Correlation Distance Matrix

Build a Pearson correlation-distance matrix for hierarchical clustering.

Description

Correlation distance measures profile shape agreement after centering.

Correlation distance measures profile shape agreement after centering. It ignores common offsets and positive scaling, unlike Euclidean distance.^[1]

Build a Pearson correlation-distance matrix for hierarchical clustering.

When to use Correlation Distance Matrix

Use this tool to build a Pearson correlation-distance matrix for hierarchical clustering.

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 Correlation Distance Matrix 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 expressionProfiles using the field table and calculation rules, then run the tool.
Read correlationDistances. 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
expressionProfiles	Expression profiles	list of list of number	Required

Enter at least two equal-length rows, each with at least two finite observations and nonzero variation. Center rows, normalize by their norms and return the square distance matrix with zero diagonal. Clamp correlations to −1..1, snapping near ±1 within 10⁻¹² to exact distances zero or two.

distance_ij=1−Pearson(profile_i,profile_j)

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

Output field	Meaning	Value type
correlationDistances	Correlation distances	list of list of number

json

{
  "input": {
    "expressionProfiles": [
      [
        1,
        2,
        3
      ],
      [
        2,
        4,
        6
      ],
      [
        3,
        2,
        1
      ]
    ]
  },
  "output": {
    "correlationDistances": [
      [
        0,
        0,
        2
      ],
      [
        0,
        0,
        2
      ],
      [
        2,
        2,
        0
      ]
    ]
  }
}

Limitations and assumptions

The tool does not cluster or normalize expression libraries. Constant rows are errors, and correlation distance is not generally a metric satisfying every geometric distance property.

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.

Alternative or Complementary methods

Use Silhouette Score: Compute a silhouette width from within- and between-cluster distances. For a complementary task, use Module Eigengene: Extract the leading principal component of a gene-by-sample module.

References

Correlation Distance Matrix — tool.io

Similar or alternative tools

Silhouette Score
Compute a silhouette width from within- and between-cluster distances.
Module Eigengene
Extract the leading principal component of a gene-by-sample module.