FracMinHash

Unlike standard MinHash which selects a fixed number of minimum hash values, FracMinHash selects all k-mer hash values that fall below a fraction threshold (s) of the maximum possible hash value. This creates a sketch whose size scales linearly with the number of distinct k-mers in the input dataset, providing a scale-invariant representation.

• Threshold parameter (s): Defines the fraction of the hash space retained (e.g., s=0.001 retains 0.1% of k-mers)
• Dynamic sketch size: Larger genomes produce proportionally larger sketches
• Hash function: Typically uses MurmurHash3 or xxHash for uniform distribution

FracMinHash provides an unbiased estimator of the containment index—the fraction of k-mers from one dataset (the query) that are present in another (the reference). This is computed as the ratio of intersecting hash values to the total hash values in the query sketch.

• Formula: Containment ≈ |Sketch(A) ∩ Sketch(B)| / |Sketch(A)|
• Key advantage: Does not require the reference sketch to be a fixed size
• Use case: Determining what fraction of a metagenomic sample matches a known genome

FracMinHash sketches enable rapid ANI estimation without expensive base-level alignment. By comparing the containment and Jaccard indices derived from sketches, tools like sourmash and skani can estimate ANI with high accuracy.

• Mash distance: Derived from Jaccard index to estimate mutation rate
• ANI formula: ANI ≈ 1 + (1/k) * ln(Jaccard) for sufficiently large k
• Benchmark: Achieves >99% correlation with BLAST-based ANI for genomes above 90% identity
• Throughput: Processes thousands of genomes per minute on consumer hardware

Standard FracMinHash treats all k-mers equally, but abundance-weighted FracMinHash variants incorporate k-mer multiplicity information to improve distance estimation for metagenomic samples with varying coverage depths.

• Weighted MinHash: Extends FracMinHash to preserve relative abundance signals
• Confidence intervals: Abundance weighting reduces variance in low-coverage regions
• Implementation: Used in tools like sourmash gather for metagenomic decomposition
• Trade-off: Increased sketch size for improved resolution of closely related strains

The scaled MinHash variant of FracMinHash uses a fixed sampling rate (e.g., 1 in 1000) rather than a fixed sketch size, ensuring that sketches from datasets of different sizes remain directly comparable without normalization.

• Parameter: Scaled factor (e.g., scaled=1000 retains 1/1000th of k-mers)
• Merge compatibility: Sketches with identical scaled parameters can be combined via union operations
• Streaming support: Enables sketching of unbounded data streams without pre-knowledge of dataset size
• Adoption: Core algorithm in sourmash for large-scale genomic indexing

FracMinHash sketches exhibit inherent error tolerance because sequencing errors generate random k-mers that are unlikely to consistently hash below the fraction threshold across multiple samples. This provides natural denoising without explicit quality filtering.

• Error k-mers: Low-abundance erroneous k-mers are stochastically excluded from the sketch
• False positive rate: Controllable via the fraction parameter (s) and k-mer size (k)
• k-mer size selection: Larger k (e.g., k=31) reduces random collisions between unrelated genomes
• Practical impact: Enables accurate comparisons directly from raw sequencing reads without assembly

An asymmetric similarity metric that measures what fraction of a query genome's k-mers are present in a reference genome. Unlike the symmetric Jaccard index, containment answers: 'How much of genome A is contained within genome B?' This is critical for metagenomic analysis where a sample may partially match a reference. FracMinHash provides an unbiased estimator of the containment index by comparing the fraction of query sketch elements that appear in the reference sketch.

A pairwise measure of genomic relatedness between two microbial genomes, calculated as the mean nucleotide identity of all orthologous genes shared between them. ANI values above 95% typically indicate the same species. FracMinHash sketches enable rapid ANI estimation without full genome alignment by leveraging the relationship between k-mer containment and sequence identity. This allows ANI computation to scale to millions of comparisons in large metagenomic datasets.

The frequency distribution of all possible nucleotide subsequences of a fixed length k within a sequencing read or genome. The k-mer spectrum serves as a fundamental compositional feature for assembly-free classification and binning algorithms. FracMinHash operates on the k-mer spectrum by hashing each k-mer and selecting only those whose hash values fall below a defined abundance threshold, creating a scalable sketch that preserves the statistical properties needed for downstream analysis.

A variant of MinHash implemented in the sourmash tool that selects hash values below a fixed fraction of the maximum hash value, rather than a fixed number of minimum values. This scaling approach makes the sketch size proportional to the number of unique k-mers in the input, enabling comparisons between datasets of vastly different sizes. FracMinHash generalizes this concept by introducing an abundance threshold that filters low-frequency k-mers, reducing noise from sequencing errors.