ObsidianVault/Running Start/CSB320 - Machine Learning Concepts/Class 5-28 (Clustering).md

#rs/class/csb320 #rs/notes

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• Everything so far has been supervised learning (mostly)
• unsupervised learning (clustering)
  • do not know the labels of data.
• clustering
  • groups instances based on feature similarity
  • results in group assignments, not target output
  • need to extrapolate meaning from clusters
  • !ClusteringBasic.excalidraw
  • applications
    • taxonomy of living things
    • clustering documents on topic
    • identify areas with similar land use
    • cluster groups of houses for city planning
  • good clustering: high intra-class similarity, low inter-class similarity
  • centroid
    • mean position of a cluster's instances \overline X_{i}=\frac{\sum_{j \in C_{i}}X_{i}}{n_{i}}
  • Inertia
    • average squared distance of the instances from the centroid I_{i}=\frac{\sum_{j \in C_{i}}|\overline X_{j} - X_{i}|^2}{n_{i}}
  • partitioning approach
    • create various partitions and evaluate based on metric (minimize sum of squared errors)
  • K-means clustering
    • assigns instances to the nearest centroid
    • need to know k number of clusters beforehand
    • algorithm
      • k points are chosen randomly as initial centroids
      • assign every data point to the closest centroid
      • compute new centroids with assigned data
      • if centroids don't change, stop. If they do repeat with new centroids
    • Choosing the optimal number of clusters
      • elbow method
        • graph inertia against k and find point where elbow of data is (curve levels off)
      • Silhouette method
        • Use silhouette coefficient to determine separation of clusters S(j) = \frac{{\overline{d_{out}(j)} - \overline{d_{in}(j)}}}{max(\overline{d_{out}(j)}, \overline{d_{in}(j)})}
        • \overline{d_{out}(j)} is the average distance of the instance i to the centroid of all other clusters
        • \overline{d_{in}(j)} is the average distance of the instance i to all other instances in its cluster
        • !SilhouetteMethod.excalidraw
    • effective for small/medium datasets
    • assumes spherical clusters
    • sensitive to initial conditions
    • equal-sized groups assumption
    • sensitive to outliers
      • k-medioids can be used
        • medioid is the most centrally located point in a cluster
        • PAM: partitioning around medioids
  • Hierarchical clustering
    • does not require number of clusters, requires stopping point
    • Agglomerative
      • starts with each instance as cluster and merges into larger clusters
      • measures distances between all clusters and merges closest two into new cluster
    • divisive
      • starts with one cluster and splits into smaller clusters
    • linkage methods
      • measure distance between two closes instances
      • measure distance between two farthest instances
      • distance between each cluster's centroid
    • dendrograms
      • used to visualize clustering hierarchy
      • basically just a cladogram
        • clades, links, leaves
    • does not assume spherical clusters
    • sensitive to outliers