FORMULAS Flashcards

Question

Pseudocode for a perceptron learning algorithm

Answer 1

P and N are inputs with class labels (1,-1) Learning rate is a hyperparameter InitialiseW: randomly, is initialising the weights and biases LINE: while Not converge do: Convergence refers to the training stoppping criteria which could be: No more errors Model stop making improvement Max number of iteration LINE: Do forwards pass Activation function LINE: if X’ e P and W^T * X’ < 0 It is saying for each sample in the positive class, check if it is negative, if it is then append the negative of the sample to the error class (delta) Next if statement: If sample is in negative class and is positive, add the sample to the error class delta After all if statements New set of weights = Weights - learning rate * sum of all errors Increase t (iterations)

Answer 2

New set of weights = Weights - learning rate * sum of all errors

Answer 3

sum of X’ when it was misclassified, you add a -X’ if it was misclassified as positive

Answer 4

W(t) - rate of learning * gradient of the cost function

Answer 5

σ(z) = 1/ (1+e^-z)

Answer 6

z = (W^T)X + b y hat = 1/(1+e^-z)

Answer 7

Put x1 into the first cluster Loop from 2 to number of data points Measure distance between data point and cluster If distance is greater than threshold and max clusters not reached Create new cluster and put that data point in it If the distance is smaller than the threshold, add it to that cluster

Answer 8

Select some cluster-cluster proximity measure g Let t be an integer denoting the current level of the hierarchy Then the general agglomerative clustering scheme can be stated as (image) Initialise: Start with each data point as its own cluster, creating N clusters Repeat: While there is one cluster - Compute the pairwise proximity g(Ci,Cj) for all cluster pairs Identify pair of clusters with smallest proximity Merge these two clusters into a new cluster Update set of clusters by removing the old ones and adding the new one Update the hierarchy to include the new cluster level t Increment t

Answer 9

μi is the centre point (centroid) of the cluster J is the sum of the distances from all the points in a cluster to μi (its centre point) small cost J implies a good clustering e.g. elements are close to their clusters

Answer 10

Initialisation Choose number of clusters (K) Initialise K centroids randomly from the data points Assignment Assign each data point to the nearest cluster centroid, using a distance metric Update Recalculate the centroids of each cluster as the mean of all data points assigned to that cluster Repeat Alternate between the assignment and update steps until stopping criteria are met stopping criteria: cluster assignments no longer change centroids stabilise max iterations reached

Answer 11

Distance between each point in the cluster to the centroid * U U is a continuous value between 0 and 1 giving the probability that the point belongs to the cluster

Answer 12

β is called temperature Small β (high temperature) are very soft, every cluster gets some weight Large β (low temperature), approaching hard k-means, assignments become nearly 0/1

Answer 13

Sum all the distances * their weights and divide by the total weights

FORMULAS Flashcards

(39 cards)