affinityprop 0.2.0

Vectorized and Parallelized Affinity Propagation
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148

use ndarray::{Array2, ArrayView1, Axis, Zip};
use num_traits::Float;

/// Generate an N x N matrix in which each (i,j) index represents the
/// similarity between row i and row j of `x`
pub(crate) fn calculate_similarity<F, S>(x: &Array2<F>, s: S) -> Array2<F>
where
    F: Float + Send + Sync,
    S: Similarity<F>,
{
    let x_dim = x.dim();
    let mut out = Array2::<F>::zeros((x_dim.0, x_dim.0));
    // Calculate values for half of matrix
    x.axis_iter(Axis(0)).enumerate().for_each(|(idx1, row1)| {
        x.axis_iter(Axis(0))
            .enumerate()
            .skip(idx1 + 1)
            .for_each(|(idx2, row2)| {
                out[[idx1, idx2]] = s.similarity(&row1, &row2);
            });
    });
    // Copy over for remaining
    (0..x_dim.0).for_each(|idx1| {
        (idx1 + 1..x_dim.0).for_each(|idx2| out[[idx2, idx1]] = out[[idx1, idx2]]);
    });
    out
}

/// Determine the similarity between two data entries.
///
/// Affinity Propagation expects *s(i,j)* > *s(i, k)* iff x<sub>i</sub> is more similar
/// to x<sub>j</sub> than to x<sub>k</sub>.
pub trait Similarity<F>
where
    F: Float + Send + Sync,
{
    fn similarity(&self, a: &ArrayView1<F>, b: &ArrayView1<F>) -> F;
}

/// Perform similarity calculation as `-1 * sum((row_i - row_j)**2)`
#[derive(Debug, Clone)]
pub struct NegEuclidean<F> {
    neg_one: F,
}

impl<F> Default for NegEuclidean<F>
where
    F: Float + Send + Sync,
{
    fn default() -> Self {
        Self {
            neg_one: F::from(-1.).unwrap(),
        }
    }
}

impl<F> Similarity<F> for NegEuclidean<F>
where
    F: Float + Send + Sync,
{
    fn similarity(&self, a: &ArrayView1<F>, b: &ArrayView1<F>) -> F {
        let mut row_diff = a - b;
        row_diff.map_inplace(|_a| *_a = (*_a).powi(2));
        self.neg_one * row_diff.sum()
    }
}

/// Perform similarity calculation as `-1 * (row_i . row_j)/(|row_i|*|row_j|)`
#[derive(Debug, Clone)]
pub struct NegCosine<F> {
    neg_one: F,
}

impl<F> Default for NegCosine<F>
where
    F: Float + Send + Sync,
{
    fn default() -> Self {
        Self {
            neg_one: F::from(-1.).unwrap(),
        }
    }
}

impl<F> Similarity<F> for NegCosine<F>
where
    F: Float + Send + Sync,
{
    fn similarity(&self, a: &ArrayView1<F>, b: &ArrayView1<F>) -> F {
        let dot_product: F = Zip::from(a).and(b).map_collect(|r1, r2| *r1 * *r2).sum();
        let x_magnitude = a.map(|r| r.powi(2)).sum().sqrt();
        let y_magnitude = b.map(|r| r.powi(2)).sum().sqrt();
        self.neg_one * dot_product / x_magnitude / y_magnitude
    }
}

/// Perform similarity calculation as `sum(log((a - b)**2))`
#[derive(Default, Debug, Clone)]
pub struct LogEuclidean;

impl<F> Similarity<F> for LogEuclidean
where
    F: Float + Send + Sync,
{
    fn similarity(&self, a: &ArrayView1<F>, b: &ArrayView1<F>) -> F {
        let mut row_diff = a - b;
        row_diff.map_inplace(|_a| *_a = (*_a).powi(2).log2());
        row_diff.sum()
    }
}

#[cfg(test)]
mod test {
    use ndarray::{arr2, Zip};

    use crate::similarity::calculate_similarity;
    use crate::{LogEuclidean, NegCosine, NegEuclidean};

    #[test]
    fn euclidean_similarity() {
        let x = arr2(&[[1., 1., 1.], [2., 2., 2.], [3., 3., 3.]]);
        let s = calculate_similarity(&x, NegEuclidean::default());
        let actual = arr2(&[[0., -3.0, -12.0], [-3.0, 0., -3.0], [-12.0, -3.0, 0.]]);
        Zip::from(&s)
            .and(&actual)
            .for_each(|a: &f64, b: &f64| assert!((a - b).abs() < 1e-4));
    }

    #[test]
    fn cosine_similarity() {
        let x = arr2(&[[3., 2., 0., 5.], [1., 0., 0., 0.]]);
        let s = calculate_similarity(&x, NegCosine::default());
        let actual = arr2(&[[0., -0.4866], [-0.4866, 0.]]);
        Zip::from(&s)
            .and(&actual)
            .for_each(|a: &f64, b: &f64| assert!((a - b).abs() < 1e-4));
    }

    #[test]
    fn log_euclidean_similarity() {
        let x = arr2(&[[1., 1., 1.], [2., 2., 2.], [3., 3., 3.]]);
        let s = calculate_similarity(&x, LogEuclidean::default());
        let actual = arr2(&[[0., 0., 6.], [0., 0., 0.], [6., 0., 0.]]);
        Zip::from(&s)
            .and(&actual)
            .for_each(|a: &f64, b: &f64| assert!((a - b).abs() < 1e-4));
    }
}