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::RngExt;
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 =
139            RandNormal::new(0.0, (2.0 * self.gamma).sqrt()).expect("operation should succeed");
140        let mut rng = if let Some(seed) = self.config.random_state {
141            RealStdRng::seed_from_u64(seed)
142        } else {
143            RealStdRng::from_seed(thread_rng().random())
144        };
145
146        self.random_weights = Some(Array2::from_shape_fn(
147            (n_features, self.n_components),
148            |_| rng.sample(normal),
149        ));
150
151        self.random_offset = Some(Array1::from_shape_fn(self.n_components, |_| {
152            rng.random_range(0.0..2.0 * std::f64::consts::PI)
153        }));
154
155        // Detect outliers and compute robust weights
156        self.detect_outliers(x)?;
157        self.compute_robust_weights(x)?;
158
159        Ok(())
160    }
161
162    /// Transform data using robust RBF features
163    pub fn transform(&self, x: &Array2<f64>) -> Result<Array2<f64>> {
164        let weights = self.random_weights.as_ref().ok_or("Model not fitted")?;
165        let offset = self.random_offset.as_ref().ok_or("Model not fitted")?;
166
167        // Compute projection: X * W + b
168        let projection = x.dot(weights) + offset;
169
170        // Apply cosine transformation with robust weights
171        let mut transformed =
172            projection.mapv(|x| (x * (2.0 / self.n_components as f64).sqrt()).cos());
173
174        // Apply robust weighting if available
175        if let Some(robust_weights) = &self.robust_weights {
176            for (mut row, &weight) in transformed
177                .rows_mut()
178                .into_iter()
179                .zip(robust_weights.iter())
180            {
181                row *= weight;
182            }
183        }
184
185        Ok(transformed)
186    }
187
188    /// Detect outliers using robust methods
189    fn detect_outliers(&mut self, x: &Array2<f64>) -> Result<()> {
190        match &self.config.estimator {
191            RobustEstimator::MVE { alpha } => {
192                self.outlier_mask = Some(self.detect_outliers_mve(x, *alpha)?);
193            }
194            RobustEstimator::MCD { alpha } => {
195                self.outlier_mask = Some(self.detect_outliers_mcd(x, *alpha)?);
196            }
197            RobustEstimator::Huber { delta } => {
198                self.outlier_mask = Some(self.detect_outliers_huber(x, *delta)?);
199            }
200            RobustEstimator::Tukey { c } => {
201                self.outlier_mask = Some(self.detect_outliers_tukey(x, *c)?);
202            }
203            _ => {
204                // Use default outlier detection based on Mahalanobis distance
205                self.outlier_mask = Some(self.detect_outliers_mahalanobis(x)?);
206            }
207        }
208
209        Ok(())
210    }
211
212    /// Detect outliers using Minimum Volume Ellipsoid
213    fn detect_outliers_mve(&self, x: &Array2<f64>, alpha: f64) -> Result<Array1<bool>> {
214        let n_samples = x.nrows();
215        let n_features = x.ncols();
216        let h = ((n_samples as f64 * alpha).floor() as usize).max(n_features + 1);
217
218        let mut best_volume = f64::INFINITY;
219        let mut best_subset = Vec::new();
220        let mut rng = thread_rng();
221
222        // Try multiple random subsets
223        for _ in 0..100 {
224            let mut subset: Vec<usize> = (0..n_samples).collect();
225            subset.shuffle(&mut rng);
226            subset.truncate(h);
227
228            // Compute covariance matrix for subset
229            let subset_data = self.extract_subset(x, &subset);
230            let (_mean, cov) = self.compute_robust_statistics(&subset_data);
231
232            // Compute volume (determinant of covariance matrix)
233            let volume = self.compute_determinant(&cov);
234
235            if volume < best_volume {
236                best_volume = volume;
237                best_subset = subset;
238            }
239        }
240
241        // Mark outliers based on best subset
242        let mut outlier_mask = Array1::from_elem(n_samples, true);
243        for &idx in &best_subset {
244            outlier_mask[idx] = false;
245        }
246
247        Ok(outlier_mask)
248    }
249
250    /// Detect outliers using Minimum Covariance Determinant
251    fn detect_outliers_mcd(&self, x: &Array2<f64>, alpha: f64) -> Result<Array1<bool>> {
252        let n_samples = x.nrows();
253        let n_features = x.ncols();
254        let h = ((n_samples as f64 * alpha).floor() as usize).max(n_features + 1);
255
256        let mut best_determinant = f64::INFINITY;
257        let mut best_subset = Vec::new();
258        let mut rng = thread_rng();
259
260        // Try multiple random subsets
261        for _ in 0..100 {
262            let mut subset: Vec<usize> = (0..n_samples).collect();
263            subset.shuffle(&mut rng);
264            subset.truncate(h);
265
266            // Iteratively improve subset
267            for _ in 0..10 {
268                let subset_data = self.extract_subset(x, &subset);
269                let (mean, cov) = self.compute_robust_statistics(&subset_data);
270                let determinant = self.compute_determinant(&cov);
271
272                if determinant < best_determinant {
273                    best_determinant = determinant;
274                    best_subset = subset.clone();
275                }
276
277                // Update subset based on distances
278                let distances = self.compute_mahalanobis_distances(x, &mean, &cov);
279                let mut indexed_distances: Vec<(usize, f64)> =
280                    distances.iter().enumerate().map(|(i, &d)| (i, d)).collect();
281                indexed_distances
282                    .sort_by(|a, b| a.1.partial_cmp(&b.1).expect("operation should succeed"));
283
284                subset = indexed_distances.iter().take(h).map(|(i, _)| *i).collect();
285            }
286        }
287
288        // Mark outliers based on best subset
289        let mut outlier_mask = Array1::from_elem(n_samples, true);
290        for &idx in &best_subset {
291            outlier_mask[idx] = false;
292        }
293
294        Ok(outlier_mask)
295    }
296
297    /// Detect outliers using Huber estimator
298    fn detect_outliers_huber(&self, x: &Array2<f64>, delta: f64) -> Result<Array1<bool>> {
299        let n_samples = x.nrows();
300        let mut outlier_mask = Array1::from_elem(n_samples, false);
301
302        // Compute robust center and scale
303        let center = self.compute_huber_center(x, delta);
304        let scale = self.compute_huber_scale(x, &center, delta);
305
306        // Mark outliers based on Huber criterion
307        for i in 0..n_samples {
308            let distance = self.compute_huber_distance(&x.row(i), &center, delta);
309            if distance > 3.0 * scale {
310                outlier_mask[i] = true;
311            }
312        }
313
314        Ok(outlier_mask)
315    }
316
317    /// Detect outliers using Tukey bisquare estimator
318    fn detect_outliers_tukey(&self, x: &Array2<f64>, c: f64) -> Result<Array1<bool>> {
319        let n_samples = x.nrows();
320        let mut outlier_mask = Array1::from_elem(n_samples, false);
321
322        // Compute robust center and scale
323        let center = self.compute_tukey_center(x, c);
324        let scale = self.compute_tukey_scale(x, &center, c);
325
326        // Mark outliers based on Tukey criterion
327        for i in 0..n_samples {
328            let distance = self.compute_tukey_distance(&x.row(i), &center, c);
329            if distance > 3.0 * scale {
330                outlier_mask[i] = true;
331            }
332        }
333
334        Ok(outlier_mask)
335    }
336
337    /// Detect outliers using Mahalanobis distance
338    fn detect_outliers_mahalanobis(&self, x: &Array2<f64>) -> Result<Array1<bool>> {
339        let n_samples = x.nrows();
340        let mut outlier_mask = Array1::from_elem(n_samples, false);
341
342        // Compute robust statistics
343        let (mean, cov) = self.compute_robust_statistics(x);
344        let distances = self.compute_mahalanobis_distances(x, &mean, &cov);
345
346        // Use chi-square threshold for outlier detection
347        let threshold = 3.0; // Approximately 99.7% confidence for normal distribution
348
349        for (i, &distance) in distances.iter().enumerate() {
350            if distance > threshold {
351                outlier_mask[i] = true;
352            }
353        }
354
355        Ok(outlier_mask)
356    }
357
358    /// Compute robust weights using IRLS
359    fn compute_robust_weights(&mut self, x: &Array2<f64>) -> Result<()> {
360        let n_samples = x.nrows();
361        let mut weights = Array1::ones(n_samples);
362
363        if self.config.use_irls {
364            for _iteration in 0..self.config.max_iterations {
365                let old_weights = weights.clone();
366
367                // Update weights based on robust loss function
368                for i in 0..n_samples {
369                    let residual = self.compute_residual(&x.row(i), i);
370                    weights[i] = self.compute_robust_weight(residual);
371                }
372
373                // Check convergence
374                let weight_change = (&weights - &old_weights).mapv(|x| x.abs()).sum();
375                if weight_change < self.config.tolerance {
376                    break;
377                }
378            }
379        }
380
381        // Set outlier weights to zero
382        if let Some(outlier_mask) = &self.outlier_mask {
383            for (i, &is_outlier) in outlier_mask.iter().enumerate() {
384                if is_outlier {
385                    weights[i] = 0.0;
386                }
387            }
388        }
389
390        self.robust_weights = Some(weights);
391        Ok(())
392    }
393
394    /// Compute residual for robust weight calculation
395    fn compute_residual(&self, sample: &ArrayView1<f64>, _index: usize) -> f64 {
396        // Simplified residual computation - in practice this would depend on the specific problem
397        sample.iter().map(|&x| x.abs()).sum::<f64>() / sample.len() as f64
398    }
399
400    /// Compute robust weight based on loss function
401    fn compute_robust_weight(&self, residual: f64) -> f64 {
402        match &self.config.loss {
403            RobustLoss::Huber { delta } => {
404                if residual.abs() <= *delta {
405                    1.0
406                } else {
407                    *delta / residual.abs()
408                }
409            }
410            RobustLoss::Tukey { c } => {
411                let u = residual / *c;
412                if u.abs() <= 1.0 {
413                    (1.0 - u * u).powi(2)
414                } else {
415                    0.0
416                }
417            }
418            RobustLoss::Cauchy { sigma } => 1.0 / (1.0 + (residual / *sigma).powi(2)),
419            RobustLoss::Welsch { sigma } => (-(residual / *sigma).powi(2)).exp(),
420            RobustLoss::Fair { c } => *c / (residual.abs() + *c),
421            _ => 1.0, // Default weight
422        }
423    }
424
425    /// Extract subset of data
426    fn extract_subset(&self, x: &Array2<f64>, indices: &[usize]) -> Array2<f64> {
427        let n_features = x.ncols();
428        let mut subset = Array2::zeros((indices.len(), n_features));
429
430        for (i, &idx) in indices.iter().enumerate() {
431            subset.row_mut(i).assign(&x.row(idx));
432        }
433
434        subset
435    }
436
437    /// Compute robust statistics (mean and covariance)
438    fn compute_robust_statistics(&self, x: &Array2<f64>) -> (Array1<f64>, Array2<f64>) {
439        let n_samples = x.nrows();
440        let n_features = x.ncols();
441
442        // Compute mean
443        let mean = x.mean_axis(Axis(0)).expect("operation should succeed");
444
445        // Compute covariance
446        let mut cov = Array2::zeros((n_features, n_features));
447        for sample in x.rows() {
448            let centered = &sample - &mean;
449            for i in 0..n_features {
450                for j in 0..n_features {
451                    cov[[i, j]] += centered[i] * centered[j];
452                }
453            }
454        }
455        cov /= (n_samples - 1) as f64;
456
457        (mean, cov)
458    }
459
460    /// Compute determinant of matrix
461    fn compute_determinant(&self, matrix: &Array2<f64>) -> f64 {
462        // Simplified determinant computation for 2x2 case
463        if matrix.nrows() == 2 && matrix.ncols() == 2 {
464            matrix[[0, 0]] * matrix[[1, 1]] - matrix[[0, 1]] * matrix[[1, 0]]
465        } else {
466            // For larger matrices, use a simplified approach
467            matrix.diag().iter().product::<f64>()
468        }
469    }
470
471    /// Compute Mahalanobis distances
472    fn compute_mahalanobis_distances(
473        &self,
474        x: &Array2<f64>,
475        mean: &Array1<f64>,
476        _cov: &Array2<f64>,
477    ) -> Array1<f64> {
478        let n_samples = x.nrows();
479        let mut distances = Array1::zeros(n_samples);
480
481        // Simplified Mahalanobis distance computation
482        for (i, sample) in x.rows().into_iter().enumerate() {
483            let centered = &sample - mean;
484            let distance = centered.dot(&centered).sqrt();
485            distances[i] = distance;
486        }
487
488        distances
489    }
490
491    /// Compute Huber center
492    fn compute_huber_center(&self, x: &Array2<f64>, _delta: f64) -> Array1<f64> {
493        // Simplified Huber center computation
494        x.mean_axis(Axis(0)).expect("operation should succeed")
495    }
496
497    /// Compute Huber scale
498    fn compute_huber_scale(&self, x: &Array2<f64>, center: &Array1<f64>, _delta: f64) -> f64 {
499        // Simplified Huber scale computation
500        let distances: Vec<f64> = x
501            .rows()
502            .into_iter()
503            .map(|row| (&row - center).mapv(|x| x.abs()).sum())
504            .collect();
505
506        let mut sorted_distances = distances;
507        sorted_distances.sort_by(|a, b| a.partial_cmp(b).expect("operation should succeed"));
508        sorted_distances[sorted_distances.len() / 2] // Median
509    }
510
511    /// Compute Huber distance
512    fn compute_huber_distance(
513        &self,
514        sample: &ArrayView1<f64>,
515        center: &Array1<f64>,
516        _delta: f64,
517    ) -> f64 {
518        (sample - center).mapv(|x| x.abs()).sum()
519    }
520
521    /// Compute Tukey center
522    fn compute_tukey_center(&self, x: &Array2<f64>, _c: f64) -> Array1<f64> {
523        // Simplified Tukey center computation
524        x.mean_axis(Axis(0)).expect("operation should succeed")
525    }
526
527    /// Compute Tukey scale
528    fn compute_tukey_scale(&self, x: &Array2<f64>, center: &Array1<f64>, _c: f64) -> f64 {
529        // Simplified Tukey scale computation
530        let distances: Vec<f64> = x
531            .rows()
532            .into_iter()
533            .map(|row| (&row - center).mapv(|x| x.abs()).sum())
534            .collect();
535
536        let mut sorted_distances = distances;
537        sorted_distances.sort_by(|a, b| a.partial_cmp(b).expect("operation should succeed"));
538        sorted_distances[sorted_distances.len() / 2] // Median
539    }
540
541    /// Compute Tukey distance
542    fn compute_tukey_distance(
543        &self,
544        sample: &ArrayView1<f64>,
545        center: &Array1<f64>,
546        _c: f64,
547    ) -> f64 {
548        (sample - center).mapv(|x| x.abs()).sum()
549    }
550
551    /// Get outlier mask
552    pub fn get_outlier_mask(&self) -> Option<&Array1<bool>> {
553        self.outlier_mask.as_ref()
554    }
555
556    /// Get robust weights
557    pub fn get_robust_weights(&self) -> Option<&Array1<f64>> {
558        self.robust_weights.as_ref()
559    }
560}
561
562/// Robust Nyström method
563pub struct RobustNystroem {
564    n_components: usize,
565    gamma: f64,
566    config: RobustKernelConfig,
567    basis_indices: Option<Vec<usize>>,
568    basis_kernel: Option<Array2<f64>>,
569    normalization: Option<Array2<f64>>,
570    robust_weights: Option<Array1<f64>>,
571    outlier_mask: Option<Array1<bool>>,
572}
573
574impl RobustNystroem {
575    /// Create a new robust Nyström method
576    pub fn new(n_components: usize) -> Self {
577        Self {
578            n_components,
579            gamma: 1.0,
580            config: RobustKernelConfig::default(),
581            basis_indices: None,
582            basis_kernel: None,
583            normalization: None,
584            robust_weights: None,
585            outlier_mask: None,
586        }
587    }
588
589    /// Set gamma parameter
590    pub fn gamma(mut self, gamma: f64) -> Self {
591        self.gamma = gamma;
592        self
593    }
594
595    /// Set robust configuration
596    pub fn with_config(mut self, config: RobustKernelConfig) -> Self {
597        self.config = config;
598        self
599    }
600
601    /// Fit the robust Nyström method
602    pub fn fit(&mut self, x: &Array2<f64>) -> Result<()> {
603        // Detect outliers
604        let mut robust_rbf = RobustRBFSampler::new(self.n_components)
605            .gamma(self.gamma)
606            .with_config(self.config.clone());
607
608        robust_rbf.fit(x)?;
609        self.outlier_mask = robust_rbf.get_outlier_mask().cloned();
610        self.robust_weights = robust_rbf.get_robust_weights().cloned();
611
612        // Sample basis points excluding outliers
613        self.sample_robust_basis_points(x)?;
614
615        // Compute robust kernel matrix
616        let basis_points = self.get_basis_points(x);
617        let kernel_matrix = self.compute_robust_kernel_matrix(&basis_points)?;
618
619        // Compute eigendecomposition
620        let (eigenvalues, eigenvectors) = self.compute_eigendecomposition(&kernel_matrix)?;
621
622        // Store normalization factors
623        self.normalization = Some(self.compute_normalization(&eigenvalues, &eigenvectors)?);
624
625        Ok(())
626    }
627
628    /// Transform data using robust Nyström features
629    pub fn transform(&self, x: &Array2<f64>) -> Result<Array2<f64>> {
630        let normalization = self.normalization.as_ref().ok_or("Model not fitted")?;
631
632        // Compute kernel values between input and basis points
633        let kernel_values = self.compute_robust_kernel_values(x)?;
634
635        // Apply normalization
636        let result = kernel_values.dot(normalization);
637
638        Ok(result)
639    }
640
641    /// Sample robust basis points
642    fn sample_robust_basis_points(&mut self, x: &Array2<f64>) -> Result<()> {
643        let n_samples = x.nrows();
644        let mut indices = Vec::new();
645        let mut rng = if let Some(seed) = self.config.random_state {
646            RealStdRng::seed_from_u64(seed)
647        } else {
648            RealStdRng::from_seed(thread_rng().random())
649        };
650
651        // Filter out outliers if available
652        let available_indices: Vec<usize> = if let Some(outlier_mask) = &self.outlier_mask {
653            (0..n_samples).filter(|&i| !outlier_mask[i]).collect()
654        } else {
655            (0..n_samples).collect()
656        };
657
658        // Sample basis points from non-outliers
659        let n_available = available_indices.len();
660        let n_basis = std::cmp::min(self.n_components, n_available);
661
662        for _ in 0..n_basis {
663            let idx = rng.random_range(0..n_available);
664            indices.push(available_indices[idx]);
665        }
666
667        self.basis_indices = Some(indices);
668        Ok(())
669    }
670
671    /// Get basis points
672    fn get_basis_points(&self, x: &Array2<f64>) -> Array2<f64> {
673        let indices = self
674            .basis_indices
675            .as_ref()
676            .expect("operation should succeed");
677        let n_features = x.ncols();
678        let mut basis_points = Array2::zeros((indices.len(), n_features));
679
680        for (i, &idx) in indices.iter().enumerate() {
681            basis_points.row_mut(i).assign(&x.row(idx));
682        }
683
684        basis_points
685    }
686
687    /// Compute robust kernel matrix
688    fn compute_robust_kernel_matrix(&self, basis_points: &Array2<f64>) -> Result<Array2<f64>> {
689        let n_basis = basis_points.nrows();
690        let mut kernel_matrix = Array2::zeros((n_basis, n_basis));
691
692        for i in 0..n_basis {
693            for j in i..n_basis {
694                let dist_sq = basis_points
695                    .row(i)
696                    .iter()
697                    .zip(basis_points.row(j).iter())
698                    .map(|(&a, &b)| (a - b).powi(2))
699                    .sum::<f64>();
700
701                let kernel_value = (-self.gamma * dist_sq).exp();
702                kernel_matrix[[i, j]] = kernel_value;
703                kernel_matrix[[j, i]] = kernel_value;
704            }
705        }
706
707        // Apply robust weighting if available
708        if let Some(weights) = &self.robust_weights {
709            let indices = self
710                .basis_indices
711                .as_ref()
712                .expect("operation should succeed");
713            for (i, &idx_i) in indices.iter().enumerate() {
714                for (j, &idx_j) in indices.iter().enumerate() {
715                    kernel_matrix[[i, j]] *= (weights[idx_i] * weights[idx_j]).sqrt();
716                }
717            }
718        }
719
720        Ok(kernel_matrix)
721    }
722
723    /// Compute eigendecomposition
724    fn compute_eigendecomposition(
725        &self,
726        kernel_matrix: &Array2<f64>,
727    ) -> Result<(Array1<f64>, Array2<f64>)> {
728        // Simplified eigendecomposition
729        let n = kernel_matrix.nrows();
730        let eigenvalues = Array1::ones(n);
731        let eigenvectors = kernel_matrix.clone();
732
733        Ok((eigenvalues, eigenvectors))
734    }
735
736    /// Compute normalization factors
737    fn compute_normalization(
738        &self,
739        eigenvalues: &Array1<f64>,
740        eigenvectors: &Array2<f64>,
741    ) -> Result<Array2<f64>> {
742        let mut normalization = Array2::zeros(eigenvectors.dim());
743
744        for i in 0..eigenvectors.nrows() {
745            for j in 0..eigenvectors.ncols() {
746                if eigenvalues[j] > 1e-10 {
747                    normalization[[i, j]] = eigenvectors[[i, j]] / eigenvalues[j].sqrt();
748                }
749            }
750        }
751
752        Ok(normalization)
753    }
754
755    /// Compute robust kernel values
756    fn compute_robust_kernel_values(&self, x: &Array2<f64>) -> Result<Array2<f64>> {
757        let indices = self
758            .basis_indices
759            .as_ref()
760            .expect("operation should succeed");
761        let n_samples = x.nrows();
762        let n_basis = indices.len();
763        let mut kernel_values = Array2::zeros((n_samples, n_basis));
764
765        for i in 0..n_samples {
766            for (j, &_basis_idx) in indices.iter().enumerate() {
767                // For now, just use a placeholder computation
768                kernel_values[[i, j]] = thread_rng().gen_range(0.0..1.0);
769            }
770        }
771
772        Ok(kernel_values)
773    }
774
775    /// Get outlier mask
776    pub fn get_outlier_mask(&self) -> Option<&Array1<bool>> {
777        self.outlier_mask.as_ref()
778    }
779
780    /// Get robust weights
781    pub fn get_robust_weights(&self) -> Option<&Array1<f64>> {
782        self.robust_weights.as_ref()
783    }
784}
785
786/// Breakdown point analysis
787pub struct BreakdownPointAnalysis {
788    estimator: RobustEstimator,
789    contamination_levels: Vec<f64>,
790    breakdown_points: HashMap<String, f64>,
791}
792
793impl Default for BreakdownPointAnalysis {
794    fn default() -> Self {
795        Self::new()
796    }
797}
798
799impl BreakdownPointAnalysis {
800    /// Create a new breakdown point analysis
801    pub fn new() -> Self {
802        Self {
803            estimator: RobustEstimator::Huber { delta: 1.345 },
804            contamination_levels: (1..=50).map(|x| x as f64 / 100.0).collect(),
805            breakdown_points: HashMap::new(),
806        }
807    }
808
809    /// Set robust estimator
810    pub fn with_estimator(mut self, estimator: RobustEstimator) -> Self {
811        self.estimator = estimator;
812        self
813    }
814
815    /// Analyze breakdown point
816    pub fn analyze(&mut self, x: &Array2<f64>) -> Result<f64> {
817        let mut breakdown_point = 0.0;
818
819        for &contamination in &self.contamination_levels {
820            let contaminated_data = self.add_contamination(x, contamination);
821            let bias = self.compute_bias(&contaminated_data, x)?;
822
823            if bias > 0.5 {
824                // Threshold for breakdown
825                breakdown_point = contamination;
826                break;
827            }
828        }
829
830        let estimator_name = format!("{:?}", self.estimator);
831        self.breakdown_points
832            .insert(estimator_name, breakdown_point);
833
834        Ok(breakdown_point)
835    }
836
837    /// Add contamination to data
838    fn add_contamination(&self, x: &Array2<f64>, contamination: f64) -> Array2<f64> {
839        let n_samples = x.nrows();
840        let n_contaminated = (n_samples as f64 * contamination) as usize;
841        let mut contaminated = x.clone();
842        let mut rng = thread_rng();
843
844        // Add outliers to random samples
845        for _ in 0..n_contaminated {
846            let idx = rng.random_range(0..n_samples);
847            for j in 0..x.ncols() {
848                contaminated[[idx, j]] += rng.random_range(-10.0..10.0);
849            }
850        }
851
852        contaminated
853    }
854
855    /// Compute bias of estimator
856    fn compute_bias(&self, contaminated: &Array2<f64>, original: &Array2<f64>) -> Result<f64> {
857        // Simplified bias computation
858        let original_mean = original
859            .mean_axis(Axis(0))
860            .expect("operation should succeed");
861        let contaminated_mean = contaminated
862            .mean_axis(Axis(0))
863            .expect("operation should succeed");
864
865        let bias = (&contaminated_mean - &original_mean)
866            .mapv(|x| x.abs())
867            .sum();
868        Ok(bias)
869    }
870
871    /// Get breakdown points for all estimators
872    pub fn get_breakdown_points(&self) -> &HashMap<String, f64> {
873        &self.breakdown_points
874    }
875}
876
877/// Influence function diagnostics
878pub struct InfluenceFunctionDiagnostics {
879    estimator: RobustEstimator,
880    influence_values: Option<Array1<f64>>,
881    leverage_values: Option<Array1<f64>>,
882    cook_distances: Option<Array1<f64>>,
883}
884
885impl Default for InfluenceFunctionDiagnostics {
886    fn default() -> Self {
887        Self::new()
888    }
889}
890
891impl InfluenceFunctionDiagnostics {
892    /// Create a new influence function diagnostics
893    pub fn new() -> Self {
894        Self {
895            estimator: RobustEstimator::Huber { delta: 1.345 },
896            influence_values: None,
897            leverage_values: None,
898            cook_distances: None,
899        }
900    }
901
902    /// Set robust estimator
903    pub fn with_estimator(mut self, estimator: RobustEstimator) -> Self {
904        self.estimator = estimator;
905        self
906    }
907
908    /// Compute influence diagnostics
909    pub fn compute(&mut self, x: &Array2<f64>, y: &Array1<f64>) -> Result<()> {
910        self.influence_values = Some(self.compute_influence_values(x, y)?);
911        self.leverage_values = Some(self.compute_leverage_values(x)?);
912        self.cook_distances = Some(self.compute_cook_distances(x, y)?);
913
914        Ok(())
915    }
916
917    /// Compute influence values
918    fn compute_influence_values(&self, x: &Array2<f64>, y: &Array1<f64>) -> Result<Array1<f64>> {
919        let n_samples = x.nrows();
920        let mut influence = Array1::zeros(n_samples);
921
922        // Compute baseline estimate
923        let baseline_estimate = self.compute_robust_estimate(x, y)?;
924
925        // Compute influence by removing each observation
926        for i in 0..n_samples {
927            let (x_reduced, y_reduced) = self.remove_observation(x, y, i);
928            let reduced_estimate = self.compute_robust_estimate(&x_reduced, &y_reduced)?;
929            influence[i] = (baseline_estimate - reduced_estimate).abs();
930        }
931
932        Ok(influence)
933    }
934
935    /// Compute leverage values
936    fn compute_leverage_values(&self, x: &Array2<f64>) -> Result<Array1<f64>> {
937        let n_samples = x.nrows();
938        let mut leverage = Array1::zeros(n_samples);
939
940        // Simplified leverage computation
941        let (mean, _cov) = self.compute_robust_statistics(x);
942
943        for i in 0..n_samples {
944            let centered = &x.row(i) - &mean;
945            leverage[i] = centered.dot(&centered); // Simplified
946        }
947
948        Ok(leverage)
949    }
950
951    /// Compute Cook's distances
952    fn compute_cook_distances(&self, x: &Array2<f64>, y: &Array1<f64>) -> Result<Array1<f64>> {
953        let n_samples = x.nrows();
954        let mut cook_distances = Array1::zeros(n_samples);
955
956        // Simplified Cook's distance computation
957        let influence = self.compute_influence_values(x, y)?;
958        let leverage = self.compute_leverage_values(x)?;
959
960        for i in 0..n_samples {
961            cook_distances[i] = influence[i] * leverage[i];
962        }
963
964        Ok(cook_distances)
965    }
966
967    /// Remove observation from dataset
968    fn remove_observation(
969        &self,
970        x: &Array2<f64>,
971        y: &Array1<f64>,
972        index: usize,
973    ) -> (Array2<f64>, Array1<f64>) {
974        let n_samples = x.nrows();
975        let n_features = x.ncols();
976
977        let mut x_reduced = Array2::zeros((n_samples - 1, n_features));
978        let mut y_reduced = Array1::zeros(n_samples - 1);
979
980        let mut reduced_idx = 0;
981        for i in 0..n_samples {
982            if i != index {
983                x_reduced.row_mut(reduced_idx).assign(&x.row(i));
984                y_reduced[reduced_idx] = y[i];
985                reduced_idx += 1;
986            }
987        }
988
989        (x_reduced, y_reduced)
990    }
991
992    /// Compute robust estimate
993    fn compute_robust_estimate(&self, _x: &Array2<f64>, y: &Array1<f64>) -> Result<f64> {
994        // Simplified robust estimate - just return mean
995        Ok(y.mean().expect("operation should succeed"))
996    }
997
998    /// Compute robust statistics
999    fn compute_robust_statistics(&self, x: &Array2<f64>) -> (Array1<f64>, Array2<f64>) {
1000        let n_samples = x.nrows();
1001        let n_features = x.ncols();
1002
1003        let mean = x.mean_axis(Axis(0)).expect("operation should succeed");
1004        let mut cov = Array2::zeros((n_features, n_features));
1005
1006        for sample in x.rows() {
1007            let centered = &sample - &mean;
1008            for i in 0..n_features {
1009                for j in 0..n_features {
1010                    cov[[i, j]] += centered[i] * centered[j];
1011                }
1012            }
1013        }
1014        cov /= (n_samples - 1) as f64;
1015
1016        (mean, cov)
1017    }
1018
1019    /// Get influence values
1020    pub fn get_influence_values(&self) -> Option<&Array1<f64>> {
1021        self.influence_values.as_ref()
1022    }
1023
1024    /// Get leverage values
1025    pub fn get_leverage_values(&self) -> Option<&Array1<f64>> {
1026        self.leverage_values.as_ref()
1027    }
1028
1029    /// Get Cook's distances
1030    pub fn get_cook_distances(&self) -> Option<&Array1<f64>> {
1031        self.cook_distances.as_ref()
1032    }
1033}
1034
1035#[allow(non_snake_case)]
1036#[cfg(test)]
1037mod tests {
1038    use super::*;
1039    use scirs2_core::ndarray::Array2;
1040
1041    #[test]
1042    fn test_robust_rbf_sampler() {
1043        let x = Array2::from_shape_vec((10, 3), (0..30).map(|i| i as f64).collect())
1044            .expect("operation should succeed");
1045
1046        let mut robust_rbf = RobustRBFSampler::new(50)
1047            .gamma(1.0)
1048            .with_config(RobustKernelConfig::default());
1049
1050        robust_rbf.fit(&x).expect("operation should succeed");
1051        let transformed = robust_rbf.transform(&x).expect("operation should succeed");
1052
1053        assert_eq!(transformed.shape(), &[10, 50]);
1054        assert!(robust_rbf.get_outlier_mask().is_some());
1055        assert!(robust_rbf.get_robust_weights().is_some());
1056    }
1057
1058    #[test]
1059    fn test_robust_estimators() {
1060        let estimators = vec![
1061            RobustEstimator::Huber { delta: 1.345 },
1062            RobustEstimator::Tukey { c: 4.685 },
1063            RobustEstimator::MVE { alpha: 0.5 },
1064            RobustEstimator::MCD { alpha: 0.5 },
1065        ];
1066
1067        let x = Array2::from_shape_vec(
1068            (8, 2),
1069            vec![
1070                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,
1071                7.0,
1072            ],
1073        )
1074        .expect("operation should succeed");
1075
1076        for estimator in estimators {
1077            let config = RobustKernelConfig {
1078                estimator,
1079                ..Default::default()
1080            };
1081
1082            let mut robust_rbf = RobustRBFSampler::new(10).with_config(config);
1083
1084            let result = robust_rbf.fit(&x);
1085            assert!(result.is_ok());
1086        }
1087    }
1088
1089    #[test]
1090    fn test_robust_nystroem() {
1091        let x = Array2::from_shape_vec((10, 3), (0..30).map(|i| i as f64).collect())
1092            .expect("operation should succeed");
1093
1094        let mut robust_nystroem = RobustNystroem::new(5)
1095            .gamma(1.0)
1096            .with_config(RobustKernelConfig::default());
1097
1098        robust_nystroem.fit(&x).expect("operation should succeed");
1099        let transformed = robust_nystroem
1100            .transform(&x)
1101            .expect("operation should succeed");
1102
1103        assert_eq!(transformed.shape(), &[10, 5]);
1104        assert!(robust_nystroem.get_outlier_mask().is_some());
1105        assert!(robust_nystroem.get_robust_weights().is_some());
1106    }
1107
1108    #[test]
1109    fn test_breakdown_point_analysis() {
1110        let x = Array2::from_shape_vec((20, 2), (0..40).map(|i| i as f64).collect())
1111            .expect("operation should succeed");
1112
1113        let mut analysis =
1114            BreakdownPointAnalysis::new().with_estimator(RobustEstimator::Huber { delta: 1.345 });
1115
1116        let breakdown_point = analysis.analyze(&x).expect("operation should succeed");
1117        assert!(breakdown_point >= 0.0 && breakdown_point <= 1.0);
1118
1119        let breakdown_points = analysis.get_breakdown_points();
1120        assert!(!breakdown_points.is_empty());
1121    }
1122
1123    #[test]
1124    fn test_influence_function_diagnostics() {
1125        let x = Array2::from_shape_vec((10, 2), (0..20).map(|i| i as f64).collect())
1126            .expect("operation should succeed");
1127        let y = Array1::from_vec((0..10).map(|i| i as f64).collect());
1128
1129        let mut diagnostics = InfluenceFunctionDiagnostics::new()
1130            .with_estimator(RobustEstimator::Huber { delta: 1.345 });
1131
1132        diagnostics
1133            .compute(&x, &y)
1134            .expect("operation should succeed");
1135
1136        assert!(diagnostics.get_influence_values().is_some());
1137        assert!(diagnostics.get_leverage_values().is_some());
1138        assert!(diagnostics.get_cook_distances().is_some());
1139
1140        let influence = diagnostics
1141            .get_influence_values()
1142            .expect("operation should succeed");
1143        assert_eq!(influence.len(), 10);
1144    }
1145
1146    #[test]
1147    fn test_robust_loss_functions() {
1148        let losses = vec![
1149            RobustLoss::Huber { delta: 1.345 },
1150            RobustLoss::Tukey { c: 4.685 },
1151            RobustLoss::Cauchy { sigma: 1.0 },
1152            RobustLoss::Welsch { sigma: 1.0 },
1153            RobustLoss::Fair { c: 1.0 },
1154        ];
1155
1156        let x = Array2::from_shape_vec((8, 2), (0..16).map(|i| i as f64).collect())
1157            .expect("operation should succeed");
1158
1159        for loss in losses {
1160            let config = RobustKernelConfig {
1161                loss,
1162                ..Default::default()
1163            };
1164
1165            let mut robust_rbf = RobustRBFSampler::new(10).with_config(config);
1166
1167            let result = robust_rbf.fit(&x);
1168            assert!(result.is_ok());
1169        }
1170    }
1171
1172    #[test]
1173    fn test_contamination_resistance() {
1174        // Create clean data
1175        let mut x = Array2::from_shape_vec((20, 2), (0..40).map(|i| i as f64 / 10.0).collect())
1176            .expect("operation should succeed");
1177
1178        // Add outliers
1179        x[[18, 0]] = 100.0;
1180        x[[18, 1]] = 100.0;
1181        x[[19, 0]] = -100.0;
1182        x[[19, 1]] = -100.0;
1183
1184        let config = RobustKernelConfig {
1185            contamination: 0.2,
1186            ..Default::default()
1187        };
1188
1189        let mut robust_rbf = RobustRBFSampler::new(10).with_config(config);
1190
1191        robust_rbf.fit(&x).expect("operation should succeed");
1192
1193        let outlier_mask = robust_rbf
1194            .get_outlier_mask()
1195            .expect("operation should succeed");
1196        assert!(outlier_mask[18] || outlier_mask[19]); // At least one outlier detected
1197    }
1198}
sklears_kernel_approximation/robust_kernels.rs

sklears_kernel_approximation/
robust_kernels.rs
