Struct Dbscan 

pub struct Dbscan<P: RegionQuery + ListPoints>
where
    P::Point: Hash + Eq + Clone,
{ /* private fields */ }

Clustering via the DBSCAN algorithm[1].

[DBSCAN] is a density-based clustering algorithm: given a set of points in some space, it groups together points that are closely packed together (points with many nearby neighbors), marking as outliers points that lie alone in low-density regions (whose nearest neighbors are too far away).^wikipedia

An instance of Dbscan is an iterator over clusters of P. Points classified as noise once all clusters are found are available via noise_points.

This uses the P::Point yielded by the iterators provided by ListPoints and RegionQuery as a unique identifier for each point. The algorithm will behave strangely if the identifier is not unique or not stable within a given execution of DBSCAN. The identifier is cloned several times in the course of execution, so it should be cheap to duplicate (e.g. a usize index, or a &T reference).

[1]: Ester, Martin; Kriegel, Hans-Peter; Sander, Jörg; Xu, Xiaowei (1996). Simoudis, Evangelos; Han, Jiawei; Fayyad, Usama M., eds. A density-based algorithm for discovering clusters in large spatial databases with noise. Proceedings of the Second International Conference on Knowledge Discovery and Data Mining (KDD-96). AAAI Press. pp. 226–231.

Examples

A basic example:

use cogset::{Dbscan, BruteScan, Euclid};

let points = [Euclid([0.1]), Euclid([0.2]), Euclid([1.0])];

let scanner = BruteScan::new(&points);
let mut dbscan = Dbscan::new(scanner, 0.2, 2);

// get the clusters themselves
let clusters = dbscan.by_ref().collect::<Vec<_>>();
// the first two points are the only cluster
assert_eq!(clusters, &[&[0, 1]]);

// now the noise
let noise = dbscan.noise_points();
// which is just the last point
assert_eq!(noise.iter().cloned().collect::<Vec<_>>(),
           &[2]);

A more complicated example that renders the output nicely:

use std::str;
use cogset::{Dbscan, BruteScan, Euclid};

fn write_points<I>(output: &mut [u8; 76], byte: u8, it: I)
    where I: Iterator<Item = Euclid<[f64; 1]>>
{
    for p in it { output[(p.0[0] * 30.0) as usize] = byte; }
}

// the points we're going to cluster, considered as points in ℝ
// with the conventional distance.
let points = [Euclid([0.25]), Euclid([0.9]), Euclid([2.0]), Euclid([1.2]),
              Euclid([1.9]), Euclid([1.1]),  Euclid([1.35]), Euclid([1.85]),
              Euclid([1.05]), Euclid([0.1]), Euclid([2.5]), Euclid([0.05]),
              Euclid([0.6]), Euclid([0.55]), Euclid([1.6])];

// print the points before clustering
let mut original = [b' '; 76];
write_points(&mut original, b'x', points.iter().cloned());
println!("{}", str::from_utf8(&original).unwrap());

// set-up the data structure that will manage the queries that
// Dbscan needs to do.
let scanner = BruteScan::new(&points);

// create the clusterer: we need 3 points to consider a group a
// cluster, and we're only looking at points 0.2 units apart.
let min_points = 3;
let epsilon = 0.2;
let mut dbscan = Dbscan::new(scanner, epsilon, min_points);

let mut clustered = [b' '; 76];

// run over all the clusters, writing each to the output
for (i, cluster) in dbscan.by_ref().enumerate() {
    // since we used `BruteScan`, `cluster` is a vector of indices
    // into `points`, not the points themselves, so lets map back
    // to the points.
    let actual_points = cluster.iter().map(|idx| points[*idx]);

    write_points(&mut clustered, b'0' + i as u8,
                 actual_points)
}
// now run over the noise points, i.e. points that aren't close
// enough to others to be in a cluster.
let noise = dbscan.noise_points();
write_points(&mut clustered, b'.',
             noise.iter().map(|idx| points[*idx]));

// print the numbered clusters
println!("{}", str::from_utf8(&clustered).unwrap());

Output:

 x x   x        x x        x   x x  x   x       x      x x  x              x
 0 0   0        . .        2   2 2  2   2       .      1 1  1              .

Implementations

impl<P: RegionQuery + ListPoints> Dbscan<P>

where P::Point: Hash + Eq + Clone,

pub fn new(points: P, eps: f64, min_points: usize) -> Dbscan<P>

Create a new DBSCAN instance, with the given eps and min_points.

eps is the maximum distance between points when creating neighbours to construct clusters. min_points is the minimum of points for a cluster.

This does not perform any significant computation immediately; clusters are found on the fly via the Iterator instance.

pub fn noise_points(&self) -> &HashSet<P::Point>

Points that have been classified as noise once the algorithm finishes.

This only makes sense to call once the iterator is exhausted, and will give unspecified nonsense if called earlier.

Trait Implementations

impl<P: RegionQuery + ListPoints> Iterator for Dbscan<P>

where P::Point: Hash + Eq + Clone,

type Item = Vec<<P as Points>::Point>

The type of the elements being iterated over.

fn next(&mut self) -> Option<Vec<P::Point>>

Advances the iterator and returns the next value.

fn next_chunk<const N: usize>( &mut self, ) -> Result<[Self::Item; N], IntoIter<Self::Item, N>>

where Self: Sized,

🔬This is a nightly-only experimental API. (iter_next_chunk)

Advances the iterator and returns an array containing the next N values.

fn size_hint(&self) -> (usize, Option<usize>)

Returns the bounds on the remaining length of the iterator.

fn count(self) -> usize

where Self: Sized,

Consumes the iterator, counting the number of iterations and returning it.

fn last(self) -> Option<Self::Item>

where Self: Sized,

Consumes the iterator, returning the last element.

fn advance_by(&mut self, n: usize) -> Result<(), NonZero<usize>>

🔬This is a nightly-only experimental API. (iter_advance_by)

Advances the iterator by n elements.

fn nth(&mut self, n: usize) -> Option<Self::Item>

Returns the nth element of the iterator.

fn step_by(self, step: usize) -> StepBy<Self>

where Self: Sized,

Creates an iterator starting at the same point, but stepping by the given amount at each iteration.

fn chain<U>(self, other: U) -> Chain<Self, <U as IntoIterator>::IntoIter>

where Self: Sized, U: IntoIterator<Item = Self::Item>,

Takes two iterators and creates a new iterator over both in sequence.

fn zip<U>(self, other: U) -> Zip<Self, <U as IntoIterator>::IntoIter>

where Self: Sized, U: IntoIterator,

‘Zips up’ two iterators into a single iterator of pairs.

fn intersperse(self, separator: Self::Item) -> Intersperse<Self>

where Self: Sized, Self::Item: Clone,

🔬This is a nightly-only experimental API. (iter_intersperse)

Creates a new iterator which places a copy of separator between adjacent items of the original iterator.

fn intersperse_with<G>(self, separator: G) -> IntersperseWith<Self, G>

where Self: Sized, G: FnMut() -> Self::Item,

🔬This is a nightly-only experimental API. (iter_intersperse)

Creates a new iterator which places an item generated by separator between adjacent items of the original iterator.

fn map<B, F>(self, f: F) -> Map<Self, F>

where Self: Sized, F: FnMut(Self::Item) -> B,

Takes a closure and creates an iterator which calls that closure on each element.

fn for_each<F>(self, f: F)

where Self: Sized, F: FnMut(Self::Item),

Calls a closure on each element of an iterator.

fn filter<P>(self, predicate: P) -> Filter<Self, P>

where Self: Sized, P: FnMut(&Self::Item) -> bool,

Creates an iterator which uses a closure to determine if an element should be yielded.

fn filter_map<B, F>(self, f: F) -> FilterMap<Self, F>

where Self: Sized, F: FnMut(Self::Item) -> Option<B>,

Creates an iterator that both filters and maps.

fn enumerate(self) -> Enumerate<Self>

where Self: Sized,

Creates an iterator which gives the current iteration count as well as the next value.

fn peekable(self) -> Peekable<Self>

where Self: Sized,

Creates an iterator which can use the peek and peek_mut methods to look at the next element of the iterator without consuming it. See their documentation for more information.

fn skip_while<P>(self, predicate: P) -> SkipWhile<Self, P>

where Self: Sized, P: FnMut(&Self::Item) -> bool,

Creates an iterator that skips elements based on a predicate.

fn take_while<P>(self, predicate: P) -> TakeWhile<Self, P>

where Self: Sized, P: FnMut(&Self::Item) -> bool,

Creates an iterator that yields elements based on a predicate.

fn map_while<B, P>(self, predicate: P) -> MapWhile<Self, P>

where Self: Sized, P: FnMut(Self::Item) -> Option<B>,

Creates an iterator that both yields elements based on a predicate and maps.

fn skip(self, n: usize) -> Skip<Self>

where Self: Sized,

Creates an iterator that skips the first n elements.

fn take(self, n: usize) -> Take<Self>

where Self: Sized,

Creates an iterator that yields the first n elements, or fewer if the underlying iterator ends sooner.

fn scan<St, B, F>(self, initial_state: St, f: F) -> Scan<Self, St, F>

where Self: Sized, F: FnMut(&mut St, Self::Item) -> Option<B>,

An iterator adapter which, like fold, holds internal state, but unlike fold, produces a new iterator.

fn flat_map<U, F>(self, f: F) -> FlatMap<Self, U, F>

where Self: Sized, U: IntoIterator, F: FnMut(Self::Item) -> U,

Creates an iterator that works like map, but flattens nested structure.

fn flatten(self) -> Flatten<Self>

where Self: Sized, Self::Item: IntoIterator,

Creates an iterator that flattens nested structure.

fn map_windows<F, R, const N: usize>(self, f: F) -> MapWindows<Self, F, N>

where Self: Sized, F: FnMut(&[Self::Item; N]) -> R,

🔬This is a nightly-only experimental API. (iter_map_windows)

Calls the given function f for each contiguous window of size N over self and returns an iterator over the outputs of f. Like slice::windows(), the windows during mapping overlap as well.

fn fuse(self) -> Fuse<Self>

where Self: Sized,

Creates an iterator which ends after the first None.

fn inspect<F>(self, f: F) -> Inspect<Self, F>

where Self: Sized, F: FnMut(&Self::Item),

Does something with each element of an iterator, passing the value on.

fn by_ref(&mut self) -> &mut Self

where Self: Sized,

Creates a “by reference” adapter for this instance of Iterator.

fn collect<B>(self) -> B

where B: FromIterator<Self::Item>, Self: Sized,

Transforms an iterator into a collection.

fn try_collect<B>( &mut self, ) -> <<Self::Item as Try>::Residual as Residual<B>>::TryType

where Self: Sized, Self::Item: Try, <Self::Item as Try>::Residual: Residual<B>, B: FromIterator<<Self::Item as Try>::Output>,

🔬This is a nightly-only experimental API. (iterator_try_collect)

Fallibly transforms an iterator into a collection, short circuiting if a failure is encountered.

fn collect_into<E>(self, collection: &mut E) -> &mut E

where E: Extend<Self::Item>, Self: Sized,

🔬This is a nightly-only experimental API. (iter_collect_into)

Collects all the items from an iterator into a collection.

fn partition<B, F>(self, f: F) -> (B, B)

where Self: Sized, B: Default + Extend<Self::Item>, F: FnMut(&Self::Item) -> bool,

Consumes an iterator, creating two collections from it.

fn is_partitioned<P>(self, predicate: P) -> bool

where Self: Sized, P: FnMut(Self::Item) -> bool,

🔬This is a nightly-only experimental API. (iter_is_partitioned)

Checks if the elements of this iterator are partitioned according to the given predicate, such that all those that return true precede all those that return false.

fn try_fold<B, F, R>(&mut self, init: B, f: F) -> R

where Self: Sized, F: FnMut(B, Self::Item) -> R, R: Try<Output = B>,

An iterator method that applies a function as long as it returns successfully, producing a single, final value.

fn try_for_each<F, R>(&mut self, f: F) -> R

where Self: Sized, F: FnMut(Self::Item) -> R, R: Try<Output = ()>,

An iterator method that applies a fallible function to each item in the iterator, stopping at the first error and returning that error.

fn fold<B, F>(self, init: B, f: F) -> B

where Self: Sized, F: FnMut(B, Self::Item) -> B,

Folds every element into an accumulator by applying an operation, returning the final result.

fn reduce<F>(self, f: F) -> Option<Self::Item>

where Self: Sized, F: FnMut(Self::Item, Self::Item) -> Self::Item,

Reduces the elements to a single one, by repeatedly applying a reducing operation.

fn try_reduce<R>( &mut self, f: impl FnMut(Self::Item, Self::Item) -> R, ) -> <<R as Try>::Residual as Residual<Option<<R as Try>::Output>>>::TryType

where Self: Sized, R: Try<Output = Self::Item>, <R as Try>::Residual: Residual<Option<Self::Item>>,

🔬This is a nightly-only experimental API. (iterator_try_reduce)

Reduces the elements to a single one by repeatedly applying a reducing operation. If the closure returns a failure, the failure is propagated back to the caller immediately.

fn all<F>(&mut self, f: F) -> bool

where Self: Sized, F: FnMut(Self::Item) -> bool,

Tests if every element of the iterator matches a predicate.

fn any<F>(&mut self, f: F) -> bool

where Self: Sized, F: FnMut(Self::Item) -> bool,

Tests if any element of the iterator matches a predicate.

fn find<P>(&mut self, predicate: P) -> Option<Self::Item>

where Self: Sized, P: FnMut(&Self::Item) -> bool,

Searches for an element of an iterator that satisfies a predicate.

fn find_map<B, F>(&mut self, f: F) -> Option<B>

where Self: Sized, F: FnMut(Self::Item) -> Option<B>,

Applies function to the elements of iterator and returns the first non-none result.

fn try_find<R>( &mut self, f: impl FnMut(&Self::Item) -> R, ) -> <<R as Try>::Residual as Residual<Option<Self::Item>>>::TryType

where Self: Sized, R: Try<Output = bool>, <R as Try>::Residual: Residual<Option<Self::Item>>,

🔬This is a nightly-only experimental API. (try_find)

Applies function to the elements of iterator and returns the first true result or the first error.

fn position<P>(&mut self, predicate: P) -> Option<usize>

where Self: Sized, P: FnMut(Self::Item) -> bool,

Searches for an element in an iterator, returning its index.

fn max(self) -> Option<Self::Item>

where Self: Sized, Self::Item: Ord,

Returns the maximum element of an iterator.

fn min(self) -> Option<Self::Item>

where Self: Sized, Self::Item: Ord,

Returns the minimum element of an iterator.

fn max_by_key<B, F>(self, f: F) -> Option<Self::Item>

where B: Ord, Self: Sized, F: FnMut(&Self::Item) -> B,

Returns the element that gives the maximum value from the specified function.

fn max_by<F>(self, compare: F) -> Option<Self::Item>

where Self: Sized, F: FnMut(&Self::Item, &Self::Item) -> Ordering,

Returns the element that gives the maximum value with respect to the specified comparison function.

fn min_by_key<B, F>(self, f: F) -> Option<Self::Item>

where B: Ord, Self: Sized, F: FnMut(&Self::Item) -> B,

Returns the element that gives the minimum value from the specified function.

fn min_by<F>(self, compare: F) -> Option<Self::Item>

where Self: Sized, F: FnMut(&Self::Item, &Self::Item) -> Ordering,

Returns the element that gives the minimum value with respect to the specified comparison function.

fn unzip<A, B, FromA, FromB>(self) -> (FromA, FromB)

where FromA: Default + Extend<A>, FromB: Default + Extend<B>, Self: Sized + Iterator<Item = (A, B)>,

Converts an iterator of pairs into a pair of containers.

fn copied<'a, T>(self) -> Copied<Self>

where T: Copy + 'a, Self: Sized + Iterator<Item = &'a T>,

Creates an iterator which copies all of its elements.

fn cloned<'a, T>(self) -> Cloned<Self>

where T: Clone + 'a, Self: Sized + Iterator<Item = &'a T>,

Creates an iterator which clones all of its elements.

fn array_chunks<const N: usize>(self) -> ArrayChunks<Self, N>

where Self: Sized,

🔬This is a nightly-only experimental API. (iter_array_chunks)

Returns an iterator over N elements of the iterator at a time.

fn sum<S>(self) -> S

where Self: Sized, S: Sum<Self::Item>,

Sums the elements of an iterator.

fn product<P>(self) -> P

where Self: Sized, P: Product<Self::Item>,

Iterates over the entire iterator, multiplying all the elements

fn cmp<I>(self, other: I) -> Ordering

where I: IntoIterator<Item = Self::Item>, Self::Item: Ord, Self: Sized,

Lexicographically compares the elements of this Iterator with those of another.

fn cmp_by<I, F>(self, other: I, cmp: F) -> Ordering

where Self: Sized, I: IntoIterator, F: FnMut(Self::Item, <I as IntoIterator>::Item) -> Ordering,

🔬This is a nightly-only experimental API. (iter_order_by)

Lexicographically compares the elements of this Iterator with those of another with respect to the specified comparison function.

fn partial_cmp<I>(self, other: I) -> Option<Ordering>

where I: IntoIterator, Self::Item: PartialOrd<<I as IntoIterator>::Item>, Self: Sized,

Lexicographically compares the PartialOrd elements of this Iterator with those of another. The comparison works like short-circuit evaluation, returning a result without comparing the remaining elements. As soon as an order can be determined, the evaluation stops and a result is returned.

fn partial_cmp_by<I, F>(self, other: I, partial_cmp: F) -> Option<Ordering>

where Self: Sized, I: IntoIterator, F: FnMut(Self::Item, <I as IntoIterator>::Item) -> Option<Ordering>,

🔬This is a nightly-only experimental API. (iter_order_by)

Lexicographically compares the elements of this Iterator with those of another with respect to the specified comparison function.

fn eq<I>(self, other: I) -> bool

where I: IntoIterator, Self::Item: PartialEq<<I as IntoIterator>::Item>, Self: Sized,

Determines if the elements of this Iterator are equal to those of another.

fn eq_by<I, F>(self, other: I, eq: F) -> bool

where Self: Sized, I: IntoIterator, F: FnMut(Self::Item, <I as IntoIterator>::Item) -> bool,

🔬This is a nightly-only experimental API. (iter_order_by)

Determines if the elements of this Iterator are equal to those of another with respect to the specified equality function.

fn ne<I>(self, other: I) -> bool

where I: IntoIterator, Self::Item: PartialEq<<I as IntoIterator>::Item>, Self: Sized,

Determines if the elements of this Iterator are not equal to those of another.

fn lt<I>(self, other: I) -> bool

where I: IntoIterator, Self::Item: PartialOrd<<I as IntoIterator>::Item>, Self: Sized,

Determines if the elements of this Iterator are lexicographically less than those of another.

fn le<I>(self, other: I) -> bool

where I: IntoIterator, Self::Item: PartialOrd<<I as IntoIterator>::Item>, Self: Sized,

Determines if the elements of this Iterator are lexicographically less or equal to those of another.

fn gt<I>(self, other: I) -> bool

where I: IntoIterator, Self::Item: PartialOrd<<I as IntoIterator>::Item>, Self: Sized,

Determines if the elements of this Iterator are lexicographically greater than those of another.

fn ge<I>(self, other: I) -> bool

where I: IntoIterator, Self::Item: PartialOrd<<I as IntoIterator>::Item>, Self: Sized,

Determines if the elements of this Iterator are lexicographically greater than or equal to those of another.

fn is_sorted(self) -> bool

where Self: Sized, Self::Item: PartialOrd,

Checks if the elements of this iterator are sorted.

fn is_sorted_by<F>(self, compare: F) -> bool

where Self: Sized, F: FnMut(&Self::Item, &Self::Item) -> bool,

Checks if the elements of this iterator are sorted using the given comparator function.

fn is_sorted_by_key<F, K>(self, f: F) -> bool

where Self: Sized, F: FnMut(Self::Item) -> K, K: PartialOrd,

Checks if the elements of this iterator are sorted using the given key extraction function.