VL 12

Question 1

What is Clustering? and why do you use it?

Answer 1

Clustering is a technique that groups similar data points together based on their similarities, without using predefined categories. It helps find patterns and structures within datasets for various applications.

• need for generalisation, grouping, classification
• 1, 2 variables –> humans can cluster (plots)
• 3, 4, … (coplot, image, pairs, PCA, MDS) –> computers should better do the clustering

Question 2

types of clustering

Answer 2

• Hierarchical Clustering:
  A set of nested clusters organized as a hierarchical tree
  –> we will get a dendrogram and a cluster id by
  dendrogram cutting
• Partitional Clustering: A division of data objects into non-overlapping subsets (clusters) such that each data object is in exactly one subset
  –> we will only get a cluster id

Question 3

What is hierarchical clustering?

Answer 3

• no need to specify numbers of cluster k before clustering starts
• the algorithm constructs a tree like hierarchy (dendrogram) which (implicitly) contains all values of k
• on one end of the tree there are k clusters each with one object and on the other end of the tree there is one cluster containing all k objects

Question 4

What do we need to cluster?

Answer 4

• needed for the clustering is a complete set, i.e. a matrix, of the (dis)similarities between all objects.
• dissimilarity coefficients may be obtained from the
  computation of distances (see last section)
• Euclidean distance, Manhattan distance, correlation, coefficient based distances are usually used
• high quality clusters with:
  – high intra-class similarity
  – low inter-class similarity
• good: small circles, long lines
• bad: large circles, short line

Question 5

Distance Matrix

Answer 5

• you can generate the distance matrix from your data by dist function:
  dist.mt = dist(data, method =´manhattan´)
• be carefully to create a distance matrix for the row or the column items, transpose your matrix if you want to switch between row and column item distances
• if the distance matrix is not generated by the dist function: use dist.mt = as.dist(matrix) to generate a distance
  matrix from a “manually” made distance matrix

Question 6

Agglomerative Clustering

Answer 6

• a distance matrix is required
• agglomerative methods start with n clusters and proceed by successive fusions until a single cluster is obtained
• 1st: two “most similar” objects are joined into cluster
• 2nd: distance matrix is reduced as rows of joined objects are merged
• hclust: hierarchical cluster analysis on a set of dissimilarities and methods for analyzing it

Question 7

hclust: hierarchical agglomerative clustering

Answer 7

• performed from a distance matrix which is stepwise reduced
• repeated recalculation for distance of merged rows to all
  remaining rows
• single linkage to merge closest rows (use smallest distance value)
  – complete linkage to merge closest rows (use the largest distance value)
  – average linkage to merge closest rows (use the average distance value)
• default for hclust is complete linkage
• computationally intensive
• don’t do this for 20.000 genes, but do this for 100 samples
• transpose matrix correctly to samples, not genes