TOM Symmetry Audit

Audit topological-overlap matrix symmetry and diagonal entries.

Description

A topological-overlap matrix should often be symmetric with unit diagonal, but those are separate checks.

A topological-overlap matrix should often be symmetric with unit diagonal, but those are separate checks. Pairwise asymmetry measures agreement between mirrored off-diagonal entries.^[1]

Audit topological-overlap matrix symmetry and diagonal entries.

When to use TOM Symmetry Audit

Use this tool to audit topological-overlap matrix symmetry and diagonal entries.

Prepare the upstream counts, expression values, sequences or record lists requested by this tool. Keep corresponding features in the same order and confirm count units, transformations and caller-selected criteria.

How to use TOM Symmetry Audit and understand its results

Prepare the upstream counts, expression values, sequences or record lists requested by this tool. Keep corresponding features in the same order and confirm count units, transformations and caller-selected criteria.
Enter overlapMatrix, tolerance using the field table and calculation rules, then run the tool.
Read maxAsymmetry, diagonalDeviations, symmetric. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
overlapMatrix	Overlap matrix	list of list of number	Required
tolerance	Tolerance	number	Required

Provide a nonempty square finite matrix and nonnegative tolerance. Return maximum off-diagonal asymmetry, diagonal deviations and an inclusive symmetry flag. A 1×1 matrix has zero asymmetry even if its diagonal differs from one.

maxAsymmetry=max_{i<j}|Mij−Mji|; diagonalDeviation_i=|Mii−1|

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
maxAsymmetry	Max asymmetry	number
diagonalDeviations	Diagonal deviations	list of number
symmetric	Symmetric	boolean

json

{
  "input": {
    "overlapMatrix": [
      [
        1,
        0.5
      ],
      [
        0.4,
        1
      ]
    ],
    "tolerance": 0.05
  },
  "output": {
    "maxAsymmetry": 0.09999999999999998,
    "diagonalDeviations": [
      0,
      0
    ],
    "symmetric": false
  }
}

Limitations and assumptions

The symmetric flag ignores diagonal deviations. Values are not required to lie in 0–1, and this does not calculate overlap, verify a network or test positive semidefiniteness.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Matrices are limited to 128 rows and 128 entries per row; other lists are limited to 100,000 entries. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors. A successfully returned false flag is an evaluated outcome; its meaning is explained above.

Alternative or Complementary methods

Use WGCNA Power Selector: Select the first WGCNA power meeting a caller-supplied scale-free-fit criterion. For a complementary task, use Correlation Distance Matrix: Build a Pearson correlation-distance matrix for hierarchical clustering.

References

TOM Symmetry Audit — tool.io

Similar or alternative tools

WGCNA Power Selector
Select the first WGCNA power meeting a caller-supplied scale-free-fit criterion.
Correlation Distance Matrix
Build a Pearson correlation-distance matrix for hierarchical clustering.