# Dimension Reduction Function Research (drfr)
This package provides a Reduction Model and Regression Model, which respectively
contains several choices for reduction and regression of data. It also contains several novelty detection methods for preprocessing
# Discription of Each Model
## Reduction Model
contains "NPPE", "UMAP", "LLE", "Hessian", "Spectral", "TSNE", "Isomap", used
as keyword argument ```tag``` in function ```get_reduction()```.
To make tag "UMAP" work properly, an install according to https://github.com/lmcinnes/umap
is needed.
## Regression Model
contains "lasso", "ridge", "MARS", used
as keyword argument ```tag``` in function ```cal_regression()```. As basis generator
either those in BasisGenerator or self made function can be used, where data X
should be the only positional argument.
## Basis Generator
contains several functions as basis generators, with form
```python
# generate_basis_function(X, p=basis_degree)
```
## Novelty Detector
The detector contains reimplemented kernel PCA, diffusion map, and robust PCA (used in Robust Hessian LLE). More methods can be found in the package [pyod by Y.Zhao et.al](https://pyod.readthedocs.io/en/latest/pyod.models.html).
Use argument ```method``` to choose a method, including ```kpca, dmap, pca, lof, ocsvm, iforest, rforest, rbhessian```.
# Installization
```python
pip install drfr
```
# Usage
```python
from drfr import ReductionModel, BasisGenerator, RegressionModel, NoveltyDetector
from sklearn import datasets
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
if __name__ == "__main__":
N = 2000
k = 24
X, color = datasets.samples_generator.make_swiss_roll(n_samples=N, noise=0.001)
basis_generator = None
outlier_quote = 0.8
poly_degree = 4
tag_red = "NPPE"
tag_reg = "MARS"
# preprocessing
scores = NoveltyDetector.evaluate_novelty(X, labels=color, method="pca")
inlier_ind = np.argwhere(scores < outlier_quote * scores.max()).flatten()
X = X[inlier_ind]
color = color[inlier_ind]
# compute embedded result
red_model = ReductionModel.ReductionModel()
y_nppe = red_model.get_reduction(X, tag=tag_red)
# compute regression weights w given X and y, and compute basis(X)*y
reg_model = RegressionModel.RegressionModel()
y_reg = reg_model.cal_regression(X, y_nppe, tag=tag_reg, basis_generator=BasisGenerator.generate_fourier,
p=poly_degree)
# draw results
fig = plt.figure()
ax = fig.add_subplot(311, projection='3d')
ax.scatter(X[:, 1], X[:, 0], X[:, 2], c=color, cmap=plt.cm.Spectral)
ax.set_title("Original data")
ax = fig.add_subplot(312)
ax.scatter(y_nppe[:, 1], y_nppe[:, 0], c=color, cmap=plt.cm.Spectral)
plt.axis('tight')
plt.xticks([]), plt.yticks([])
plt.title('Projected data with method' + tag_red)
ax = fig.add_subplot(313)
ax.scatter(y_reg[:, 1], y_reg[:, 0], c=color, cmap=plt.cm.Spectral)
plt.axis('tight')
plt.xticks([]), plt.yticks([])
plt.title("NPPE embedded data regressed by " + tag_reg + " Model\n" + "with basis degree" + poly_degree.__str__())
plt.show()
```
