Weighting schemes

class composes.transformation.scaling.ppmi_weighting.PpmiWeighting

Positive Point-wise Mutual Information.

\(pmi(r,c) = log\frac{P(r,c)}{P(r)P(c)}\)

\(ppmi(r,c)= pmi(r,c) \text{ if } pmi(r,c)\geq 0 \text{ else } 0\)

class composes.transformation.scaling.plmi_weighting.PlmiWeighting

Positive Local Mutual Information.

\(plmi(r,c)=ppmi(r,c)count(r,c)\)

class composes.transformation.scaling.epmi_weighting.EpmiWeighting

Exponential Point-wise Mutual Information.

\(epmi(r,c) = \frac{P(r,c)}{P(r)P(c)}\)

class composes.transformation.scaling.plog_weighting.PlogWeighting

Positive Log Weighting

\(plog(r,c)= log(r,c) \text{ if } log(r,c) \geq 0 \text{ else } 0\)

Normalization

class composes.transformation.scaling.normalization.Normalization(**kwargs)

Normalizes the a space according to a some criterion.

Available criteria:

sum: Default. The result matrix \(X\) will satisfy: \(\sum_{i,j} X_{ij}=1\)

length: The result matrix \(X\) will satisfy: \(\sqrt{\sum_{i,j} X_{ij}^2}=1\)

class composes.transformation.scaling.row_normalization.RowNormalization(**kwargs)

Normalizes the rows of a space according to a some criterion.

Available criteria:

length: Default. Each row \(X_i\) of the result matrix will satisfy: \(\sqrt{\sum_j X_{ij}^2}=1\)

sum: Each row \(X_i\) of the result matrix will satisfy: \(\sum_j X_{ij}=1\)

Dimensionality reduction

class composes.transformation.dim_reduction.svd.Svd(reduced_dimension)

Performs truncated Singular Value Decomposition to a reduced dimension \(k\).

Given an input matrix \(X\), it computes the decomposition:

\(X = U \Sigma V^{T}\)

It returns \(U \Sigma\) truncated to dimension \(min(k,rank(X))\)

class composes.transformation.dim_reduction.nmf.Nmf(reduced_dimension)

Performs Non-negative Matrix Factorization to reduced dimension \(k\).

Given an input non-negative matrix \(X\), it computes the decomposition:

\(X \approx WH\) where W and H are non-negative matrices which minimize \(||X-WH||_{2}\)

It returns the matrix W.

Feature selection

class composes.transformation.feature_selection.top_feature_selection.TopFeatureSelection(reduced_dimension, **kwargs)

Sorts the columns of a space according to some criterion and returns a space containing only the top \(k\) ones.

Available criteria:

sum: Default. Ranks columns according to the sum on their elements.

length: Ranks columns according to their vector length.