### Poisson Learning Fit Method Setup

Source: https://jwcalder.github.io/GraphLearning/ssl.html

Prepares the graph and source term for Poisson learning. It modifies the weight matrix and calculates the source term based on one-hot encoded labels and their mean.

```python
n = self.graph.num_nodes
unique_labels = np.unique(train_labels)
k = len(unique_labels)

#Zero out diagonal for faster convergence
W = self.graph.weight_matrix
W = W - sparse.spdiags(W.diagonal(),0,n,n)
G = graph.graph(W)

#Poisson source term
onehot = utils.labels_to_onehot(train_labels,k)
source = np.zeros((n, onehot.shape[1]))
source[train_ind] = onehot - np.mean(onehot, axis=0)
```

--------------------------------

### Two Moons Dataset SSL Example

Source: https://jwcalder.github.io/GraphLearning/ssl.html

Demonstrates semi-supervised learning on the two-moons dataset using the Laplace algorithm. Requires training data and a weight matrix.

```python
import numpy as np
import graphlearning as gl
import matplotlib.pyplot as plt
import sklearn.datasets as datasets

X,labels = datasets.make_moons(n_samples=500,noise=0.1)
W = gl.weightmatrix.knn(X,10)

train_ind = gl.trainsets.generate(labels, rate=5)
train_labels = labels[train_ind]

model = gl.ssl.laplace(W)
pred_labels = model.fit_predict(train_ind, train_labels)

accuracy = gl.ssl.ssl_accuracy(pred_labels, labels, train_ind)   
print("Accuracy: %.2f%%"%accuracy)

plt.scatter(X[:,0],X[:,1], c=pred_labels)
plt.scatter(X[train_ind,0],X[train_ind,1], c='r')
plt.show()
```

--------------------------------

### PoissonMBO Initialization and Example

Source: https://jwcalder.github.io/GraphLearning/ssl.html

Initializes the PoissonMBO model and demonstrates its usage on the MNIST dataset with one label per class. It shows how to load data, construct the graph, train the model, and evaluate accuracy.

```python
import graphlearning as gl

labels = gl.datasets.load('mnist', labels_only=True)
W = gl.weightmatrix.knn('mnist', 10, metric='vae')

num_train_per_class = 1
train_ind = gl.trainsets.generate(labels, rate=num_train_per_class)
train_labels = labels[train_ind]

class_priors = gl.utils.class_priors(labels)
model = gl.ssl.poisson_mbo(W, class_priors)
pred_labels = model.fit_predict(train_ind,train_labels,all_labels=labels)

accuracy = gl.ssl.ssl_accuracy(labels,pred_labels,train_ind)
print(model.name + ': %.2f%%'%accuracy)
```

--------------------------------

### Gradient Descent Solver Setup for Poisson Learning

Source: https://jwcalder.github.io/GraphLearning/ssl.html

Sets up matrices for the gradient descent solver in Poisson learning. It calculates the degree matrix 'D' and the matrix 'P' based on the graph's weight matrix.

```python
elif self.solver == "gradient_descent":

    #Setup matrices
    D = G.degree_matrix(p=-1)
    P = D*W.transpose()
    Db = D*source
```

--------------------------------

### Model Change Active Learning Example

Source: https://jwcalder.github.io/GraphLearning/active_learning.html

Demonstrates the Model Change active learning algorithm. It initializes an active learner, iteratively selects query points, simulates human labeling, and updates the learner. Useful for scenarios where selecting points that maximally change the model is desired.

```python
import graphlearning.active_learning as al
import graphlearning as gl
import numpy as np
import matplotlib.pyplot as plt
import sklearn.datasets as datasets

X,labels = datasets.make_moons(n_samples=500,noise=0.1)
W = gl.weightmatrix.knn(X,10)
train_ind = gl.trainsets.generate(labels, rate=5)
plt.scatter(X[:,0],X[:,1], c=labels)
plt.scatter(X[train_ind,0],X[train_ind,1], c='r')
plt.show()

# compute initial, low-rank (spectral truncation) covariance matrix 
evals, evecs = model.graph.eigen_decomp(normalization='normalized', k=50)
C = np.diag(1. / (evals + 1e-11))
AL = gl.active_learning.active_learner(model, gl.active_learning.model_change, train_ind, y[train_ind], C=C.copy(), V=evecs.copy())

for i in range(10):
    query_points = AL.select_queries() # return this iteration's newly chosen points
    query_labels = y[query_points] # simulate the human in the loop process
    AL.update(query_points, query_labels) # update the active_learning object's labeled set

    # plot
    plt.scatter(X[:,0],X[:,1], c=y)
    plt.scatter(X[AL.labeled_ind,0],X[AL.labeled_ind,1], c='r')
    plt.scatter(X[query_points,0],X[query_points,1], c='r', marker='*', s=200, edgecolors='k', linewidths=1)
    plt.show()
    print(AL.labeled_ind)
    print(AL.labels)
```

--------------------------------

### Uncertainty Sampling Active Learning Example

Source: https://jwcalder.github.io/GraphLearning/active_learning.html

Demonstrates how to use the uncertainty sampling active learning algorithm. It involves initializing the active learner, selecting queries, simulating human labeling, and updating the labeled set iteratively. Useful for scenarios where model uncertainty is a key indicator of informative samples.

```python
import graphlearning.active_learning as al
import graphlearning as gl
import numpy as np
import matplotlib.pyplot as plt
import sklearn.datasets as datasets

X,labels = datasets.make_moons(n_samples=500,noise=0.1)
W = gl.weightmatrix.knn(X,10)
train_ind = gl.trainsets.generate(labels, rate=5)
plt.scatter(X[:,0],X[:,1], c=labels)
plt.scatter(X[train_ind,0],X[train_ind,1], c='r')
plt.show()


model = gl.ssl.laplace(W)
AL = gl.active_learning.active_learner(model, gl.active_learning.unc_sampling, train_ind, y[train_ind])

for i in range(10):
    query_points = AL.select_queries() # return this iteration's newly chosen points
    query_labels = y[query_points] # simulate the human in the loop process
    AL.update(query_points, query_labels) # update the active_learning object's labeled set

    # plot
    plt.scatter(X[:,0],X[:,1], c=y)
    plt.scatter(X[AL.labeled_ind,0],X[AL.labeled_ind,1], c='r')
    plt.scatter(X[query_points,0],X[query_points,1], c='r', marker='*', s=200, edgecolors='k', linewidths=1)
    plt.show()
    print(AL.labeled_ind)
    print(AL.labels)
```

--------------------------------

### Get Node Neighbors

Source: https://jwcalder.github.io/GraphLearning/graph.html

Retrieves the neighbors of a specified node. Optionally returns the weights of these neighbors.

```python
def neighbors(self, i, return_weights=False):
    """Neighbors
    =======

    Returns neighbors of node i.
    ## Parameters 

    **`i`**:`int `
        Index of vertex to return neighbors of. 

    **`return_weights`**:`bool (optional)` , default=`False`
        Whether to return the weights of neighbors as well.
    """
    
```

--------------------------------

### VAE Initialization and Training Execution

Source: https://jwcalder.github.io/GraphLearning/weightmatrix.html

Sets up the VAE model, optimizer, and data loaders, then executes the training loop for a specified number of epochs. Includes GPU configuration and data preprocessing. Requires `torch`, `optim`, `DataLoader`, `MyDataset`, `VAE`, `device`, `kwargs`, `batch_size`, `learning_rate`, and `epochs` to be defined.

```python
from torch import nn, optim
from torch.nn import functional as F
from torchvision import datasets, transforms
from torchvision.utils import save_image
from torch.utils.data import DataLoader
import numpy as np
import torch

# Assuming layer_widths, no_cuda, batch_size, learning_rate, epochs are defined elsewhere
# Assuming data and target are numpy arrays or similar structures

layer_widths = [data.shape[1]] + layer_widths
log_interval = 10    #how many batches to wait before logging training status

#GPU settings
cuda = not no_cuda and torch.cuda.is_available()
device = torch.device("cuda" if cuda else "cpu")
kwargs = {'num_workers': 1, 'pin_memory': True} if cuda else {}

#Convert to torch dataloaders
data = data - data.min()
data = data/data.max()
data = torch.from_numpy(data).float()
target = np.zeros((data.shape[0],)).astype(int)
target = torch.from_numpy(target).long()
dataset = MyDataset(data, target)
data_loader = DataLoader(dataset, batch_size=batch_size, shuffle=True, **kwargs)

#Put model on GPU and set up optimizer
model = VAE(layer_widths).to(device)
optimizer = optim.Adam(model.parameters(), lr=learning_rate)

#Training epochs
for epoch in range(1, epochs + 1):
    train(epoch)
```

--------------------------------

### Fokker-Planck Clustering Example

Source: https://jwcalder.github.io/GraphLearning/clustering.html

Demonstrates Fokker-Planck clustering on the two-skies dataset. Requires graphlearning, numpy, and matplotlib.

```python
import numpy as np
import graphlearning as gl
import matplotlib.pyplot as plt

X,L = gl.datasets.two_skies(1000)
W = gl.weightmatrix.knn(X,10)

knn_ind,knn_dist = gl.weightmatrix.knnsearch(X,50)
rho = 1/np.max(knn_dist,axis=1)

model = gl.clustering.fokker_planck(W,num_clusters=2,t=1000,beta=0.5,rho=rho)
labels = model.fit_predict()

plt.scatter(X[:,0],X[:,1], c=labels)
plt.show()
```

--------------------------------

### Initialize SSL Class Priors

Source: https://jwcalder.github.io/GraphLearning/ssl.html

Initializes the SSL Class Priors with various parameters controlling reweighting, normalization, mean shift, and solver tolerance. Sets up the accuracy filename based on selected options.

```python
def __init__(self, W, class_priors, reweighting='none', normalization='combinatorial', mean_shift=False, tol=1e-5, order=1, X=None, tau=0):
        """Class Priors

        Whether to shift output to mean zero.
    tol : float (optional), default=1e-5
        Tolerance for conjugate gradient solver.
    alpha : float (optional), default=2
        Parameter for `properly` reweighting.
    zeta : float (optional), default=1e7
        Parameter for `properly` reweighting.
    r : float (optional), default=0.1
        Radius for `properly` reweighting.

    References
    ---------
    [1] X. Zhu, Z. Ghahramani, and J. D. Lafferty. [Semi-supervised learning using gaussian fields 
    and harmonic functions.](https://www.aaai.org/Papers/ICML/2003/ICML03-118.pdf) Proceedings 
    of the 20th International Conference on Machine Learning (ICML-03), 2003.

    [2] J. Calder, B. Cook, M. Thorpe, D. Slepcev. [Poisson Learning: Graph Based Semi-Supervised
    Learning at Very Low Label Rates.](http://proceedings.mlr.press/v119/calder20a.html), 
    Proceedings of the 37th International Conference on Machine Learning, PMLR 119:1306-1316, 2020.

    [3] Z. Shi, S. Osher, and W. Zhu. [Weighted nonlocal laplacian on interpolation from sparse data.](https://idp.springer.com/authorize/casa?redirect_uri=https://link.springer.com/article/10.1007/s10915-017-0421-z&casa_token=33Z7gqJy3mMAAAAA:iMO0pGmpn_qf5PioVIGocSRq_p4CDm-KNOQhgIC1uvqG9pWlZ6t7I-IZtSJfocFDEHCdMpK8j7Fx1XbzDQ)
    Journal of Scientific Computing 73.2 (2017): 1164-1177.

    [4] J. Calder, D. Slepčev. [Properly-weighted graph Laplacian for semi-supervised learning.](https://link.springer.com/article/10.1007/s00245-019-09637-3) Applied mathematics & optimization (2019): 1-49.
    """
        super().__init__(W, class_priors)

        self.reweighting = reweighting
        self.normalization = normalization
        self.mean_shift = mean_shift
        self.tol = tol
        self.order = order
        self.X = X

        #Set up tau
        if type(tau) in [float,int]:
            self.tau = np.ones(self.graph.num_nodes)*tau
        elif type(tau) is np.ndarray:
            self.tau = tau

        #Setup accuracy filename
        fname = '_laplace' 
        self.name = 'Laplace Learning'
        if self.reweighting != 'none':
            fname += '_' + self.reweighting
            self.name += ': ' + self.reweighting + ' reweighted'
        if self.normalization != 'combinatorial':
            fname += '_' + self.normalization
            self.name += ' ' + self.normalization
        if self.mean_shift:
            fname += '_meanshift'
            self.name += ' with meanshift'
        if self.order > 1:
            fname += '_order%d'%int(self.order)
            self.name += ' order %d'%int(self.order)
        if np.max(self.tau) > 0:
            fname += '_tau_%.3f'%np.max(self.tau)
            self.name += ' tau=%.3f'%np.max(self.tau)

        self.accuracy_filename = fname
```

--------------------------------

### Get Neighbors of a Node

Source: https://jwcalder.github.io/GraphLearning/graph.html

Retrieves the indices of a node's neighbors. Optionally returns edge weights if `return_weights` is True.

```python
def neighbors(self, i, return_weights=False):
    """Neighbors
    ======

    Returns neighbors of node i.

    Parameters
    ----------
    i : int 
        Index of vertex to return neighbors of.
    return_weights : bool (optional), default=False
        Whether to return the weights of neighbors as well.

    Returns
    -------
    N : numpy array, int
        Array of nearest neighbor indices.
    W : numpy array, float
        Weights of edges to neighbors. 
    """
    
    N = self.weight_matrix[i,:].nonzero()[1]
    N = N[N != i]

    if return_weights:
        return N, self.weight_matrix[i,N].toarray().flatten()
    else:
        return N
```

--------------------------------

### Initialize and Run Active Learner

Source: https://jwcalder.github.io/GraphLearning/active_learning.html

Demonstrates initializing an active learner with a pre-computed covariance matrix and then iteratively selecting and updating with queried points. Useful for active learning on graphs where initial graph properties are known.

```python
import graphlearning.active_learning as al
import graphlearning as gl
import numpy as np
import matplotlib.pyplot as plt
import sklearn.datasets as datasets

X,labels = datasets.make_moons(n_samples=500,noise=0.1)
W = gl.weightmatrix.knn(X,10)
train_ind = gl.trainsets.generate(labels, rate=5)
plt.scatter(X[:,0],X[:,1], c=labels)
plt.scatter(X[train_ind,0],X[train_ind,1], c='r')
plt.show()

# compute initial, low-rank (spectral truncation) covariance matrix 
evals, evecs = model.graph.eigen_decomp(normalization='normalized', k=50)
C = np.diag(1. / (evals + 1e-11))
AL = gl.active_learning.active_learner(model, gl.active_learning.model_change_var_opt, train_ind, y[train_ind], C=C.copy(), V=evecs.copy())

for i in range(10):
    query_points = AL.select_queries() # return this iteration's newly chosen points
    query_labels = y[query_points] # simulate the human in the loop process
    AL.update(query_points, query_labels) # update the active_learning object's labeled set

    # plot
    plt.scatter(X[:,0],X[:,1], c=y)
    plt.scatter(X[AL.labeled_ind,0],X[AL.labeled_ind,1], c='r')
    plt.scatter(X[query_points,0],X[query_points,1], c='r', marker='*', s=200, edgecolors='k', linewidths=1)
    plt.show()
    print(AL.labeled_ind)
    print(AL.labels)
```

--------------------------------

### Get Neighbors of a Node

Source: https://jwcalder.github.io/GraphLearning/graph.html

Retrieves the indices of a node's neighbors. Optionally, it can also return the weights of the edges connecting to these neighbors.

```python
def neighbors(self, i, return_weights=False):
        """Neighbors
        ======

        Returns neighbors of node i.

        Parameters
        ----------
        i : int 
            Index of vertex to return neighbors of.
        return_weights : bool (optional), default=False
            Whether to return the weights of neighbors as well.

        Returns
        -------
        N : numpy array, int
            Array of nearest neighbor indices.
        W : numpy array, float
            Weights of edges to neighbors. 
        """
        
        N = self.weight_matrix[i,:].nonzero()[1]
        N = N[N != i]

        if return_weights:
            return N, self.weight_matrix[i,N].toarray().flatten()
        else:
            return N
```

--------------------------------

### Get SSL Accuracy Filename

Source: https://jwcalder.github.io/GraphLearning/ssl.html

Constructs and returns the filename for storing SSL accuracy results, appending '_classpriors' if class priors are used.

```python
def get_accuracy_filename(self):
        """Get accuracy filename
        ========

        Returns name of the file that will store the accuracy results for `ssl_trials.py`.

        Returns
        -------
        fname : str
            Accuracy filename.
        """

        fname = self.accuracy_filename
        if self.class_priors is not None:
            fname += '_classpriors'
        fname += '_accuracy.csv'
        return fname
```

--------------------------------

### poisson.__init__

Source: https://jwcalder.github.io/GraphLearning/ssl.html

Initializes the Poisson learning model, which solves the Poisson equation for semi-supervised learning.

```APIDOC
## poisson.__init__

### Description
Initializes the Poisson learning model, which solves the Poisson equation for semi-supervised learning.

### Parameters
#### Path Parameters
- **W** (optional) - The graph weight matrix.
- **class_priors** (optional) - Prior probabilities for each class.
- **solver** (str, optional) - The solver to use (default: 'conjugate_gradient').
- **p** (int, optional) - The power parameter for the graph Laplacian (default: 1).
- **use_cuda** (bool, optional) - Whether to use CUDA for computation (default: False).
- **min_iter** (int, optional) - Minimum number of iterations (default: 50).
- **max_iter** (int, optional) - Maximum number of iterations (default: 1000).
- **tol** (float, optional) - Tolerance for convergence (default: 1e-3).
- **spectral_cutoff** (int, optional) - Spectral cutoff for the graph Laplacian (default: 10).
```

--------------------------------

### Initialize Centered Kernel SSL Algorithm

Source: https://jwcalder.github.io/GraphLearning/ssl.html

Initializes the Centered Kernel SSL algorithm. Parameters include graph weight matrix, class priors, solver tolerance, and number of power iterations for eigenvalue calculation.

```python
class centered_kernel (W=None, class_priors=None, tol=1e-10, power_it=100, alpha=1.05) 
    """# Centered Kernel Method
Semi-supervised learning via the centered kernel method of [1].
## Parameters 

**`W`**:`numpy array, scipy sparse matrix,` or `graphlearning graph object (optional)`, default=`None`
    Weight matrix representing the graph. 

**`class_priors`**:`numpy array (optional)` , default=`None`
    Class priors (fraction of data belonging to each class). If provided, the predict function will attempt to automatic balance the label predictions to predict the correct number of nodes in each class. 

**`tol`**:`float (optional)` , default=`1e-10`
    Tolerance to solve equation. 

**`power_it`**:`int (optional)` , default=`100`
    Number of power iterations to find largest eigenvalue. 

**`alpha`**:`float (optional)` , default = 1.05
    Value of αα as a fraction of largest eigenvalue.
"""
```

--------------------------------

### INCRES Clustering

Source: https://jwcalder.github.io/GraphLearning/clustering.html

Implements the INCRES clustering algorithm. This example uses the MNIST dataset and requires graphlearning. The 'vae' metric for knn is used.

```python
import graphlearning as gl

W = gl.weightmatrix.knn('mnist', 10, metric='vae')
labels = gl.datasets.load('mnist', labels_only=True)

model = gl.clustering.incres(W, num_clusters=10)
pred_labels = model.fit_predict(all_labels=labels)

accuracy = gl.clustering.clustering_accuracy(pred_labels,labels)
print('Clustering Accuracy: %.2f%%'%accuracy)
```

--------------------------------

### INCRES Clustering MNIST Example

Source: https://jwcalder.github.io/GraphLearning/clustering.html

Applies INCRES clustering to the MNIST dataset. Requires graphlearning and uses VAE metric for KNN graph.

```python
import graphlearning as gl

W = gl.weightmatrix.knn('mnist', 10, metric='vae')
labels = gl.datasets.load('mnist', labels_only=True)

model = gl.clustering.incres(W, num_clusters=10)
pred_labels = model.fit_predict(all_labels=labels)

accuracy = gl.clustering.clustering_accuracy(pred_labels,labels)
```

--------------------------------

### Convert Scipy Sparse to Torch Sparse

Source: https://jwcalder.github.io/GraphLearning/utils.html

Converts a SciPy sparse matrix to a PyTorch sparse tensor. Requires the PyTorch library to be installed.

```python
def torch_sparse(A):
    """Torch sparse matrix, from scipy sparse
    ======

    Converts a scipy sparse matrix into a torch sparse matrix.

    Parameters
    ----------
    A : (n,n) scipy sparse matrix
        Matrix to convert to torch sparse

    Returns
    -------
    A_torch : (n,n) torch.sparse.FloatTensor
        Sparse matrix in torch form.
    """

    import torch

    A = A.tocoo()
    values = A.data
    indices = np.vstack((A.row, A.col))

    i = torch.LongTensor(indices)
    v = torch.FloatTensor(values)
    shape = A.shape

    A_torch = torch.sparse.FloatTensor(i, v, torch.Size(shape))

    return A_torch
```

--------------------------------

### Initialize and Run Sigma Optimization Active Learner

Source: https://jwcalder.github.io/GraphLearning/active_learning.html

Demonstrates initializing the Sigma Optimization active learner with a pre-computed covariance matrix and eigenvectors, then iteratively selecting and updating labeled data.

```python
import graphlearning.active_learning as al
import graphlearning as gl
import numpy as np
import matplotlib.pyplot as plt
import sklearn.datasets as datasets

X,labels = datasets.make_moons(n_samples=500,noise=0.1)
W = gl.weightmatrix.knn(X,10)
train_ind = gl.trainsets.generate(labels, rate=5)
plt.scatter(X[:,0],X[:,1], c=labels)
plt.scatter(X[train_ind,0],X[train_ind,1], c='r')
plt.show()

# compute initial, low-rank (spectral truncation) covariance matrix 
evals, evecs = model.graph.eigen_decomp(normalization='normalized', k=50)
C = np.diag(1. / (evals + 1e-11))
AL = gl.active_learning.active_learner(model, gl.active_learning.sigma_opt, train_ind, y[train_ind], C=C.copy(), V=evecs.copy())

for i in range(10):
    query_points = AL.select_queries() # return this iteration's newly chosen points
    query_labels = y[query_points] # simulate the human in the loop process
    AL.update(query_points, query_labels) # update the active_learning object's labeled set

    # plot
    plt.scatter(X[:,0],X[:,1], c=y)
    plt.scatter(X[AL.labeled_ind,0],X[AL.labeled_ind,1], c='r')
    plt.scatter(X[query_points,0],X[query_points,1], c='r', marker='*', s=200, edgecolors='k', linewidths=1)
    plt.show()
    print(AL.labeled_ind)
    print(AL.labels)
```

--------------------------------

### Get Neighbors of a Node

Source: https://jwcalder.github.io/GraphLearning/graph.html

Retrieves the indices of a node's neighbors. Optionally, it can also return the weights of the edges connecting to these neighbors. Self-loops are excluded.

```python
    def neighbors(self, i, return_weights=False):
        """Neighbors
        ======

        Returns neighbors of node i.

        Parameters
        ----------
        i : int 
            Index of vertex to return neighbors of.
        return_weights : bool (optional), default=False
            Whether to return the weights of neighbors as well.

        Returns
        -------
        N : numpy array, int
            Array of nearest neighbor indices.
        W : numpy array, float
            Weights of edges to neighbors. 
        """
        
        N = self.weight_matrix[i,:].nonzero()[1]
        N = N[N != i]

        if return_weights:
            return N, self.weight_matrix[i,N].toarray().flatten()
        else:
            return N
```

--------------------------------

### Initialize Tau and Filename

Source: https://jwcalder.github.io/GraphLearning/ssl.html

Sets up the tau parameter and constructs an accuracy filename based on various graph learning configurations.

```python
#Set up tau
        if type(tau) in [float,int]:
            self.tau = np.ones(self.graph.num_nodes)*tau
        elif type(tau) is np.ndarray:
            self.tau = tau

        #Setup accuracy filename
        fname = '_laplace' 
        self.name = 'Laplace Learning'
        if self.reweighting != 'none':
            fname += '_' + self.reweighting
            self.name += ': ' + self.reweighting + ' reweighted'
        if self.normalization != 'combinatorial':
            fname += '_' + self.normalization
            self.name += ' ' + self.normalization
        if self.mean_shift:
            fname += '_meanshift'
            self.name += ' with meanshift'
        if self.order > 1:
            fname += '_order%d'%int(self.order)
            self.name += ' order %d'%int(self.order)
        if np.max(self.tau) > 0:
            fname += '_tau_%.3f'%np.max(self.tau)
            self.name += ' tau=%.3f'%np.max(self.tau)

        self.accuracy_filename = fname
```

--------------------------------

### Multiclass MBO Initialization

Source: https://jwcalder.github.io/GraphLearning/ssl.html

Initializes the Multiclass MBO algorithm with graph, class priors, and various learning parameters.

```python
class multiclass_mbo(ssl):
    def __init__(self, W=None, class_priors=None, Ns=6, T=10, dt=0.15, mu=50, num_eig=50):
        """Multiclass MBO
        ===================

        Semi-supervised learning via the Multiclass MBO method [1].

        Parameters
        ----------
        W : numpy array, scipy sparse matrix, or graphlearning graph object (optional), default=None
            Weight matrix representing the graph.
        class_priors : numpy array (optional), default=None
            Class priors (fraction of data belonging to each class). If provided, the predict function
            will attempt to automatic balance the label predictions to predict the correct number of
            nodes in each class.
        Ns : int (optional), default=6
            Number of inner iterations.
        T : int (optional), default=10
            Number of outer iterations.
        dt : float (optional), default=0.15
            Time step.
        mu : float (optional), default=50
            Fidelity penalty.
        num_eig : int (optional), default=300
            Number of eigenvectors.
        
        References
        ---------
        [1] C. Garcia-Cardona, E. Merkurjev, A.L. Bertozzi, A. Flenner, and A.G. Percus. [Multiclass data segmentation using diffuse interface methods on graphs.](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.743.9516&rep=rep1&type=pdf) IEEE transactions on pattern analysis and machine intelligence, 36(8), 1600-1613, 2014.
        """
        super().__init__(W, class_priors)

        self.Ns = Ns
        self.T = T
        self.dt = dt
        self.mu = mu
        self.num_eig = num_eig
        self.requires_eig = True

        #Setup accuracy filename
        self.accuracy_filename = '_multiclass_mbo_Ns_%d_T_%d_dt_%.3f_mu_%.2f'%(Ns,T,dt,mu)
        self.name = 'Multiclass MBO'
```

--------------------------------

### Volume MBO Initialization

Source: https://jwcalder.github.io/GraphLearning/ssl.html

Initializes the Volume MBO model. Requires class priors and optionally sets temperature and volume constraint.

```python
if class_priors is None:
    sys.exit("Class priors must be provided for Volume MBO.")
self.class_counts = (self.graph.num_nodes*class_priors).astype(int)
self.temperature = temperature
self.volume_constraint = volume_constraint
```

--------------------------------

### Get accuracy filename for SSL trials

Source: https://jwcalder.github.io/GraphLearning/ssl.html

Constructs and returns the filename for storing accuracy results generated by `ssl_trials.py`. Appends '_classpriors' to the filename if class priors are used.

```python
def get_accuracy_filename(self):
    """Get accuracy filename
    ========

    Returns name of the file that will store the accuracy results for `ssl_trials.py`.

    Returns
    -------
    fname : str
        Accuracy filename.
    """

    fname = self.accuracy_filename
    if self.class_priors is not None:
        fname += '_classpriors'
    fname += '_accuracy.csv'
    return fname
```

--------------------------------

### Poisson Learning with Gradient Descent

Source: https://jwcalder.github.io/GraphLearning/ssl.html

Demonstrates semi-supervised learning using the Poisson model with the gradient descent solver. Requires graphlearning, numpy, and scikit-learn. The example visualizes accuracy and training points.

```python
import numpy as np
import graphlearning as gl
import matplotlib.pyplot as plt
import sklearn.datasets as datasets

X,labels = datasets.make_moons(n_samples=500,noise=0.1)
W = gl.weightmatrix.knn(X,10,symmetrize=False)

train_ind = gl.trainsets.generate(labels, rate=5)
train_labels = labels[train_ind]

model = gl.ssl.poisson(W, solver='gradient_descent')
pred_labels = model.fit_predict(train_ind, train_labels)

accuracy = gl.ssl.ssl_accuracy(pred_labels, labels, train_ind)   
print("Accuracy: %.2f%%"%accuracy)

plt.scatter(X[:,0],X[:,1], c=pred_labels)
plt.scatter(X[train_ind,0],X[train_ind,1], c='r')
plt.show()
```

--------------------------------

### Initialize Volume MBO

Source: https://jwcalder.github.io/GraphLearning/ssl.html

Initializes the Volume MBO model. Requires class priors to be provided. Sets up graph, temperature, and volume constraint parameters.

```python
class volume_mbo(ssl):
    def __init__(self, W=None, class_priors=None, temperature=0.1, volume_constraint=0.5):
        """Volume MBO
        ===================

        Semi-supervised learning with the VolumeMBO method [1]. class_priors must be provided.

        Parameters
        ----------
        W : numpy array, scipy sparse matrix, or graphlearning graph object (optional), default=None
            Weight matrix representing the graph.
        class_priors : numpy array
            Class priors (fraction of data belonging to each class).
        temperature : float (optional), default=0.1
            Temperature for volume constrained MBO.
        volume_constraint : float (optional), default=0.5
            The number of points in each class is constrained to be a mulitple \(\lambda\) of the true
            class size, where 
            \[ \text{volume_constraint} \leq \lambda \leq 2-\text{volume_constraint}.\]
            Setting `volume_constraint=1` yields the tightest constraint.

        References
        ----------
        [1] M. Jacobs, E. Merkurjev, and S. Esedoḡlu. [Auction dynamics: A volume constrained MBO scheme.](https://www.sciencedirect.com/science/article/pii/S0021999117308033?casa_token=kNahPd2vu50AAAAA:uJQYQVnmMBV_oL0CG1UcOIulY4vhclMGTztm-jjAzy9Lns7rtoOnKs4iyvLOjKXaHU-D6qrQJT4) Journal of Computational Physics 354:288-310, 2018. 
        """
        super().__init__(W, None)

        if class_priors is None:
            sys.exit("Class priors must be provided for Volume MBO.")
        self.class_counts = (self.graph.num_nodes*class_priors).astype(int)
        self.temperature = temperature
        self.volume_constraint = volume_constraint

        #Setup accuracy filename and model name
        self.accuracy_filename = '_volume_mbo_temp_%.2f_vol_%.2f'%(temperature,volume_constraint)
        self.name = 'Volume MBO (T=%.2f, V=%.2f)'%(temperature,volume_constraint)
```

--------------------------------

### Initialize Modularity MBO Class

Source: https://jwcalder.github.io/GraphLearning/ssl.html

Initializes the Modularity MBO class with graph parameters and learning settings. Sets up the accuracy filename and model name.

```python
class modularity_mbo(ssl):
    def __init__(self, W=None, class_priors=None, gamma=0.5, epsilon=1, lamb=1, T=20, Ns=5):
        """Modularity MBO
        ===================

        Semi-supervised learning via the Modularity MBO method [1].

        Parameters
        ----------
        W : numpy array, scipy sparse matrix, or graphlearning graph object (optional), default=None
            Weight matrix representing the graph.
        class_priors : numpy array (optional), default=None
            Class priors (fraction of data belonging to each class). If provided, the predict function
            will attempt to automatic balance the label predictions to predict the correct number of
            nodes in each class.
        gamma : float (optional), default=0.5
            Parameter in algorithm.
        epsilon : float (optional), default=1
            Parameter in algorithm.
        lamb : float (optional), default=1
            Parameter in algorithm.
        T : int (optional), default=20
            Number of outer iterations.
        Ns : int (optional), default=5
            Number of inner iterations.
        
        References
        ---------
        [1] Z.M. Boyd, E. Bae, X.C. Tai, and A.L. Bertozzi. [Simplified energy landscape for modularity using total variation.](https://publications.ffi.no/nb/item/asset/dspace:4288/1619750.pdf) SIAM Journal on Applied Mathematics, 78(5), 2439-2464, 2018.
        """
        super().__init__(W, class_priors)

        self.gamma = gamma
        self.epsilon = epsilon
        self.lamb = lamb
        self.requires_eig = True
        self.T = T
        self.Ns = Ns

        #Setup accuracy filename
        self.accuracy_filename = '_modularity_mbo_gamma_%.2f_epsilon_%.2f_lamb_%.2f'%(gamma,epsilon,lamb)
        self.name = 'Modularity MBO'

```

--------------------------------

### Model Change Variance Optimization Initialization

Source: https://jwcalder.github.io/GraphLearning/active_learning.html

Initializes the model_change_var_opt class, which combines Model Change and Variance Optimization for active learning. This setup is suitable for scenarios where both model alteration and uncertainty reduction are desired.

```python
import graphlearning.active_learning as al
import graphlearning as gl
import numpy as np
import matplotlib.pyplot as plt
import sklearn.datasets as datasets

X,labels = datasets.make_moons(n_samples=500,noise=0.1)
W = gl.weightmatrix.knn(X,10)
train_ind = gl.trainsets.generate(labels, rate=5)
plt.scatter(X[:,0],X[:,1], c=labels)
plt.scatter(X[train_ind,0],X[train_ind,1], c='r')
plt.show()
```

--------------------------------

### Poisson Learning Initialization

Source: https://jwcalder.github.io/GraphLearning/ssl.html

Initializes the Poisson learning model with specified parameters. Supports different solvers and GPU acceleration for gradient descent. Note that if p is not 1, the solver defaults to 'spectral'.

```python
super().__init__(W, class_priors)
if solver not in ['conjugate_gradient', 'spectral', 'gradient_descent']:
    sys.exit("Invalid Poisson solver")
self.solver = solver
self.p = p
if p != 1:
    self.solver = 'spectral'
self.use_cuda = use_cuda
self.min_iter = min_iter
self.max_iter = max_iter
self.tol = tol
self.spectral_cutoff = spectral_cutoff

#Setup accuracy filename
fname = '_poisson' 
if self.p != 1:
    fname += '_p%.2f'%p
if self.solver == 'spectral':
    fname += '_N%d'%self.spectral_cutoff
    self.requries_eig = True
self.accuracy_filename = fname

#Setup Algorithm name
self.name = 'Poisson Learning'
```

--------------------------------

### Active Learning Workflow with Graph Learning

Source: https://jwcalder.github.io/GraphLearning/active_learning.html

Demonstrates the common workflow for active learning using the graphlearning library. This includes defining a model and acquisition function, instantiating the active learner, selecting query points, acquiring labels, and updating the learner.

```python
import graphlearning as gl

# define ssl model and acquisition function
model = gl.ssl.laplace(W)                   # graph-based ssl classifier with a given graph
acq_func = gl.active_learning.unc_sampling  # acquisition function for prioritizing which points to query


# instantiate active learner object
AL = gl.active_learner(
     model=model,                                    
     acq_function=acq_func,   
     labeled_ind=..,                        # indices of initially labeled nodes 
     labels=,                               # (integer) labels for initially labeled nodes
     policy='max',                         # active learning policy (i.e., 'max', or 'prop')
     **kwargs=...                           # other keyword arguments for the specified acq_function
    )

# select next query points
query_point = AL.select_queries(
                batch_size=1               # number of query points to select at this iteration
               ) 

# acquire label for query points
query_labels = y[query_point] 


# update the labeled data of active_learner object (including the graph-based ssl ``model`` outputs)
AL.update(query_points, query_labels) 

```

--------------------------------

### ARS Initialization and Execution

Source: https://jwcalder.github.io/GraphLearning/graph.html

Handles initialization for the ARS algorithm, including PCA-based initialization or random initialization, and then calls the C extension for the main ARS computation. This snippet is part of a larger function and assumes prior setup.

```python
#Import c extensions
from . import cextensions

if use_pca and (X.shape[1] > init_dim):
    X = X - np.mean(X, axis=0)
    vals, Q = sparse.linalg.eigsh(X.T@X, k=init_dim, which='LM')
    X = X@Q

#Type casting and memory blocking
X = np.ascontiguousarray(X,dtype=np.float64)
#Y = np.zeros((X.shape[0],dim),dtype=float)
#Y = X[:,-dim:].copy()
#Y -= np.mean(Y,axis=0)
#sig = np.sqrt(np.sum(Y*Y,axis=0))
#Y = Y/sig
#print(np.mean(Y,axis=0))
#print(np.sum(Y*Y,axis=0))
#Y = Y*0.001

if type(init) == np.ndarray:
    skip_random_init = True
    Y = init.copy()
    Y = np.ascontiguousarray(Y,dtype=np.float64)
elif init == 'pca':
    skip_random_init = True
    pca = PCA(n_components=dim,svd_solver="randomized")
    pca.set_output(transform="default")
    Y = pca.fit_transform(X).astype(np.float32, copy=False)
    Y = Y / np.std(Y[:, 0]) * 1e-4
    Y = np.ascontiguousarray(Y,dtype=np.float64)
else:
    skip_random_init = False
    Y = np.zeros((X.shape[0],dim))
    Y = np.ascontiguousarray(Y,dtype=np.float64)

cextensions.ars(X,Y,dim,perplexity,kappa,iters,time_step,theta1,theta2,alpha,num_early,int(prog),int(skip_random_init),int(dump))

return Y
```

--------------------------------

### Modularity MBO Initialization

Source: https://jwcalder.github.io/GraphLearning/ssl.html

Initializes the Modularity MBO algorithm with graph, class priors, and specific algorithm parameters.

```python
class modularity_mbo(ssl):
    def __init__(self, W=None, class_priors=None, gamma=0.5, epsilon=1, lamb=1, T=20, Ns=5):
        """Modularity MBO
        ===================

        Semi-supervised learning via the Modularity MBO method [1].

        Parameters
        ----------
        W : numpy array, scipy sparse matrix, or graphlearning graph object (optional), default=None
            Weight matrix representing the graph.
        class_priors : numpy array (optional), default=None
            Class priors (fraction of data belonging to each class). If provided, the predict function
            will attempt to automatic balance the label predictions to predict the correct number of
            nodes in each class.
        gamma : float (optional), default=0.5
            Parameter in algorithm.
        epsilon : float (optional), default=1
            Parameter in algorithm.
        """
        super().__init__(W, class_priors)

        self.gamma = gamma
        self.epsilon = epsilon
        self.lamb = lamb
        self.T = T
        self.Ns = Ns
        self.requires_eig = True

        #Setup accuracy filename
        self.accuracy_filename = '_modularity_mbo_gamma_%.2f_epsilon_%.2f_lamb_%.2f_T_%d_Ns_%d'%(gamma,epsilon,lamb,T,Ns)
        self.name = 'Modularity MBO'
```

--------------------------------

### Load Accuracy Scores from CSV

Source: https://jwcalder.github.io/GraphLearning/ssl.html

Loads accuracy scores from CSV files generated by `ssl_trials`. It calculates and returns summary statistics (mean and standard deviation of accuracy) across multiple trials for different numbers of training examples.

```python
def load_accuracy(self, tag=''):
        """Loads accuracy scores from each trial from csv files created by `ssl_trials`
        and returns summary statistics (mean and standard deviation of accuracy).

        Parameters
        ----------
        tag : str (optional), default=''
            An extra identifying tag to add to the accuracy filename.

        Returns
        -------
        num_train : numpy array
            Number of training examples in each label rate experiment.
        acc_mean : numpy array
            Mean accuracy over all trials in each experiment.
        acc_stddev : numpy array
            Standard deviation of accuracy over all trials in each experiment.
        num_trials : int
            Number of trials for each label rate.
        """

        accuracy_filename = os.path.join(results_dir, tag+self.get_accuracy_filename())
        X = utils.csvread(accuracy_filename)
        num_train = np.unique(X[:,0])

        acc_mean = []
        acc_stddev = []
        for n in num_train:
            Y = X[X[:,0]==n,1:]
            acc_mean += [np.mean(Y,axis=0)]
            acc_stddev += [np.std(Y,axis=0)]

        num_trials = int(len(X[:,0])/len(num_train))
        acc_mean = np.array(acc_mean)
        acc_stddev = np.array(acc_stddev)
        return num_train, acc_mean, acc_stddev, num_trials
```

--------------------------------

### Initialize AMLE SSL Algorithm

Source: https://jwcalder.github.io/GraphLearning/ssl.html

Initializes the AMLE SSL algorithm with various parameters controlling the solver and output. The `weighted` parameter affects solver speed by determining if the graph is converted to a 0/1 adjacency matrix.

```python
class amle(ssl):
    def __init__(self, W=None, class_priors=None, tol=1e-3, max_num_it=1e5, weighted=False, prog=False):
        """AMLE learning
        ===================

        Semi-supervised learning by the Absolutely Minimal Lipschitz Extension (AMLE). This is the same as
        p-Laplace with \(p=\infty\), except that AMLE has an option `weighted=False` that significantly 
        accelerates the solver.

        Parameters
        ----------
        W : numpy array, scipy sparse matrix, or graphlearning graph object (optional), default=None
            (n,n) Weight matrix representing the graph.
        class_priors : numpy array (optional), default=None
            Class priors (fraction of data belonging to each class). If provided, the predict function
            will attempt to automatic balance the label predictions to predict the correct number of
            nodes in each class.
        tol : float (optional), default=1e-3
            Tolerance with which to solve the equation.
        max_num_it : int (optional), default=1e5
            Maximum number of iterations
        weighted : bool (optional), default=False
            When False, the graph is converted to a 0/1 adjacency matrix, which affords a much faster solver.
        prog : bool (optional), default=False
            Whether to print progress information.
        """
        super().__init__(W, class_priors)

        self.tol = tol
        self.max_num_it = max_num_it
        self.weighted = weighted
        self.prog = prog
        self.onevsrest = True

        #Setup accuracy filename and model name
        self.accuracy_filename = '_amle'
        if not self.weighted:
            self.accuracy_filename += '_unweighted'
        self.name = 'AMLE'

```