Do you mean k-means clustering or k-nearest neighbors? I ask because the other responses at the time of writing seemed to be talking about k-means Well, k-nearest neighbors is what you said, so... Suppose I want to predict whether or not a person is a lawyer, suppose I know feature measurements X, Y, and Z about this person, and suppose I have a data set including measurements X, Y, and Z of many people, and whether or not they are lawyers. I then compute distances from my given person's data (X,Y,Z) to each of the people's data in the data set. I then choose the k nearest people, and run a voting scheme (for example, if he majority of them are lawyers then I predict that the given person is a lawyer). So basically, classification and regression. k-means, on the other hand, is an unsupervised learning technique used to cluster similar data. More on reddit.com

Yes, your understanding is correct. Let’s make a toy problem to help answer your second two questions. Say I have two labeled mushrooms with features. Edible mushroom, X_e has features [1,0,1] and non-edible mushroom X_n = [6, 5, 11]. Now i give you a mystery mushroom X_i and tell you its features are [1,1,2]. Do you think it’s more likely to be edible or not edible? We just trained a simple KNN classifier with k=1. But eyeballing isn’t a very systematic way of playing this game, especially at scale; so we need some way to formalize our intuition that X_i is closer to X_e than X_n. Euclidean distance is one way of doing that- in our toy example, sqrt(sum((X_i - X_e)2 )) = sqrt(12 + 12 ) = sqrt(2) and sqrt(sum((X_i - X_n)2 )) = sqrt(200). So we can say, at least in euclidean space, X_i is closer (or less far away) to X_e than to X_n. In KNN X_e « votes » its class, which in this case is « edible ». For larger numbers of k, other closest neighbors also have a vote, which is why chosen ‘k’ is almost always odd. The same process can be repeated irrespective of number of features (whether 3 or 20), but in higher dimensions, the things get counterintuitive (curse of dimensionality), so KNN eventually struggles when data dimensionality is too high. More on reddit.com

We used DBSCAN in a fraud detection pipeline that performer extremely well. However due to extreme RAM requirements of DBSCAN we had to first run a clustering algorithm down over our data points. We ran the clustering algorithm with 50.000 clusters. The cluster centers was then picked as the new data points. We could then run dbscan on the cluster centers. Each cluster center that was deemed an outlier had all corresponding (original) data points set as outliers as well. Due to randomness of the clustering algorithm we ran the algorithm 15 times. An original data point had to be marked an outlier for 50% of the runs in order to be classified as outlier. More on reddit.com

Because it is a method for learning to predict new cases from training data. K is a meta-parameter controlling model complexity. Prediction are learned from the training data at test time. More on reddit.com