Model & Pattern

This is yet another post on theoretical background and explanation related to data mining...

This part is on descriptive modelling and pattern structure recognition.

Definition:

• instances = data objects observed and analysed (sometimes referred to as objects, data points...)

• variables= characteristics measured (for continuous) or observed (for categorical) for each instance

Notation:

• n data objects (sample size)

• X generic input variables. When it is a vector, its component variable j is expressed with subscript: X_j

• x denotes some observed instance, and when we have p-variables, we denote x₁ .. x_p as the the real-valued for the 1.. p variables measured on the particular object or instance.

• x_k(i) correspond to the measure for variable X_k of the i-th data objects, where i has 1 .. N.

• x (in bold) correspond to the vector of n observation of a single variable x.

• X (capital in bold) correspond to the matrix N x p, containing N input p-vector x_p(1..N).