API Reference¶

Context¶

class fca.Context(data_frame)[source]¶

Implements Formal Context.

Formal context can be understand as triplet \(<A,B,I>\) where A are objects, \(B\) are attributes and \(I\) is relation \(A\) x \(B\). If \(<x1, y2>\) is from \(I\), that means that object x1 has attribute y2.

Parameters:	data_frames (`pandas.DataFrame`) – Context is using `pandas.DataFrame` as inner representation of relation \(I\). Than `pandas.Index` are used for \(A\) and \(B\) representation and they are include in `pandas.DataFrame` as index and columns. Data should included only True/False values or in can be scaled with `pandas.DataFrame.get_dummies()` to multiple columns with 0/1 values.

data_frame¶: pandas.DataFrame – Complete dataset related to formal context.

objects¶: pandas.Index – All objects from context.

attributes¶: pandas.Index – All attributes from context.

all_attributes()[source]¶: Return bool numpy array filled by True values. Lenght of this array is equals to number of attribute

all_objects()[source]¶: Return bool numpy array filled by True values. Lenght of this array is equals to number of objects

clarificate()[source]¶: Inplace operation which clarify the context. Clarificated context is context which does not have duplicate columns/rows. Only one of these columns/rows is included.

down(attributes, out=None)[source]¶

Find all objects covered by the attributes.

Parameters:	attributes (`numpy.array`) – Numpy bool array, if index contains True value, attributes with this index is included in selection. out (`numpy.array`) – If value is None (default) output is outputed to newly allocated array, otherwise provided array is used.
Returns:	objects – NumPy array with boolean values representing if object on index is part of the result.
Return type:	`numpy.array`

empty_attributes()[source]¶: Return bool numpy array filled by False values. Lenght of this array is equals to number of attributes

empty_objects()[source]¶: Return bool numpy array filled by False values. Lenght of this array is equals to number of objects

number_of_attributes()[source]¶: Return number of attributes

number_of_objects()[source]¶: Return number of objects

up(objects, out=None)[source]¶

Find all attributes covered by the objects.

Parameters:	objects (`numpy.array`) – Numpy bool array, if index contains True value, objects with this index is included in selection. out (`numpy.array`) – If value is None (default) output is outputed to newly allocated array, otherwise provided array is used.
Returns:	attributes – NumPy array with boolean values representing if attribute on index is part of the result.
Return type:	`numpy.array`

Concept¶

class fca.Concept(extent, intent)[source]¶

Implements Formal Concept.

Formal concept in Context \(c\) is pair \(<A,B>\), where \(A\) is subset of \(X\), \(B\) is subset of \(Y\) such that \(c.up(A) = B\) and \(c.down(B) = A\).

This formal definition is not required, but you have to include extent (objects) and intent (attributes) to create concept.

Parameters:	extent (`numpy.array`) – All object (covered by attributes) in concept, empty list is allowed. Represented as `numpy.array` of bool values. intent (`numpy.array`) – All attributes (covered by objects) in concept, empty list is allowed. Represented as `numpy.array` of bool values.

extent¶: numpy.array – All object (covered by attributes) in concept. Represented as numpy.array of bool values.

intent¶: numpy.array – All attributes (covered by objects) in concept. Represented as numpy.array of bool values.

human_readable(context)[source]¶: Return human readable strings of extent and intent

static load_list(infile)[source]¶: load list of concepts from file via numpy.load

static save_list(list_of_concepts, outfile)[source]¶: save list of concepts into file via numpy.savez

CloseByOne Algorithm¶

class fca.algorithms.CloseByOne[source]¶

Implements algorithm CloseByOne from Sergei O. Kuznetsov

CbO lists all formal concepts by a systematic search in the space of all formal concepts, avoiding to list the same concept multiple times by performing a canonicity test.

(cite: https://www.sciencedirect.com/science/article/pii/S0020025511004804)

More information about the algorithm can be found here: https://link.springer.com/chapter/10.1007/978-3-540-48247-5_47

static generate_concepts(context)[source]¶

Lists all formal concepts by a systematic search in the space of all formal concepts, avoiding to list the same concept multiple times by performing a canonicity test.

Parameters:	context (`fca.Context`) – Context where the concepts should be found.
Returns:	output – List of concepts.
Return type:	list

static generate_from(context, concept, y, n, Yj, intent, output)[source]¶

Recursively descends through the space of formal concepts, beginning with \(<A,B>\).

Parameters:	context (`fca.Context`) – Context where the concepts should be find. concept (`fca.Concept`) – Initial formal concept. y – Index of first attribute to be processed. n – Number of columns in context. Yj – Preallocated `numpy.array` for better performance. intent – Preallocated intent for better performance. output (list) – Output list for formal concepts.

FastCloseByOne Algorithm¶

class fca.algorithms.FastCloseByOne[source]¶

Implements algorithm FastCloseByOne from Jan Outrata, Vilem Vychodil

FCbO lists all formal concepts by a systematic search in the space of all formal concepts, avoiding to list the same concept multiple times by performing a canonicity test. The algorithm uses set of already computed intents which fails canonicity test.

(cite: https://www.sciencedirect.com/science/article/pii/S0020025511004804)

More information about the algorithm can be found here: https://www.sciencedirect.com/science/article/pii/S0020025511004804

static fast_generate_from(context, concept, y, n, Yj, Nj, intent, output)[source]¶