupervised learning on a vehicular dataset using k$-$means clustering to identify cluster centroids for three different ECU signatures, namely steering, speed, and RPM$.$

Note: This data set was obtained from three sedan vehicles of a single make $($Nissan$).$ It has been pre$-$ processed to obtain the columns relevant to the signatures you will need to use as inputs. These columns are ECU$300($steering$),$ ECU$1$F$9($tachometer$),$ and ECU$280($speed$).$ They contain physical $($or actual$)$ values of these signatures at different time instants. For those interested, the units of speed and tachometer are in miles per hour $($mph$)$ and revolutions per minute $($RPM$).$

Instructions:

$1)$ Navigate to colab.research.google.com in your browser and open the $$ECU Clustering.ipynb$$ Python notebook file using Google Colab $($File $>$ Open Notebook $($or ctrl$+$o$)).$

$2)$ Execute cells individually by clicking on the $$Run cell$$ icon. Alternatively, after you select a cell, you can hit $($ctrl$+$enter$)$ to execute it$.$

$3)$ The notebook has been segregated into three sections: Section $1,2,$ and $3$ contain the k$-$ means clustering implementations for ECU signatures speed, tachometer, and steering, respectively.

$4)$ The following are cells where you need to make modifications for completing the table.

a$)$ Code cells $3,7,$ and $11$ need to be modified to accommodate a MinMax scaling function to normalize the input data $($ECU signatures. Use the same scaling function for all the ECU signatures.

b$)$ Identify the optimal number of clusters $($K$)$ and the sum of squared error $($SSE$)$ using the elbow method for each of the three ECU signatures.

c$)$ Verify your choice of clusters by comparing the results of a clustering metric called the Calinski$-$Harabasz $($CH$)$ score by using different numbers of clusters.

d$)$ Provide descriptive statistics, that is$,$ the minimum, maximum, and mean, for each cluster and for each ECU signature. Use subscripts to designate the statistics for that particular cluster. For instance, the mean value for cluster $1$ could be written as Mean$1.$

Populate the following three tables with your observations.

Table I: Evaluating number of clusters for speed ECU signature

Number of Clusters $($K$)$ SSE $($Elbow Method$)$ CH Score Min, Max, Mean

K $=3$

K $=4$

K $=5$

Table II: Evaluating number of clusters for RPM ECU signature

Number of Clusters $($K$)$ SSE $($Elbow Method$)$ CH Score Min, Max, Mean

K $=3$

K $=4$

K $=5$

Table III: Evaluating number of clusters for steering ECU signature

Number of Clusters $($K$)$ SSE $($Elbow Method$)$ CH Score Min, Max, Mean

K $=3$

K $=4$

K $=5$

Answer the following questions based on your findings.

$1.$ How does the CH score change as the number of clusters $($K$)$ is increased? Provide a justification for your answer.

$2.$ Why can$$t metrics such as precision or recall be used to evaluate the performance of clustering algorithms like k$-$means$++?$

$3.$ What is the optimal number of clusters $($K$)$ that shows consensus among the elbow evaluation method and the CH score?