Which Of The Following Can Be Modeled With A Linear Function? Select All That Apply.

▸ Unsupervised Learning :

For which of the following tasks might K-means clustering be a suitable algorithm
Select all that apply.
- Given a set of news articles from many different news websites, find out what are the main topics covered.
  K-means can cluster the articles and then we can inspect them or use other methods to infer what topic each cluster represents
- Given historical weather records, predict if tomorrow's weather will be sunny or rainy.
- From the user usage patterns on a website, figure out what different groups of users exist.
  We can cluster the users with K-means to find different, distinct groups.
- Given many emails, you want to determine if they are Spam or Non-Spam emails.
- Given a database of information about your users, automatically group them into different market segments.
  You can use K-means to cluster the database entries, and each cluster will correspond to a different market segment.
- Given sales data from a large number of products in a supermarket, figure out which products tend to form coherent groups (say are frequently purchased together) and thus should be put on the same shelf.
  If you cluster the sales data with K-means, each cluster should correspond to coherent groups of items.
- Given sales data from a large number of products in a supermarket, estimate future sales for each of these products.

Suppose we have three cluster centroids $\mu_1 = \begin{bmatrix} 1\\ 2 \end{bmatrix}$ , $\mu_2 = \begin{bmatrix} -3\\ 0 \end{bmatrix}$ and $\mu_3 = \begin{bmatrix} 4\\ 2 \end{bmatrix}$ .
Furthermore, we have a training example $x^{(i)} = \begin{bmatrix} -1\\ 2 \end{bmatrix}$ . After a cluster assignment
step, what will $C^{(i)}$ be?

K-means is an iterative algorithm, and two of the following steps are repeatedly carried out in its inner-loop. Which two?

Suppose you have an unlabeled dataset $\{x^{(1)}, ... , x^{(m)}\}$ . You run K-means with 50 different random initializations, and obtain 50 different clusterings of the data.
What is the recommended way for choosing which one of these 50 clusterings to use?

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Which of the following statements are true? Select all that apply.
- On every iteration of K-means, the cost function $J(C^{(1)}, ... , C^{(m)}, \mu_1, ... , \mu_k)$ (the distortion function) should either stay the same or decrease; in particular, it should not increase.
  Both the cluster assignment and cluster update steps decrese the cost / distortion function, so it should never increase after an iteration of K-means.
- A good way to initialize K-means is to select K (distinct) examples from the training set and set the cluster centroids equal to these selected examples.
  This is the recommended method of initialization.
- K-Means will always give the same results regardless of the initialization of the centroids.
- Once an example has been assigned to a particular centroid, it will never be reassigned to another different centroid
- For some datasets, the "right" or "correct" value of K (the number of clusters) can be ambiguous, and hard even for a human expert looking carefully at the data to decide.
  In many datasets, different choices of K will give different clusterings which appear quite reasonable. With no labels on the data, we cannot say one is better than the other.
- The standard way of initializing K-means is setting $\mu_1 = ... = \mu_k$ to be equal to a vector of zeros.
- If we are worried about K-means getting stuck in bad local optima, one way to ameliorate (reduce) this problem is if we try using multiple random initializations.
  Since each run of K-means is independent, multiple runs can find different optima, and some should avoid bad local optima.
- Since K-Means is an unsupervised learning algorithm, it cannot overfit the data, and thus it is always better to have as large a number of clusters as is computationally feasible.

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