sklears_kernel_approximation/
robust_kernels.rs

1//! Robust kernel methods with outlier resistance
2//!
3//! This module provides robust kernel approximation methods that are resistant
4//! to outliers and contamination in the data, including robust estimators,
5//! breakdown point analysis, and influence function diagnostics.
6
7use scirs2_core::ndarray::{Array1, Array2, ArrayView1, Axis};
8use scirs2_core::random::essentials::Normal as RandNormal;
9use scirs2_core::random::rngs::StdRng as RealStdRng;
10use scirs2_core::random::seq::SliceRandom;
11use scirs2_core::random::Rng;
12use scirs2_core::random::{thread_rng, SeedableRng};
13use sklears_core::error::Result;
14use std::collections::HashMap;
15
16/// Robust estimation method
17#[derive(Clone, Debug, PartialEq)]
18/// RobustEstimator
19pub enum RobustEstimator {
20    /// Huber M-estimator
21    Huber { delta: f64 },
22    /// Tukey bisquare estimator
23    Tukey { c: f64 },
24    /// Hampel estimator
25    Hampel { a: f64, b: f64, c: f64 },
26    /// Minimum Volume Ellipsoid (MVE)
27    MVE { alpha: f64 },
28    /// Minimum Covariance Determinant (MCD)
29    MCD { alpha: f64 },
30    /// S-estimator
31    SEstimator { breakdown_point: f64 },
32    /// MM-estimator
33    MMEstimator { efficiency: f64 },
34    /// L1-estimator (LAD regression)
35    L1,
36    /// Quantile regression estimator
37    Quantile { tau: f64 },
38}
39
40/// Robust loss function
41#[derive(Clone, Debug, PartialEq)]
42/// RobustLoss
43pub enum RobustLoss {
44    /// Huber loss
45    Huber { delta: f64 },
46    /// Epsilon-insensitive loss
47    EpsilonInsensitive { epsilon: f64 },
48    /// Tukey bisquare loss
49    Tukey { c: f64 },
50    /// Cauchy loss
51    Cauchy { sigma: f64 },
52    /// Welsch loss
53    Welsch { sigma: f64 },
54    /// Fair loss
55    Fair { c: f64 },
56    /// Logistic loss
57    Logistic { alpha: f64 },
58    /// Quantile loss
59    Quantile { tau: f64 },
60}
61
62/// Robust kernel configuration
63#[derive(Clone, Debug)]
64/// RobustKernelConfig
65pub struct RobustKernelConfig {
66    /// Robust estimator method
67    pub estimator: RobustEstimator,
68    /// Robust loss function
69    pub loss: RobustLoss,
70    /// Maximum number of iterations for robust estimation
71    pub max_iterations: usize,
72    /// Convergence tolerance
73    pub tolerance: f64,
74    /// Contamination fraction
75    pub contamination: f64,
76    /// Whether to use iteratively reweighted least squares
77    pub use_irls: bool,
78    /// Random state for reproducibility
79    pub random_state: Option<u64>,
80}
81
82impl Default for RobustKernelConfig {
83    fn default() -> Self {
84        Self {
85            estimator: RobustEstimator::Huber { delta: 1.345 },
86            loss: RobustLoss::Huber { delta: 1.345 },
87            max_iterations: 100,
88            tolerance: 1e-6,
89            contamination: 0.1,
90            use_irls: true,
91            random_state: None,
92        }
93    }
94}
95
96/// Robust RBF kernel sampler
97pub struct RobustRBFSampler {
98    n_components: usize,
99    gamma: f64,
100    config: RobustKernelConfig,
101    random_weights: Option<Array2<f64>>,
102    random_offset: Option<Array1<f64>>,
103    robust_weights: Option<Array1<f64>>,
104    outlier_mask: Option<Array1<bool>>,
105}
106
107impl RobustRBFSampler {
108    /// Create a new robust RBF sampler
109    pub fn new(n_components: usize) -> Self {
110        Self {
111            n_components,
112            gamma: 1.0,
113            config: RobustKernelConfig::default(),
114            random_weights: None,
115            random_offset: None,
116            robust_weights: None,
117            outlier_mask: None,
118        }
119    }
120
121    /// Set gamma parameter
122    pub fn gamma(mut self, gamma: f64) -> Self {
123        self.gamma = gamma;
124        self
125    }
126
127    /// Set robust configuration
128    pub fn with_config(mut self, config: RobustKernelConfig) -> Self {
129        self.config = config;
130        self
131    }
132
133    /// Fit the robust RBF sampler
134    pub fn fit(&mut self, x: &Array2<f64>) -> Result<()> {
135        let n_features = x.ncols();
136
137        // Initialize random weights
138        let normal = RandNormal::new(0.0, (2.0 * self.gamma).sqrt()).unwrap();
139        let mut rng = if let Some(seed) = self.config.random_state {
140            RealStdRng::seed_from_u64(seed)
141        } else {
142            RealStdRng::from_seed(thread_rng().gen())
143        };
144
145        self.random_weights = Some(Array2::from_shape_fn(
146            (n_features, self.n_components),
147            |_| rng.sample(normal),
148        ));
149
150        self.random_offset = Some(Array1::from_shape_fn(self.n_components, |_| {
151            rng.gen_range(0.0..2.0 * std::f64::consts::PI)
152        }));
153
154        // Detect outliers and compute robust weights
155        self.detect_outliers(x)?;
156        self.compute_robust_weights(x)?;
157
158        Ok(())
159    }
160
161    /// Transform data using robust RBF features
162    pub fn transform(&self, x: &Array2<f64>) -> Result<Array2<f64>> {
163        let weights = self.random_weights.as_ref().ok_or("Model not fitted")?;
164        let offset = self.random_offset.as_ref().ok_or("Model not fitted")?;
165
166        // Compute projection: X * W + b
167        let projection = x.dot(weights) + offset;
168
169        // Apply cosine transformation with robust weights
170        let mut transformed =
171            projection.mapv(|x| (x * (2.0 / self.n_components as f64).sqrt()).cos());
172
173        // Apply robust weighting if available
174        if let Some(robust_weights) = &self.robust_weights {
175            for (mut row, &weight) in transformed
176                .rows_mut()
177                .into_iter()
178                .zip(robust_weights.iter())
179            {
180                row *= weight;
181            }
182        }
183
184        Ok(transformed)
185    }
186
187    /// Detect outliers using robust methods
188    fn detect_outliers(&mut self, x: &Array2<f64>) -> Result<()> {
189        match &self.config.estimator {
190            RobustEstimator::MVE { alpha } => {
191                self.outlier_mask = Some(self.detect_outliers_mve(x, *alpha)?);
192            }
193            RobustEstimator::MCD { alpha } => {
194                self.outlier_mask = Some(self.detect_outliers_mcd(x, *alpha)?);
195            }
196            RobustEstimator::Huber { delta } => {
197                self.outlier_mask = Some(self.detect_outliers_huber(x, *delta)?);
198            }
199            RobustEstimator::Tukey { c } => {
200                self.outlier_mask = Some(self.detect_outliers_tukey(x, *c)?);
201            }
202            _ => {
203                // Use default outlier detection based on Mahalanobis distance
204                self.outlier_mask = Some(self.detect_outliers_mahalanobis(x)?);
205            }
206        }
207
208        Ok(())
209    }
210
211    /// Detect outliers using Minimum Volume Ellipsoid
212    fn detect_outliers_mve(&self, x: &Array2<f64>, alpha: f64) -> Result<Array1<bool>> {
213        let n_samples = x.nrows();
214        let n_features = x.ncols();
215        let h = ((n_samples as f64 * alpha).floor() as usize).max(n_features + 1);
216
217        let mut best_volume = f64::INFINITY;
218        let mut best_subset = Vec::new();
219        let mut rng = thread_rng();
220
221        // Try multiple random subsets
222        for _ in 0..100 {
223            let mut subset: Vec<usize> = (0..n_samples).collect();
224            subset.shuffle(&mut rng);
225            subset.truncate(h);
226
227            // Compute covariance matrix for subset
228            let subset_data = self.extract_subset(x, &subset);
229            let (_mean, cov) = self.compute_robust_statistics(&subset_data);
230
231            // Compute volume (determinant of covariance matrix)
232            let volume = self.compute_determinant(&cov);
233
234            if volume < best_volume {
235                best_volume = volume;
236                best_subset = subset;
237            }
238        }
239
240        // Mark outliers based on best subset
241        let mut outlier_mask = Array1::from_elem(n_samples, true);
242        for &idx in &best_subset {
243            outlier_mask[idx] = false;
244        }
245
246        Ok(outlier_mask)
247    }
248
249    /// Detect outliers using Minimum Covariance Determinant
250    fn detect_outliers_mcd(&self, x: &Array2<f64>, alpha: f64) -> Result<Array1<bool>> {
251        let n_samples = x.nrows();
252        let n_features = x.ncols();
253        let h = ((n_samples as f64 * alpha).floor() as usize).max(n_features + 1);
254
255        let mut best_determinant = f64::INFINITY;
256        let mut best_subset = Vec::new();
257        let mut rng = thread_rng();
258
259        // Try multiple random subsets
260        for _ in 0..100 {
261            let mut subset: Vec<usize> = (0..n_samples).collect();
262            subset.shuffle(&mut rng);
263            subset.truncate(h);
264
265            // Iteratively improve subset
266            for _ in 0..10 {
267                let subset_data = self.extract_subset(x, &subset);
268                let (mean, cov) = self.compute_robust_statistics(&subset_data);
269                let determinant = self.compute_determinant(&cov);
270
271                if determinant < best_determinant {
272                    best_determinant = determinant;
273                    best_subset = subset.clone();
274                }
275
276                // Update subset based on distances
277                let distances = self.compute_mahalanobis_distances(x, &mean, &cov);
278                let mut indexed_distances: Vec<(usize, f64)> =
279                    distances.iter().enumerate().map(|(i, &d)| (i, d)).collect();
280                indexed_distances.sort_by(|a, b| a.1.partial_cmp(&b.1).unwrap());
281
282                subset = indexed_distances.iter().take(h).map(|(i, _)| *i).collect();
283            }
284        }
285
286        // Mark outliers based on best subset
287        let mut outlier_mask = Array1::from_elem(n_samples, true);
288        for &idx in &best_subset {
289            outlier_mask[idx] = false;
290        }
291
292        Ok(outlier_mask)
293    }
294
295    /// Detect outliers using Huber estimator
296    fn detect_outliers_huber(&self, x: &Array2<f64>, delta: f64) -> Result<Array1<bool>> {
297        let n_samples = x.nrows();
298        let mut outlier_mask = Array1::from_elem(n_samples, false);
299
300        // Compute robust center and scale
301        let center = self.compute_huber_center(x, delta);
302        let scale = self.compute_huber_scale(x, &center, delta);
303
304        // Mark outliers based on Huber criterion
305        for i in 0..n_samples {
306            let distance = self.compute_huber_distance(&x.row(i), &center, delta);
307            if distance > 3.0 * scale {
308                outlier_mask[i] = true;
309            }
310        }
311
312        Ok(outlier_mask)
313    }
314
315    /// Detect outliers using Tukey bisquare estimator
316    fn detect_outliers_tukey(&self, x: &Array2<f64>, c: f64) -> Result<Array1<bool>> {
317        let n_samples = x.nrows();
318        let mut outlier_mask = Array1::from_elem(n_samples, false);
319
320        // Compute robust center and scale
321        let center = self.compute_tukey_center(x, c);
322        let scale = self.compute_tukey_scale(x, &center, c);
323
324        // Mark outliers based on Tukey criterion
325        for i in 0..n_samples {
326            let distance = self.compute_tukey_distance(&x.row(i), &center, c);
327            if distance > 3.0 * scale {
328                outlier_mask[i] = true;
329            }
330        }
331
332        Ok(outlier_mask)
333    }
334
335    /// Detect outliers using Mahalanobis distance
336    fn detect_outliers_mahalanobis(&self, x: &Array2<f64>) -> Result<Array1<bool>> {
337        let n_samples = x.nrows();
338        let mut outlier_mask = Array1::from_elem(n_samples, false);
339
340        // Compute robust statistics
341        let (mean, cov) = self.compute_robust_statistics(x);
342        let distances = self.compute_mahalanobis_distances(x, &mean, &cov);
343
344        // Use chi-square threshold for outlier detection
345        let threshold = 3.0; // Approximately 99.7% confidence for normal distribution
346
347        for (i, &distance) in distances.iter().enumerate() {
348            if distance > threshold {
349                outlier_mask[i] = true;
350            }
351        }
352
353        Ok(outlier_mask)
354    }
355
356    /// Compute robust weights using IRLS
357    fn compute_robust_weights(&mut self, x: &Array2<f64>) -> Result<()> {
358        let n_samples = x.nrows();
359        let mut weights = Array1::ones(n_samples);
360
361        if self.config.use_irls {
362            for _iteration in 0..self.config.max_iterations {
363                let old_weights = weights.clone();
364
365                // Update weights based on robust loss function
366                for i in 0..n_samples {
367                    let residual = self.compute_residual(&x.row(i), i);
368                    weights[i] = self.compute_robust_weight(residual);
369                }
370
371                // Check convergence
372                let weight_change = (&weights - &old_weights).mapv(|x| x.abs()).sum();
373                if weight_change < self.config.tolerance {
374                    break;
375                }
376            }
377        }
378
379        // Set outlier weights to zero
380        if let Some(outlier_mask) = &self.outlier_mask {
381            for (i, &is_outlier) in outlier_mask.iter().enumerate() {
382                if is_outlier {
383                    weights[i] = 0.0;
384                }
385            }
386        }
387
388        self.robust_weights = Some(weights);
389        Ok(())
390    }
391
392    /// Compute residual for robust weight calculation
393    fn compute_residual(&self, sample: &ArrayView1<f64>, _index: usize) -> f64 {
394        // Simplified residual computation - in practice this would depend on the specific problem
395        sample.iter().map(|&x| x.abs()).sum::<f64>() / sample.len() as f64
396    }
397
398    /// Compute robust weight based on loss function
399    fn compute_robust_weight(&self, residual: f64) -> f64 {
400        match &self.config.loss {
401            RobustLoss::Huber { delta } => {
402                if residual.abs() <= *delta {
403                    1.0
404                } else {
405                    *delta / residual.abs()
406                }
407            }
408            RobustLoss::Tukey { c } => {
409                let u = residual / *c;
410                if u.abs() <= 1.0 {
411                    (1.0 - u * u).powi(2)
412                } else {
413                    0.0
414                }
415            }
416            RobustLoss::Cauchy { sigma } => 1.0 / (1.0 + (residual / *sigma).powi(2)),
417            RobustLoss::Welsch { sigma } => (-(residual / *sigma).powi(2)).exp(),
418            RobustLoss::Fair { c } => *c / (residual.abs() + *c),
419            _ => 1.0, // Default weight
420        }
421    }
422
423    /// Extract subset of data
424    fn extract_subset(&self, x: &Array2<f64>, indices: &[usize]) -> Array2<f64> {
425        let n_features = x.ncols();
426        let mut subset = Array2::zeros((indices.len(), n_features));
427
428        for (i, &idx) in indices.iter().enumerate() {
429            subset.row_mut(i).assign(&x.row(idx));
430        }
431
432        subset
433    }
434
435    /// Compute robust statistics (mean and covariance)
436    fn compute_robust_statistics(&self, x: &Array2<f64>) -> (Array1<f64>, Array2<f64>) {
437        let n_samples = x.nrows();
438        let n_features = x.ncols();
439
440        // Compute mean
441        let mean = x.mean_axis(Axis(0)).unwrap();
442
443        // Compute covariance
444        let mut cov = Array2::zeros((n_features, n_features));
445        for sample in x.rows() {
446            let centered = &sample - &mean;
447            for i in 0..n_features {
448                for j in 0..n_features {
449                    cov[[i, j]] += centered[i] * centered[j];
450                }
451            }
452        }
453        cov /= (n_samples - 1) as f64;
454
455        (mean, cov)
456    }
457
458    /// Compute determinant of matrix
459    fn compute_determinant(&self, matrix: &Array2<f64>) -> f64 {
460        // Simplified determinant computation for 2x2 case
461        if matrix.nrows() == 2 && matrix.ncols() == 2 {
462            matrix[[0, 0]] * matrix[[1, 1]] - matrix[[0, 1]] * matrix[[1, 0]]
463        } else {
464            // For larger matrices, use a simplified approach
465            matrix.diag().iter().product::<f64>()
466        }
467    }
468
469    /// Compute Mahalanobis distances
470    fn compute_mahalanobis_distances(
471        &self,
472        x: &Array2<f64>,
473        mean: &Array1<f64>,
474        _cov: &Array2<f64>,
475    ) -> Array1<f64> {
476        let n_samples = x.nrows();
477        let mut distances = Array1::zeros(n_samples);
478
479        // Simplified Mahalanobis distance computation
480        for (i, sample) in x.rows().into_iter().enumerate() {
481            let centered = &sample - mean;
482            let distance = centered.dot(&centered).sqrt();
483            distances[i] = distance;
484        }
485
486        distances
487    }
488
489    /// Compute Huber center
490    fn compute_huber_center(&self, x: &Array2<f64>, _delta: f64) -> Array1<f64> {
491        // Simplified Huber center computation
492        x.mean_axis(Axis(0)).unwrap()
493    }
494
495    /// Compute Huber scale
496    fn compute_huber_scale(&self, x: &Array2<f64>, center: &Array1<f64>, _delta: f64) -> f64 {
497        // Simplified Huber scale computation
498        let distances: Vec<f64> = x
499            .rows()
500            .into_iter()
501            .map(|row| (&row - center).mapv(|x| x.abs()).sum())
502            .collect();
503
504        let mut sorted_distances = distances;
505        sorted_distances.sort_by(|a, b| a.partial_cmp(b).unwrap());
506        sorted_distances[sorted_distances.len() / 2] // Median
507    }
508
509    /// Compute Huber distance
510    fn compute_huber_distance(
511        &self,
512        sample: &ArrayView1<f64>,
513        center: &Array1<f64>,
514        _delta: f64,
515    ) -> f64 {
516        (sample - center).mapv(|x| x.abs()).sum()
517    }
518
519    /// Compute Tukey center
520    fn compute_tukey_center(&self, x: &Array2<f64>, _c: f64) -> Array1<f64> {
521        // Simplified Tukey center computation
522        x.mean_axis(Axis(0)).unwrap()
523    }
524
525    /// Compute Tukey scale
526    fn compute_tukey_scale(&self, x: &Array2<f64>, center: &Array1<f64>, _c: f64) -> f64 {
527        // Simplified Tukey scale computation
528        let distances: Vec<f64> = x
529            .rows()
530            .into_iter()
531            .map(|row| (&row - center).mapv(|x| x.abs()).sum())
532            .collect();
533
534        let mut sorted_distances = distances;
535        sorted_distances.sort_by(|a, b| a.partial_cmp(b).unwrap());
536        sorted_distances[sorted_distances.len() / 2] // Median
537    }
538
539    /// Compute Tukey distance
540    fn compute_tukey_distance(
541        &self,
542        sample: &ArrayView1<f64>,
543        center: &Array1<f64>,
544        _c: f64,
545    ) -> f64 {
546        (sample - center).mapv(|x| x.abs()).sum()
547    }
548
549    /// Get outlier mask
550    pub fn get_outlier_mask(&self) -> Option<&Array1<bool>> {
551        self.outlier_mask.as_ref()
552    }
553
554    /// Get robust weights
555    pub fn get_robust_weights(&self) -> Option<&Array1<f64>> {
556        self.robust_weights.as_ref()
557    }
558}
559
560/// Robust Nyström method
561pub struct RobustNystroem {
562    n_components: usize,
563    gamma: f64,
564    config: RobustKernelConfig,
565    basis_indices: Option<Vec<usize>>,
566    basis_kernel: Option<Array2<f64>>,
567    normalization: Option<Array2<f64>>,
568    robust_weights: Option<Array1<f64>>,
569    outlier_mask: Option<Array1<bool>>,
570}
571
572impl RobustNystroem {
573    /// Create a new robust Nyström method
574    pub fn new(n_components: usize) -> Self {
575        Self {
576            n_components,
577            gamma: 1.0,
578            config: RobustKernelConfig::default(),
579            basis_indices: None,
580            basis_kernel: None,
581            normalization: None,
582            robust_weights: None,
583            outlier_mask: None,
584        }
585    }
586
587    /// Set gamma parameter
588    pub fn gamma(mut self, gamma: f64) -> Self {
589        self.gamma = gamma;
590        self
591    }
592
593    /// Set robust configuration
594    pub fn with_config(mut self, config: RobustKernelConfig) -> Self {
595        self.config = config;
596        self
597    }
598
599    /// Fit the robust Nyström method
600    pub fn fit(&mut self, x: &Array2<f64>) -> Result<()> {
601        // Detect outliers
602        let mut robust_rbf = RobustRBFSampler::new(self.n_components)
603            .gamma(self.gamma)
604            .with_config(self.config.clone());
605
606        robust_rbf.fit(x)?;
607        self.outlier_mask = robust_rbf.get_outlier_mask().cloned();
608        self.robust_weights = robust_rbf.get_robust_weights().cloned();
609
610        // Sample basis points excluding outliers
611        self.sample_robust_basis_points(x)?;
612
613        // Compute robust kernel matrix
614        let basis_points = self.get_basis_points(x);
615        let kernel_matrix = self.compute_robust_kernel_matrix(&basis_points)?;
616
617        // Compute eigendecomposition
618        let (eigenvalues, eigenvectors) = self.compute_eigendecomposition(&kernel_matrix)?;
619
620        // Store normalization factors
621        self.normalization = Some(self.compute_normalization(&eigenvalues, &eigenvectors)?);
622
623        Ok(())
624    }
625
626    /// Transform data using robust Nyström features
627    pub fn transform(&self, x: &Array2<f64>) -> Result<Array2<f64>> {
628        let normalization = self.normalization.as_ref().ok_or("Model not fitted")?;
629
630        // Compute kernel values between input and basis points
631        let kernel_values = self.compute_robust_kernel_values(x)?;
632
633        // Apply normalization
634        let result = kernel_values.dot(normalization);
635
636        Ok(result)
637    }
638
639    /// Sample robust basis points
640    fn sample_robust_basis_points(&mut self, x: &Array2<f64>) -> Result<()> {
641        let n_samples = x.nrows();
642        let mut indices = Vec::new();
643        let mut rng = if let Some(seed) = self.config.random_state {
644            RealStdRng::seed_from_u64(seed)
645        } else {
646            RealStdRng::from_seed(thread_rng().gen())
647        };
648
649        // Filter out outliers if available
650        let available_indices: Vec<usize> = if let Some(outlier_mask) = &self.outlier_mask {
651            (0..n_samples).filter(|&i| !outlier_mask[i]).collect()
652        } else {
653            (0..n_samples).collect()
654        };
655
656        // Sample basis points from non-outliers
657        let n_available = available_indices.len();
658        let n_basis = std::cmp::min(self.n_components, n_available);
659
660        for _ in 0..n_basis {
661            let idx = rng.gen_range(0..n_available);
662            indices.push(available_indices[idx]);
663        }
664
665        self.basis_indices = Some(indices);
666        Ok(())
667    }
668
669    /// Get basis points
670    fn get_basis_points(&self, x: &Array2<f64>) -> Array2<f64> {
671        let indices = self.basis_indices.as_ref().unwrap();
672        let n_features = x.ncols();
673        let mut basis_points = Array2::zeros((indices.len(), n_features));
674
675        for (i, &idx) in indices.iter().enumerate() {
676            basis_points.row_mut(i).assign(&x.row(idx));
677        }
678
679        basis_points
680    }
681
682    /// Compute robust kernel matrix
683    fn compute_robust_kernel_matrix(&self, basis_points: &Array2<f64>) -> Result<Array2<f64>> {
684        let n_basis = basis_points.nrows();
685        let mut kernel_matrix = Array2::zeros((n_basis, n_basis));
686
687        for i in 0..n_basis {
688            for j in i..n_basis {
689                let dist_sq = basis_points
690                    .row(i)
691                    .iter()
692                    .zip(basis_points.row(j).iter())
693                    .map(|(&a, &b)| (a - b).powi(2))
694                    .sum::<f64>();
695
696                let kernel_value = (-self.gamma * dist_sq).exp();
697                kernel_matrix[[i, j]] = kernel_value;
698                kernel_matrix[[j, i]] = kernel_value;
699            }
700        }
701
702        // Apply robust weighting if available
703        if let Some(weights) = &self.robust_weights {
704            let indices = self.basis_indices.as_ref().unwrap();
705            for (i, &idx_i) in indices.iter().enumerate() {
706                for (j, &idx_j) in indices.iter().enumerate() {
707                    kernel_matrix[[i, j]] *= (weights[idx_i] * weights[idx_j]).sqrt();
708                }
709            }
710        }
711
712        Ok(kernel_matrix)
713    }
714
715    /// Compute eigendecomposition
716    fn compute_eigendecomposition(
717        &self,
718        kernel_matrix: &Array2<f64>,
719    ) -> Result<(Array1<f64>, Array2<f64>)> {
720        // Simplified eigendecomposition
721        let n = kernel_matrix.nrows();
722        let eigenvalues = Array1::ones(n);
723        let eigenvectors = kernel_matrix.clone();
724
725        Ok((eigenvalues, eigenvectors))
726    }
727
728    /// Compute normalization factors
729    fn compute_normalization(
730        &self,
731        eigenvalues: &Array1<f64>,
732        eigenvectors: &Array2<f64>,
733    ) -> Result<Array2<f64>> {
734        let mut normalization = Array2::zeros(eigenvectors.dim());
735
736        for i in 0..eigenvectors.nrows() {
737            for j in 0..eigenvectors.ncols() {
738                if eigenvalues[j] > 1e-10 {
739                    normalization[[i, j]] = eigenvectors[[i, j]] / eigenvalues[j].sqrt();
740                }
741            }
742        }
743
744        Ok(normalization)
745    }
746
747    /// Compute robust kernel values
748    fn compute_robust_kernel_values(&self, x: &Array2<f64>) -> Result<Array2<f64>> {
749        let indices = self.basis_indices.as_ref().unwrap();
750        let n_samples = x.nrows();
751        let n_basis = indices.len();
752        let mut kernel_values = Array2::zeros((n_samples, n_basis));
753
754        for i in 0..n_samples {
755            for (j, &_basis_idx) in indices.iter().enumerate() {
756                // For now, just use a placeholder computation
757                kernel_values[[i, j]] = thread_rng().gen_range(0.0..1.0);
758            }
759        }
760
761        Ok(kernel_values)
762    }
763
764    /// Get outlier mask
765    pub fn get_outlier_mask(&self) -> Option<&Array1<bool>> {
766        self.outlier_mask.as_ref()
767    }
768
769    /// Get robust weights
770    pub fn get_robust_weights(&self) -> Option<&Array1<f64>> {
771        self.robust_weights.as_ref()
772    }
773}
774
775/// Breakdown point analysis
776pub struct BreakdownPointAnalysis {
777    estimator: RobustEstimator,
778    contamination_levels: Vec<f64>,
779    breakdown_points: HashMap<String, f64>,
780}
781
782impl Default for BreakdownPointAnalysis {
783    fn default() -> Self {
784        Self::new()
785    }
786}
787
788impl BreakdownPointAnalysis {
789    /// Create a new breakdown point analysis
790    pub fn new() -> Self {
791        Self {
792            estimator: RobustEstimator::Huber { delta: 1.345 },
793            contamination_levels: (1..=50).map(|x| x as f64 / 100.0).collect(),
794            breakdown_points: HashMap::new(),
795        }
796    }
797
798    /// Set robust estimator
799    pub fn with_estimator(mut self, estimator: RobustEstimator) -> Self {
800        self.estimator = estimator;
801        self
802    }
803
804    /// Analyze breakdown point
805    pub fn analyze(&mut self, x: &Array2<f64>) -> Result<f64> {
806        let mut breakdown_point = 0.0;
807
808        for &contamination in &self.contamination_levels {
809            let contaminated_data = self.add_contamination(x, contamination);
810            let bias = self.compute_bias(&contaminated_data, x)?;
811
812            if bias > 0.5 {
813                // Threshold for breakdown
814                breakdown_point = contamination;
815                break;
816            }
817        }
818
819        let estimator_name = format!("{:?}", self.estimator);
820        self.breakdown_points
821            .insert(estimator_name, breakdown_point);
822
823        Ok(breakdown_point)
824    }
825
826    /// Add contamination to data
827    fn add_contamination(&self, x: &Array2<f64>, contamination: f64) -> Array2<f64> {
828        let n_samples = x.nrows();
829        let n_contaminated = (n_samples as f64 * contamination) as usize;
830        let mut contaminated = x.clone();
831        let mut rng = thread_rng();
832
833        // Add outliers to random samples
834        for _ in 0..n_contaminated {
835            let idx = rng.gen_range(0..n_samples);
836            for j in 0..x.ncols() {
837                contaminated[[idx, j]] += rng.gen_range(-10.0..10.0);
838            }
839        }
840
841        contaminated
842    }
843
844    /// Compute bias of estimator
845    fn compute_bias(&self, contaminated: &Array2<f64>, original: &Array2<f64>) -> Result<f64> {
846        // Simplified bias computation
847        let original_mean = original.mean_axis(Axis(0)).unwrap();
848        let contaminated_mean = contaminated.mean_axis(Axis(0)).unwrap();
849
850        let bias = (&contaminated_mean - &original_mean)
851            .mapv(|x| x.abs())
852            .sum();
853        Ok(bias)
854    }
855
856    /// Get breakdown points for all estimators
857    pub fn get_breakdown_points(&self) -> &HashMap<String, f64> {
858        &self.breakdown_points
859    }
860}
861
862/// Influence function diagnostics
863pub struct InfluenceFunctionDiagnostics {
864    estimator: RobustEstimator,
865    influence_values: Option<Array1<f64>>,
866    leverage_values: Option<Array1<f64>>,
867    cook_distances: Option<Array1<f64>>,
868}
869
870impl Default for InfluenceFunctionDiagnostics {
871    fn default() -> Self {
872        Self::new()
873    }
874}
875
876impl InfluenceFunctionDiagnostics {
877    /// Create a new influence function diagnostics
878    pub fn new() -> Self {
879        Self {
880            estimator: RobustEstimator::Huber { delta: 1.345 },
881            influence_values: None,
882            leverage_values: None,
883            cook_distances: None,
884        }
885    }
886
887    /// Set robust estimator
888    pub fn with_estimator(mut self, estimator: RobustEstimator) -> Self {
889        self.estimator = estimator;
890        self
891    }
892
893    /// Compute influence diagnostics
894    pub fn compute(&mut self, x: &Array2<f64>, y: &Array1<f64>) -> Result<()> {
895        self.influence_values = Some(self.compute_influence_values(x, y)?);
896        self.leverage_values = Some(self.compute_leverage_values(x)?);
897        self.cook_distances = Some(self.compute_cook_distances(x, y)?);
898
899        Ok(())
900    }
901
902    /// Compute influence values
903    fn compute_influence_values(&self, x: &Array2<f64>, y: &Array1<f64>) -> Result<Array1<f64>> {
904        let n_samples = x.nrows();
905        let mut influence = Array1::zeros(n_samples);
906
907        // Compute baseline estimate
908        let baseline_estimate = self.compute_robust_estimate(x, y)?;
909
910        // Compute influence by removing each observation
911        for i in 0..n_samples {
912            let (x_reduced, y_reduced) = self.remove_observation(x, y, i);
913            let reduced_estimate = self.compute_robust_estimate(&x_reduced, &y_reduced)?;
914            influence[i] = (baseline_estimate - reduced_estimate).abs();
915        }
916
917        Ok(influence)
918    }
919
920    /// Compute leverage values
921    fn compute_leverage_values(&self, x: &Array2<f64>) -> Result<Array1<f64>> {
922        let n_samples = x.nrows();
923        let mut leverage = Array1::zeros(n_samples);
924
925        // Simplified leverage computation
926        let (mean, _cov) = self.compute_robust_statistics(x);
927
928        for i in 0..n_samples {
929            let centered = &x.row(i) - &mean;
930            leverage[i] = centered.dot(&centered); // Simplified
931        }
932
933        Ok(leverage)
934    }
935
936    /// Compute Cook's distances
937    fn compute_cook_distances(&self, x: &Array2<f64>, y: &Array1<f64>) -> Result<Array1<f64>> {
938        let n_samples = x.nrows();
939        let mut cook_distances = Array1::zeros(n_samples);
940
941        // Simplified Cook's distance computation
942        let influence = self.compute_influence_values(x, y)?;
943        let leverage = self.compute_leverage_values(x)?;
944
945        for i in 0..n_samples {
946            cook_distances[i] = influence[i] * leverage[i];
947        }
948
949        Ok(cook_distances)
950    }
951
952    /// Remove observation from dataset
953    fn remove_observation(
954        &self,
955        x: &Array2<f64>,
956        y: &Array1<f64>,
957        index: usize,
958    ) -> (Array2<f64>, Array1<f64>) {
959        let n_samples = x.nrows();
960        let n_features = x.ncols();
961
962        let mut x_reduced = Array2::zeros((n_samples - 1, n_features));
963        let mut y_reduced = Array1::zeros(n_samples - 1);
964
965        let mut reduced_idx = 0;
966        for i in 0..n_samples {
967            if i != index {
968                x_reduced.row_mut(reduced_idx).assign(&x.row(i));
969                y_reduced[reduced_idx] = y[i];
970                reduced_idx += 1;
971            }
972        }
973
974        (x_reduced, y_reduced)
975    }
976
977    /// Compute robust estimate
978    fn compute_robust_estimate(&self, _x: &Array2<f64>, y: &Array1<f64>) -> Result<f64> {
979        // Simplified robust estimate - just return mean
980        Ok(y.mean().unwrap())
981    }
982
983    /// Compute robust statistics
984    fn compute_robust_statistics(&self, x: &Array2<f64>) -> (Array1<f64>, Array2<f64>) {
985        let n_samples = x.nrows();
986        let n_features = x.ncols();
987
988        let mean = x.mean_axis(Axis(0)).unwrap();
989        let mut cov = Array2::zeros((n_features, n_features));
990
991        for sample in x.rows() {
992            let centered = &sample - &mean;
993            for i in 0..n_features {
994                for j in 0..n_features {
995                    cov[[i, j]] += centered[i] * centered[j];
996                }
997            }
998        }
999        cov /= (n_samples - 1) as f64;
1000
1001        (mean, cov)
1002    }
1003
1004    /// Get influence values
1005    pub fn get_influence_values(&self) -> Option<&Array1<f64>> {
1006        self.influence_values.as_ref()
1007    }
1008
1009    /// Get leverage values
1010    pub fn get_leverage_values(&self) -> Option<&Array1<f64>> {
1011        self.leverage_values.as_ref()
1012    }
1013
1014    /// Get Cook's distances
1015    pub fn get_cook_distances(&self) -> Option<&Array1<f64>> {
1016        self.cook_distances.as_ref()
1017    }
1018}
1019
1020#[allow(non_snake_case)]
1021#[cfg(test)]
1022mod tests {
1023    use super::*;
1024    use scirs2_core::ndarray::Array2;
1025
1026    #[test]
1027    fn test_robust_rbf_sampler() {
1028        let x = Array2::from_shape_vec((10, 3), (0..30).map(|i| i as f64).collect()).unwrap();
1029
1030        let mut robust_rbf = RobustRBFSampler::new(50)
1031            .gamma(1.0)
1032            .with_config(RobustKernelConfig::default());
1033
1034        robust_rbf.fit(&x).unwrap();
1035        let transformed = robust_rbf.transform(&x).unwrap();
1036
1037        assert_eq!(transformed.shape(), &[10, 50]);
1038        assert!(robust_rbf.get_outlier_mask().is_some());
1039        assert!(robust_rbf.get_robust_weights().is_some());
1040    }
1041
1042    #[test]
1043    fn test_robust_estimators() {
1044        let estimators = vec![
1045            RobustEstimator::Huber { delta: 1.345 },
1046            RobustEstimator::Tukey { c: 4.685 },
1047            RobustEstimator::MVE { alpha: 0.5 },
1048            RobustEstimator::MCD { alpha: 0.5 },
1049        ];
1050
1051        let x = Array2::from_shape_vec(
1052            (8, 2),
1053            vec![
1054                1.0, 2.0, 2.0, 3.0, 3.0, 4.0, 4.0, 5.0, 100.0, 100.0, 101.0, 101.0, 5.0, 6.0, 6.0,
1055                7.0,
1056            ],
1057        )
1058        .unwrap();
1059
1060        for estimator in estimators {
1061            let config = RobustKernelConfig {
1062                estimator,
1063                ..Default::default()
1064            };
1065
1066            let mut robust_rbf = RobustRBFSampler::new(10).with_config(config);
1067
1068            let result = robust_rbf.fit(&x);
1069            assert!(result.is_ok());
1070        }
1071    }
1072
1073    #[test]
1074    fn test_robust_nystroem() {
1075        let x = Array2::from_shape_vec((10, 3), (0..30).map(|i| i as f64).collect()).unwrap();
1076
1077        let mut robust_nystroem = RobustNystroem::new(5)
1078            .gamma(1.0)
1079            .with_config(RobustKernelConfig::default());
1080
1081        robust_nystroem.fit(&x).unwrap();
1082        let transformed = robust_nystroem.transform(&x).unwrap();
1083
1084        assert_eq!(transformed.shape(), &[10, 5]);
1085        assert!(robust_nystroem.get_outlier_mask().is_some());
1086        assert!(robust_nystroem.get_robust_weights().is_some());
1087    }
1088
1089    #[test]
1090    fn test_breakdown_point_analysis() {
1091        let x = Array2::from_shape_vec((20, 2), (0..40).map(|i| i as f64).collect()).unwrap();
1092
1093        let mut analysis =
1094            BreakdownPointAnalysis::new().with_estimator(RobustEstimator::Huber { delta: 1.345 });
1095
1096        let breakdown_point = analysis.analyze(&x).unwrap();
1097        assert!(breakdown_point >= 0.0 && breakdown_point <= 1.0);
1098
1099        let breakdown_points = analysis.get_breakdown_points();
1100        assert!(!breakdown_points.is_empty());
1101    }
1102
1103    #[test]
1104    fn test_influence_function_diagnostics() {
1105        let x = Array2::from_shape_vec((10, 2), (0..20).map(|i| i as f64).collect()).unwrap();
1106        let y = Array1::from_vec((0..10).map(|i| i as f64).collect());
1107
1108        let mut diagnostics = InfluenceFunctionDiagnostics::new()
1109            .with_estimator(RobustEstimator::Huber { delta: 1.345 });
1110
1111        diagnostics.compute(&x, &y).unwrap();
1112
1113        assert!(diagnostics.get_influence_values().is_some());
1114        assert!(diagnostics.get_leverage_values().is_some());
1115        assert!(diagnostics.get_cook_distances().is_some());
1116
1117        let influence = diagnostics.get_influence_values().unwrap();
1118        assert_eq!(influence.len(), 10);
1119    }
1120
1121    #[test]
1122    fn test_robust_loss_functions() {
1123        let losses = vec![
1124            RobustLoss::Huber { delta: 1.345 },
1125            RobustLoss::Tukey { c: 4.685 },
1126            RobustLoss::Cauchy { sigma: 1.0 },
1127            RobustLoss::Welsch { sigma: 1.0 },
1128            RobustLoss::Fair { c: 1.0 },
1129        ];
1130
1131        let x = Array2::from_shape_vec((8, 2), (0..16).map(|i| i as f64).collect()).unwrap();
1132
1133        for loss in losses {
1134            let config = RobustKernelConfig {
1135                loss,
1136                ..Default::default()
1137            };
1138
1139            let mut robust_rbf = RobustRBFSampler::new(10).with_config(config);
1140
1141            let result = robust_rbf.fit(&x);
1142            assert!(result.is_ok());
1143        }
1144    }
1145
1146    #[test]
1147    fn test_contamination_resistance() {
1148        // Create clean data
1149        let mut x =
1150            Array2::from_shape_vec((20, 2), (0..40).map(|i| i as f64 / 10.0).collect()).unwrap();
1151
1152        // Add outliers
1153        x[[18, 0]] = 100.0;
1154        x[[18, 1]] = 100.0;
1155        x[[19, 0]] = -100.0;
1156        x[[19, 1]] = -100.0;
1157
1158        let config = RobustKernelConfig {
1159            contamination: 0.2,
1160            ..Default::default()
1161        };
1162
1163        let mut robust_rbf = RobustRBFSampler::new(10).with_config(config);
1164
1165        robust_rbf.fit(&x).unwrap();
1166
1167        let outlier_mask = robust_rbf.get_outlier_mask().unwrap();
1168        assert!(outlier_mask[18] || outlier_mask[19]); // At least one outlier detected
1169    }
1170}
sklears_kernel_approximation/robust_kernels.rs

sklears_kernel_approximation/
robust_kernels.rs
