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use num_traits::Float;
use std::cmp::Ordering;
use std::collections::HashSet;
/// Possible methodologies for calculating the center of clusters
#[derive(Debug, PartialEq)]
pub enum Center {
/// The elementwise mean of all data points in a cluster.
/// The output is not guaranteed to be an observed data point.
Centroid,
/// Calculates the geographical centroid for lat/lon coordinates.
/// Assumes input coordinates are in degrees (latitude, longitude).
/// Output coordinates are also in degrees.
GeoCentroid,
/// The point in a cluster with the minimum distance to all other points. Computationally more
/// expensive than centroids as requires calculation of pairwise distances (using the selected
/// distance metric). The output will be an observed data point in the cluster.
Medoid,
}
impl Center {
pub(crate) fn calc_centers<T: Float, F: Fn(&[T], &[T]) -> T>(
&self,
data: &[Vec<T>],
labels: &[i32],
dist_func: F,
) -> Vec<Vec<T>> {
match self {
Center::Centroid => self.calc_centroids(data, labels),
Center::GeoCentroid => self.calc_geo_centroids(data, labels),
Center::Medoid => self.calc_medoids(data, labels, dist_func),
}
}
fn calc_centroids<T: Float>(&self, data: &[Vec<T>], labels: &[i32]) -> Vec<Vec<T>> {
// All points weighted equally for now
let weights = vec![T::one(); data.len()];
Center::calc_weighted_centroids(data, labels, &weights)
}
fn calc_weighted_centroids<T: Float>(
data: &[Vec<T>],
labels: &[i32],
weights: &[T],
) -> Vec<Vec<T>> {
let n_dims = data[0].len();
let n_clusters = labels
.iter()
.filter(|&&label| label != -1)
.collect::<HashSet<_>>()
.len();
let mut centroids = Vec::with_capacity(n_clusters);
for cluster_id in 0..n_clusters as i32 {
let mut count = T::zero();
let mut element_wise_mean = vec![T::zero(); n_dims];
for n in 0..data.len() {
if cluster_id == labels[n] {
count = count + T::one();
element_wise_mean = data[n]
.iter()
.zip(element_wise_mean.iter())
.map(|(&element, &sum)| (element * weights[n]) + sum)
.collect();
}
}
for element in element_wise_mean.iter_mut() {
*element = *element / count;
}
centroids.push(element_wise_mean);
}
centroids
}
/// Calculates the geographical centeroid for each cluster.
///
/// This method is specifically designed for geographical data where each point
/// is represented by latitude and longitude coordinates.
///
/// # Arguments
///
/// * `data` - A slice of vectors, where each vector contains [latitude, longitude] in degrees.
/// * `labels` - A slice of cluster labels corresponding to each data point.
///
/// # Returns
///
/// A vector of cluster centers, where each center is a vector of [latitude, longitude] in degrees.
///
/// # Notes
///
/// - Assumes input coordinates are in degrees.
/// - Output coordinates are in degrees.
/// - Points with label -1 are considered noise and are ignored in calculations.
/// - Uses a spherical approximation of the Earth for calculations.
fn calc_geo_centroids<T: Float>(&self, data: &[Vec<T>], labels: &[i32]) -> Vec<Vec<T>> {
let n_clusters = labels
.iter()
.filter(|&&label| label != -1)
.collect::<HashSet<_>>()
.len();
let mut centers = vec![vec![T::zero(), T::zero(), T::zero()]; n_clusters];
let mut counts = vec![T::zero(); n_clusters];
for (point, &label) in data.iter().zip(labels.iter()) {
if label != -1 {
let cluster_index = label as usize;
let lat = point[0].to_radians();
let lon = point[1].to_radians();
let x = lon.cos() * lat.cos();
let y = lon.sin() * lat.cos();
let z = lat.sin();
centers[cluster_index][0] = centers[cluster_index][0] + x;
centers[cluster_index][1] = centers[cluster_index][1] + y;
centers[cluster_index][2] = centers[cluster_index][2] + z;
counts[cluster_index] = counts[cluster_index] + T::one();
}
}
for (center, &count) in centers.iter_mut().zip(counts.iter()) {
if count > T::zero() {
let x = center[0] / count;
let y = center[1] / count;
let z = center[2] / count;
let lon = y.atan2(x);
let hyp = (x * x + y * y).sqrt();
let lat = z.atan2(hyp);
// Convert back to degrees
center[0] = lat.to_degrees();
center[1] = lon.to_degrees();
}
}
centers.iter().map(|c| vec![c[0], c[1]]).collect()
}
fn calc_medoids<T: Float, F: Fn(&[T], &[T]) -> T>(
&self,
data: &[Vec<T>],
labels: &[i32],
dist_func: F,
) -> Vec<Vec<T>> {
let n_clusters = labels
.iter()
.filter(|&&label| label != -1)
.collect::<HashSet<_>>()
.len();
let mut medoids = Vec::with_capacity(n_clusters);
for cluster_id in 0..n_clusters as i32 {
let cluster_data = data
.iter()
.zip(labels.iter())
.filter(|(_datapoint, &label)| label == cluster_id)
.map(|(datapoint, _label)| datapoint)
.collect::<Vec<&Vec<_>>>();
let n_samples = cluster_data.len();
let medoid_idx = (0..n_samples)
.map(|i| {
(0..n_samples)
.map(|j| dist_func(cluster_data[i], cluster_data[j]))
.fold(T::zero(), std::ops::Add::add)
})
.enumerate()
.min_by(|(_idx_a, sum_a), (_idx_b, sum_b)| {
sum_a.partial_cmp(sum_b).unwrap_or(Ordering::Equal)
})
.map(|(idx, _sum)| idx)
.unwrap_or(0);
medoids.push(cluster_data[medoid_idx].clone())
}
medoids
}
}