## intro

clusters can be different in different tasks for the same dataset

different methods

… blabla …

## mixture function

designate domain-specific assumptions

Assumption: data is generated on mixture function

blabla …

## hierarchical clustering

• bottom-up
• min
• max
• top-down

bottom-up:

two samples per time, take the two with smallest distance as a cluster, update the dist between new cluster and others using the min/max distance

## spectral clustering

• PCA
• LDA(linear determinant analysis
• spectrum embedding (in manifold learning)

adjacency matrix -> generalized to -> similarity matrix (weighted)

• full connectivity
• local
• k-nn
• $\epsilon$-radius

find a cut of a graph that makes some criteria optimal.

### min binary cut

to minimize:

however, the result ofter just only separate a single outlier point as a cluster, and others in a total form a cluster

-> normalize the cut with similar size for both clusters

• use cardinality (count of vertices in a set)
• use volume (sum of degree of vertices in a set)

to solve this in the following secitons

### laplace matrix properties

• number of the eigen vectors of a laplace matrix w.r.t the eigen value 0, equals to the number of connected subgraphs of the graph

• classical
• Ncut
• Ng’s algo.