Analysis tools for similarity measures

The analysis tools can be used to study the properties of similarity measures and similarity matrices.

class madas.analysis.MetricSpaceTest(fingerprints: List[Fingerprint] | None = None, similarity_matrix: SimilarityMatrix | None = None, show_progress: bool = True)

Class for fingerprints to test if the fingerprints and their respective similarity measures span a metric space.

Usage:

mst = MetricSpaceTest(fingerprints: List[Fingerprint])

is_metric = all(mst())

call_single(test_name: str) → bool

Call a single test.

Arguments:

test_name: str

Name of the test. Choose from: ‘uniqueness’, ‘identity’, ‘symmetry’, ‘triangle inequality’

Returns:

result: bool

Result of the test.

Raises:

KeyError: Name of the test is not recogized.

static identity(similarity_matrix: SimilarityMatrix, show_progress: bool = True)

Test identity property of a similarity matrix.

Tests: S(i,i) == 1 for all fingerprints i and similarity S

Arguments:

similarity_matrix: SimilarityMatrix

Similarity matrix to test.

Keyword arguments:

show_progress: bool

Show progress of test.

default: True

Returns:

result: bool

Result of the test: True: identical fingerprints have S == 1, False else

static symmetry(similarity_matrix: SimilarityMatrix, show_progress: bool = True)

Test symmetry property of a similarity matrix. The threshold for being equal is 1e-8.

Tests: S(i,j) == S(j,i) for fingerprints i,j and similarity S

Arguments:

similarity_matrix: SimilarityMatrix

Similarity matrix to test.

Keyword arguments:

show_progress: bool

Show progress of test.

default: True

Returns:

result: bool

Result of the test: True: matrix is symmetric, False else

static triangle_inequality(similarity_matrix: SimilarityMatrix, show_progress: bool = True)

Test triangle inequality property of a similarity matrix. The threshold for being equal is 1e-8.

Tests: S(i,k) + S(j,k) <= S(j,i) + 1 for fingerprints i,j,k and similarity S

Arguments:

similarity_matrix: SimilarityMatrix

Similarity matrix to test.

Keyword arguments:

show_progress: bool

Show progress of test.

default: True

Returns:

result: bool

Result of the test: True: matrix obays triangle inequality, False else

static uniqueness(similarity_matrix: SimilarityMatrix, fingerprints: List[Fingerprint], show_progress: bool = True)

Test uniqueness property of a similarity matrix.

Tests: i != j -> S(i,j) != 1 for fingerprints i,j and similarity S

Arguments:

similarity_matrix: SimilarityMatrix

Similarity matrix to test.

fingerprints: List[Fingerprint]

List of fingerprints to verfy if two fingerprints are equal.

Keyword arguments:

show_progress: bool

Show progress of test.

default: True

Returns:

result: bool

Result of the test: True: fingerprints are unique, False else

class madas.analysis.StrideSpectrumComparison(grid_id: str = 'nonuniform:-2:0.05:1.05:0.3:8:0.5:-1:1:1024', cutoff: List[float] = [-1, 1], eref_stepsize: float = 0.1, show_progress: bool = True, **kwargs)

Compare two spectra by “striding” small spectum-fingerprint feature regions along the x-axis.

Usage:

For spectra 1 and 2 with x-values x1 and x2 and y-values y1 and y2:

ssc = StrideSpectrumComparison() stride_list, similarities = ssc(x1, y1, x2, y2)

Returns:

stride_list: list of float

List of strides that were used for calculating the similarities

similarities: list of float

Similiarity of the spectra in a window centered at the respective stride