This is a draft cheat sheet. It is a work in progress and is not finished yet.
formulas
standard units: z = (original - mean) / standard deviation |
β1 = cov(x,y) / var(x) |
cov(x,y) = (∑ (y_i - ȳ)(x_i - x̄)) / n |
corr(xy) = cov(x,y) / (s_x * s_y) |
hierarchical clustering
find successive clusters using previously established clusters
- common approach is bottom-up: start with each element in a separate cluster |
single linkage: use minimum distance
complete linkage: use maximum distance
average linkage: use average linkage |
"minimum distance between group 1 points and group 2 points is larger than the minimum within-group distance for the same points" |
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k-means
k-means algorithm: 1. construct clusters by associating each point with the closest centroid, 2. calculate new centroids for each set; repeat both till convergence |
as k increases, average variance of clusters decreases |
use features (x_n) to partition data into K clusters (represented by its centroid -- center of points in the cluster) |
goal is to minimize intra-class centroid points distances and find cnk (0 - 1 cluster membership) and µk (centroids) that minimize |
artificial neural networks
activation functions:
- sigmoid (0, 1)
sigmoid(z) = (exp z) / (1+exp z)
- hyperbolic tangent (-1, 1)
tanh(z) = (exp (z) – exp(-z) ) / (exp(z) + exp(-z)) |
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