Where is the center Consider the following n 7 points 54 95

Where is the center? Consider the following n = 7 points: 5.4, 9.5, 9.6, 1.5, 9.7, 9.5, 4.8. Find the center c separately for the three cases below: A 2-norm center that minimizes sigmma^n_i = 1 |x_i - c|^2. A 1-norm center that minimizes sigmma^n_i = 1 |x_i - c|. An infinity-norm center that minimizes max^n_i = 1 |x_i - c|. Explain, in words, what interpretation the three centers have, respectively.

Solution

1))))))))))

inorder to minimizethe objective function we should take the center from the datapoints suchthat the center value should be comparitvly neare to the each and every datapoint.

so better to choose mean of the datpoints as a center and then calculate the objective function

as we are taking mean as center which is close to every data point comparitivly then by subtracting it with every data points gives the smaller values

thus the objective function is minimized.

2))))))

in this perspective also mean is considered to minimize the objective function as a center

3)))))))))

In this case consider the center that minimixes the objective funtion and the datavalue that is maximum