HeatGeo

https://krishnaswamylab.github.io/HeatGeo/
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HeatGeo is a Python package for dimensionality reduction that preserves heat-geodesic dissimilarity...
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### Install HeatGeo Package

Source: https://krishnaswamylab.github.io/HeatGeo/index.html

Install the HeatGeo package using pip. For development, install with the 'dev' extra.

```bash
pip install heatgeo
```

```bash
pip install heatgeo['dev']
```

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

### GET /utils/time_entropy

Source: https://krishnaswamylab.github.io/HeatGeo/utils.html

Computes the time entropy for a given heat kernel.

```APIDOC
## GET /utils/time_entropy

### Description
Calculates the time entropy based on the provided heat kernel H.

### Parameters
#### Request Body
- **H** (object) - Required - The heat kernel matrix.
```

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

### Get Scanpy Graph

Source: https://krishnaswamylab.github.io/HeatGeo/graph.html

Retrieves the Scanpy graph. The 'knn' parameter defaults to 5.

```python
get_scanpy_graph (X, knn=5, **kwargs)
```

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

### Get Alpha Decay Graph

Source: https://krishnaswamylab.github.io/HeatGeo/graph.html

Retrieves the alpha-decay graph. Parameters include 'knn', 'decay', 'anisotropy', and 'n_pca'.

```python
get_alpha_decay_graph (X, knn:int=5, decay:float=40.0,
                        anisotropy:float=0, n_pca:int=None, **kwargs)
```

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

### Get kNN Graph

Source: https://krishnaswamylab.github.io/HeatGeo/graph.html

Retrieves the k-Nearest Neighbors (kNN) graph. The 'knn' parameter defaults to 5.

```python
get_knn_graph (X, knn=5, **kwargs)
```

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

### GET /utils/get_optimal_heat

Source: https://krishnaswamylab.github.io/HeatGeo/utils.html

Calculates the optimal heat kernel for a given embedding operator using Chebyshev approximation.

```APIDOC
## GET /utils/get_optimal_heat

### Description
Select the optimal tau for the heat kernel using Chebyshev approximation.

### Parameters
#### Request Body
- **emb_op** (object) - Required - The embedding operator.
- **tau_max** (float) - Optional - Maximum tau value (default: 50).
- **n_tau** (int) - Optional - Number of tau steps (default: 20).

### Response
#### Success Response (200)
- **H** (np.array) - Heat kernel with optimal tau (n_nodes, n_nodes).
```

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

### Get UMAP Graph

Source: https://krishnaswamylab.github.io/HeatGeo/graph.html

Retrieves the UMAP graph. The 'knn' parameter defaults to 5, which is different from UMAP's default of 15.

```python
get_umap_graph (X, knn=5, **kwargs)
```

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

### Initialize HeatFilter

Source: https://krishnaswamylab.github.io/HeatGeo/heat_filter.html

Wrapper for the approximation of the heat kernel. Supported methods include 'pygsp', 'mar', and 'euler'.

```python
HeatFilter (graph:Any, tau:float, order:int, method:str)
```

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

### classic

Source: https://krishnaswamylab.github.io/HeatGeo/mds.html

Performs classical MDS (CMDS) using random SVD.

```APIDOC
## classic

### Description
Performs fast Classical Multidimensional Scaling (CMDS) using random Singular Value Decomposition (SVD).

### Parameters
- **D** (array-like, shape=[n_samples, n_samples]) - Pairwise distances.
- **n_components** (int, optional) - Number of dimensions to embed into. Defaults to 2.
- **random_state** (int, RandomState or None, optional) - Numpy random state.

### Returns
- **Y** (array-like, embedded data [n_sample, ndim]) - Embedded data.
```

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

### PhateBasic Wrapper

Source: https://krishnaswamylab.github.io/HeatGeo/other_emb.html

A wrapper for PHATE, providing a simplified interface for dimensionality reduction. Requires additional packages.

```python
PhateBasic (knn:int, anisotropy:int=0, decay:int=40, n_pca:int=40,
             tau:Union[int,str]='auto', emb_dim:int=2)
```

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

### Compute heat kernel approximation with expm_multiply

Source: https://krishnaswamylab.github.io/HeatGeo/cheb.html

Calculates the product of the matrix exponential and a vector using Chebyshev approximation.

```python
expm_multiply (L, X, phi, tau, K=None, err=1e-32)
```

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

### PhateBasic

Source: https://krishnaswamylab.github.io/HeatGeo/other_emb.html

Wrapper for PHATE embedding.

```APIDOC
## PhateBasic

### Description
Wrapper for PHATE.

### Parameters
- **knn** (int) - Required
- **anisotropy** (int) - Optional - Default: 0
- **decay** (int) - Optional - Default: 40
- **n_pca** (int) - Optional - Default: 40
- **tau** (Union[int, str]) - Optional - Default: 'auto'
- **emb_dim** (int) - Optional - Default: 2
```

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

### RandWalkGeo

Source: https://krishnaswamylab.github.io/HeatGeo/other_emb.html

HeatGeo implementation using a random walk matrix instead of a Heat kernel.

```APIDOC
## RandWalkGeo

### Description
HeatGeo with a random walk matrix instead of Heat kernel.

### Parameters
- **knn** (int) - Required
- **anisotropy** (int) - Optional - Default: 0
- **decay** (int) - Optional - Default: 40
- **n_pca** (int) - Optional - Default: 40
- **tau** (int) - Optional - Default: 10
- **emb_dim** (int) - Optional - Default: 2
- **filter_method** (str) - Optional - Default: 'exact'
- **order** (int) - Optional - Default: 32
- **lap_type** (str) - Optional - Default: 'normalized'
- **log_normalize** (bool) - Optional - Default: False
- **scale_factor** (float) - Optional - Default: 1
- **denoising** (bool) - Optional - Default: False
- **n_ref** (int) - Optional - Default: 50
- **n_svd** (int) - Optional - Default: 50
- **graph_type** (str) - Optional - Default: 'alpha'
```

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

### HeatGeo Class Initialization

Source: https://krishnaswamylab.github.io/HeatGeo/embedding.html

Initializes the HeatGeo embedding class with specific parameters for graph construction and diffusion regularization.

```APIDOC
## HeatGeo

### Description
Base class for Heat Geo embedding methods, supporting various graph types and regularization parameters.

### Parameters
- **knn** (int) - Required - Number of neighbors considered to build the graph.
- **anisotropy** (int) - Optional - Default: 0
- **decay** (int) - Optional - Default: 40
- **n_pca** (int) - Optional - Default: 40
- **tau** (int) - Optional - Default: 10
- **emb_dim** (int) - Optional - Default: 2
- **filter_method** (str) - Optional - Default: 'mar'
- **order** (int) - Optional - Default: 32
- **lap_type** (str) - Optional - Default: 'normalized'
- **tau_min** (float) - Optional - Default: 0.1
- **tau_max** (float) - Optional - Default: 200
- **n_tau** (int) - Optional - Default: 1
- **log_normalize** (bool) - Optional - Default: False
- **scale_factor** (float) - Optional - Default: 1.0
- **denoising** (bool) - Optional - Default: False
- **graph_type** (str) - Optional - Default: 'alpha'
- **harnack_regul** (float) - Optional - Default: 0 - Harnack regularization parameter, between 0 and 1.
- **denoise_regul** (float) - Optional - Default: 0.0 - Corresponds to ρ in the paper.
```

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

### BaseEmb Class Initialization

Source: https://krishnaswamylab.github.io/HeatGeo/embedding.html

Initializes the BaseEmb class, providing foundational methods for embedding techniques.

```APIDOC
## BaseEmb

### Description
Base class for embedding methods providing core configuration for diffusion kernels and MDS solvers.

### Parameters
- **knn** (int) - Required - Number of nearest neighbors.
- **anisotropy** (int) - Optional - Default: 0 - Anisotropy parameter in the diffusion kernel.
- **decay** (int) - Optional - Default: 40 - Decay parameter in the diffusion kernel.
- **n_pca** (int) - Optional - Default: 40 - Number of principal components to use for knn estimation.
- **tau** (Union[int, str]) - Optional - Default: 'auto' - Diffusion time.
- **emb_dim** (int) - Optional - Default: 2 - Embedding dimension.
- **order** (int) - Optional - Default: 32 - Order of the Chebyshev approximation, or steps in Euler’s method.
- **random_state** (int) - Optional - Default: 42 - Random state for the embedding.
- **scale_factor** (float) - Optional - Default: 2.0 - Power when computing the distance matrix.
- **solver** (str) - Optional - Default: 'sgd' - Solver to use for MDS.
- **lap_type** (str) - Optional - Default: 'normalized' - Type of Laplacian to use for the graph.
- **filter_method** (str) - Optional - Default: 'pygsp' - Method to use for Heat approx.
- **graph_type** (str) - Optional - Default: 'alpha' - Type of graph to use for the embedding.
```

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

### Graph Construction Methods

Source: https://krishnaswamylab.github.io/HeatGeo/graph.html

Functions to generate graphs from input data X using different kernel strategies.

```APIDOC
## get_umap_graph
### Description
Generates a UMAP graph from input data.
### Method
FUNCTION
### Parameters
#### Arguments
- **X** (array) - Required - Input data
- **knn** (int) - Optional - Number of neighbors, defaults to 5
- **kwargs** (dict) - Optional - Additional arguments

## get_scanpy_graph
### Description
Generates a graph using Scanpy methods.
### Parameters
- **X** (array) - Required - Input data
- **knn** (int) - Optional - Number of neighbors, defaults to 5
- **kwargs** (dict) - Optional - Additional arguments

## get_alpha_decay_graph
### Description
Generates an alpha-decay kernel graph.
### Parameters
- **X** (array) - Required - Input data
- **knn** (int) - Optional - Number of neighbors, defaults to 5
- **decay** (float) - Optional - Decay factor, defaults to 40.0
- **anisotropy** (float) - Optional - Anisotropy factor, defaults to 0
- **n_pca** (int) - Optional - Number of PCA components
- **kwargs** (dict) - Optional - Additional arguments

## get_knn_graph
### Description
Generates a K-Nearest Neighbors graph.
### Parameters
- **X** (array) - Required - Input data
- **knn** (int) - Optional - Number of neighbors, defaults to 5
- **kwargs** (dict) - Optional - Additional arguments
```

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

### Create HeatGeo Embedding

Source: https://krishnaswamylab.github.io/HeatGeo/index.html

Instantiate the HeatGeo class and use fit_transform to create an embedding for the given data. The knn parameter controls the number of nearest neighbors.

```python
from heatgeo.embedding import HeatGeo
emb_op = HeatGeo(knn=5)
emb = emb_op.fit_transform(data)
```

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

### Classic MDS Implementation

Source: https://krishnaswamylab.github.io/HeatGeo/mds.html

Fast Classical MDS (CMDS) using random SVD. Takes pairwise distances as input.

```python
classic (D, n_components=2, random_state=None)
```

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

### RandWalkGeo Implementation

Source: https://krishnaswamylab.github.io/HeatGeo/other_emb.html

Use RandWalkGeo for embeddings based on a random walk matrix instead of the standard Heat kernel. Requires additional packages.

```python
RandWalkGeo (knn:int, anisotropy:int=0, decay:int=40, n_pca:int=40,
              tau:int=10, emb_dim:int=2, filter_method:str='exact',
              order:int=32, lap_type:str='normalized',
              log_normalize:bool=False, scale_factor:float=1,
              denoising:bool=False, n_ref:int=50, n_svd:int=50,
              graph_type:str='alpha')
```

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

### ShortestPath Embedding

Source: https://krishnaswamylab.github.io/HeatGeo/other_emb.html

Generates shortest path embeddings with various graph construction parameters. Requires additional packages.

```python
ShortestPath (knn:int, anisotropy:int=0, decay:int=40, n_pca:int=40,
               graph_type:str='alpha', **kwargs)
```

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

### Perform HeatEuler Discretization

Source: https://krishnaswamylab.github.io/HeatGeo/heat_filter.html

Implicit Euler discretization of the heat equation using Cholesky prefactorization.

```python
HeatEuler (L, t, K)
```

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

### HeatFilter API

Source: https://krishnaswamylab.github.io/HeatGeo/heat_filter.html

Wrapper for the approximation of the heat kernel. It supports different methods like Chebyshev polynomials ('pygsp', 'mar') and Backward Euler ('euler').

```APIDOC
## HeatFilter

### Description
Wrapper for the approximation of the heat kernel.

### Method
Constructor

### Endpoint
N/A (Class constructor)

### Parameters
#### Path Parameters
None

#### Query Parameters
None

#### Request Body
None

### Request Example
```json
{
  "graph": "<Graph object>",
  "tau": 0.1,
  "order": 32,
  "method": "pygsp"
}
```

### Response
#### Success Response (200)
Returns a callable function for applying the heat filter.

#### Response Example
```json
{
  "message": "Heat filter function returned"
}
```
```

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

### SGD MDS Implementation

Source: https://krishnaswamylab.github.io/HeatGeo/mds.html

Metric MDS using stochastic gradient descent. Accepts pairwise distances and optional initialization.

```python
sgd (D, w=None, n_components=2, random_state=None, init=None)
```

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

### HeatEuler API

Source: https://krishnaswamylab.github.io/HeatGeo/heat_filter.html

Implicit Euler discretization of the heat equation using Cholesky prefactorization.

```APIDOC
## HeatEuler

### Description
Implicit Euler discretization of the heat equation using Cholesky prefactorization.

### Method
Constructor

### Endpoint
N/A (Class constructor)

### Parameters
#### Path Parameters
None

#### Query Parameters
None

#### Request Body
None

### Request Example
```json
{
  "L": "<Laplacian matrix>",
  "t": 0.1,
  "K": "<Cholesky factor>"
}
```

### Response
#### Success Response (200)
Represents the implicit Euler discretization object.

#### Response Example
```json
{
  "message": "HeatEuler object created"
}
```
```

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

### Calculate optimal heat kernel

Source: https://krishnaswamylab.github.io/HeatGeo/utils.html

Computes the heat kernel with an optimal tau value determined by Chebyshev approximation.

```python
get_optimal_heat (emb_op, tau_max:float=50, n_tau:int=20)
```

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

### SMACOF MDS Implementation

Source: https://krishnaswamylab.github.io/HeatGeo/mds.html

Metric and non-metric MDS using the SMACOF algorithm. Requires pairwise distances as input.

```python
smacof (D, n_components=2, metric=True, init=None, random_state=None,
         verbose=0, max_iter=3000, eps=1e-06, n_jobs=1)
```

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

### compute_chebychev_coeff_all

Source: https://krishnaswamylab.github.io/HeatGeo/cheb.html

Computes the K+1 Chebyshev coefficients for the specified functions.

```APIDOC
## compute_chebychev_coeff_all

### Description
Compute the K+1 Chebychev coefficients for our functions.

### Parameters
- **phi** (float) - Required - Scaling parameter.
- **tau** (float) - Required - Time parameter.
- **K** (int) - Required - Degree of approximation.
```

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

### sgd

Source: https://krishnaswamylab.github.io/HeatGeo/mds.html

Performs metric MDS using stochastic gradient descent.

```APIDOC
## sgd

### Description
Performs metric Multidimensional Scaling (MDS) using stochastic gradient descent (SGD).

### Parameters
- **D** (array-like, shape=[n_samples, n_samples]) - Pairwise distances.
- **w** (array-like or None) - Weights for SGD.
- **n_components** (int, optional) - Number of dimensions to embed into. Defaults to 2.
- **random_state** (int or None, optional) - Numpy random state.
- **init** (array-like or None, optional) - Initialization algorithm or state to use for MMDS.

### Returns
- **Y** (array-like, embedded data [n_sample, ndim]) - Embedded data.
```

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

### Compute Chebyshev coefficients

Source: https://krishnaswamylab.github.io/HeatGeo/cheb.html

Calculates the K+1 Chebyshev coefficients for the specified functions.

```python
compute_chebychev_coeff_all (phi, tau, K)
```

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

### ShortestPath

Source: https://krishnaswamylab.github.io/HeatGeo/other_emb.html

Shortest path embedding with different graph construction.

```APIDOC
## ShortestPath

### Description
Shortest path embedding with different graph construction.

### Parameters
- **knn** (int) - Required
- **anisotropy** (int) - Optional - Default: 0
- **decay** (int) - Optional - Default: 40
- **n_pca** (int) - Optional - Default: 40
- **graph_type** (str) - Optional - Default: 'alpha'
- **kwargs** (dict) - Optional
```

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

### expm_multiply

Source: https://krishnaswamylab.github.io/HeatGeo/cheb.html

Computes the matrix exponential multiplied by a vector using Chebyshev approximation.

```APIDOC
## expm_multiply

### Description
Computes the matrix exponential multiplied by a vector.

### Parameters
- **L** (matrix) - Required - The graph Laplacian matrix.
- **X** (vector) - Required - The input vector.
- **phi** (float) - Required - Scaling parameter.
- **tau** (float) - Required - Time parameter.
- **K** (int) - Optional - Degree of approximation.
- **err** (float) - Optional - Error tolerance.
```

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

### Calculate eta bounds

Source: https://krishnaswamylab.github.io/HeatGeo/cheb.html

Functions to compute specific or generic eta error bounds.

```python
get_bound_eta_specific (phi, x, tau, K)
```

```python
get_bound_eta_generic (phi, x, tau, K)
```

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

### DiffusionMap Embedding

Source: https://krishnaswamylab.github.io/HeatGeo/other_emb.html

Implements Diffusion Map embedding with flexible graph construction options. Requires additional packages.

```python
DiffusionMap (knn:int=0, decay:int=40, n_pca:int=40, tau:float=1,
               emb_dim:int=2, anisotropy:int=0, graph_type:str='alpha',
               **kwargs)
```

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

### Compute time entropy

Source: https://krishnaswamylab.github.io/HeatGeo/utils.html

Calculates the time entropy for a given heat kernel matrix.

```python
time_entropy (H)
```

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

### POST /utils/interpolate

Source: https://krishnaswamylab.github.io/HeatGeo/utils.html

Performs interpolation between two points over a specified number of steps.

```APIDOC
## POST /utils/interpolate

### Description
Interpolates between x0 and x1 over n_steps.

### Parameters
#### Request Body
- **x0** (object) - Required - Starting point.
- **x1** (object) - Required - Ending point.
- **n_steps** (int) - Required - Number of interpolation steps.
```

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

### Calculate generic epsilon bound

Source: https://krishnaswamylab.github.io/HeatGeo/cheb.html

Computes the generic epsilon error bound.

```python
get_bound_eps_generic (phi, x, tau, K)
```

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

### Calculate error bound E

Source: https://krishnaswamylab.github.io/HeatGeo/cheb.html

Computes the error bound E given K and C.

```python
E (K, C)
```

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

### Calculate error bound g

Source: https://krishnaswamylab.github.io/HeatGeo/cheb.html

Computes the error bound g given K and C.

```python
g (K, C)
```

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

### smacof

Source: https://krishnaswamylab.github.io/HeatGeo/mds.html

Performs metric and non-metric MDS using the SMACOF algorithm.

```APIDOC
## smacof

### Description
Performs metric and non-metric Multidimensional Scaling (MDS) using the SMACOF algorithm.

### Method
SMACOF (Scaling by MAking use of COmputational FLuid dynamics)

### Parameters
- **D** (array-like, shape=[n_samples, n_samples]) - Pairwise distances.
- **n_components** (int, optional) - Number of dimensions to embed into. Defaults to 2.
- **metric** (bool, optional) - Use metric MDS. If False, uses non-metric MDS. Defaults to True.
- **init** (array-like or None, optional) - Initialization state.
- **random_state** (int, RandomState or None, optional) - Numpy random state.
- **verbose** (int or bool, optional) - Verbosity level. Defaults to 0.
- **max_iter** (int, optional) - Maximum number of iterations. Defaults to 3000.
- **eps** (float, optional) - Stopping criterion. Defaults to 1e-6.
- **n_jobs** (int, optional) - Number of jobs to run in parallel. Defaults to 1.

### Returns
- **Y** (array-like, shape=[n_samples, n_components]) - Embedded data.
```

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

### Determine minimal K for error bound

Source: https://krishnaswamylab.github.io/HeatGeo/cheb.html

Finds the smallest K such that the approximation error is less than or equal to the specified threshold.

```python
reverse_bound (f, phi, x, tau, err)
```

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

### reverse_bound

Source: https://krishnaswamylab.github.io/HeatGeo/cheb.html

Determines the minimal degree K required to satisfy an error bound.

```APIDOC
## reverse_bound

### Description
Returns the minimal K such that f(phi, x, tau, K) <= err.

### Parameters
- **f** (function) - Required - The error function.
- **phi** (float) - Required - Scaling parameter.
- **x** (float) - Required - Input value.
- **tau** (float) - Required - Time parameter.
- **err** (float) - Required - Error tolerance.
```

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

### Diffusion Operator Functions

Source: https://krishnaswamylab.github.io/HeatGeo/graph.html

Functions to compute diffusion metrics on pygsp graphs.

```APIDOC
## diff_aff
### Description
Compute the diffusion affinity for a pygsp graph.
### Parameters
- **graph** (pygsp.graph) - Required - The input graph

## kernel_degree
### Description
Compute the kernel degree for a pygsp graph.
### Parameters
- **graph** (pygsp.graph) - Required - The input graph

## diff_op
### Description
Compute the diffusion operator for a pygsp graph.
### Parameters
- **graph** (pygsp.graph) - Required - The input graph
```

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

### Compute Diffusion Affinity

Source: https://krishnaswamylab.github.io/HeatGeo/graph.html

Computes the diffusion affinity for a pygsp graph.

```python
diff_aff (graph)
```

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

### Interpolate data

Source: https://krishnaswamylab.github.io/HeatGeo/utils.html

Performs interpolation between two points over a specified number of steps.

```python
interpolate (x0, x1, n_steps)
```

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

### Compute Kernel Degree

Source: https://krishnaswamylab.github.io/HeatGeo/graph.html

Computes the kernel degree for a pygsp graph.

```python
kernel_degree (graph)
```

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

### Compute Diffusion Operator

Source: https://krishnaswamylab.github.io/HeatGeo/graph.html

Computes the diffusion operator for a pygsp graph.

```python
diff_op (graph)
```

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

### DiffusionMap

Source: https://krishnaswamylab.github.io/HeatGeo/other_emb.html

Diffusion Map embedding with different graph construction.

```APIDOC
## DiffusionMap

### Description
Diffusion Map embedding with different graph construction.

### Parameters
- **knn** (int) - Optional - Default: 0
- **decay** (int) - Optional - Default: 40
- **n_pca** (int) - Optional - Default: 40
- **tau** (float) - Optional - Default: 1
- **emb_dim** (int) - Optional - Default: 2
- **anisotropy** (int) - Optional - Default: 0
- **graph_type** (str) - Optional - Default: 'alpha'
- **kwargs** (dict) - Optional
```

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

### Calculate Bergamaschi bounds

Source: https://krishnaswamylab.github.io/HeatGeo/cheb.html

Functions to compute specific or generic Bergamaschi error bounds.

```python
get_bound_bergamaschi_specific (phi, x, tau, K)
```

```python
get_bound_bergamaschi_generic (phi, x, tau, K)
```

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

### embed_MDS

Source: https://krishnaswamylab.github.io/HeatGeo/mds.html

Embeds data into a lower-dimensional space using MDS.

```APIDOC
## embed_MDS

### Description
Embeds data into a lower-dimensional space using Multidimensional Scaling (MDS).

### Parameters
- **X** (array-like) - Input data or pairwise distances.
- **ndim** (int, optional) - Number of dimensions to embed into. Defaults to 2.
- **seed** (int, optional) - Random seed for reproducibility. Defaults to 2.
- **solver** (str, optional) - The solver to use for MDS. Defaults to 'sgd'.
- **how** (str, optional) - Method for embedding ('metric' or 'non-metric'). Defaults to 'metric'.
- **input_is_dist** (bool, optional) - Whether the input X is a distance matrix. Defaults to True.
- **distance_metric** (str, optional) - The distance metric to use if input_is_dist is False. Defaults to 'euclidean'.
- **mds_weights** (array-like or None, optional) - Weights for MDS. Defaults to None.
```

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

### Embed MDS Function

Source: https://krishnaswamylab.github.io/HeatGeo/mds.html

Function signature for embedding data using MDS with various solver options.

```python
embed_MDS (X, ndim=2, seed=2, solver='sgd', how='metric',
            input_is_dist=True, distance_metric='euclidean',
            mds_weights=None)
```
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