Heat Geo embedding

In this page we define the Heat Geo embedding class HeatGeo and the BaseEmb class.

The main parameters of HeatGeo are

• the number of neighbors knn considered to build the graph,

• the diffusion time tau which can be set to "auto" or fixed to any positive real number

• denoise_regul a float in [0,1], which corresponds to \(\rho\) in the paper with \(\rho=1\) uses only the triplet distance,

• harnack_regul is the weight parameter for the volume term in Def. 4.1. If it is too large all points will collapse together, we suggest using values in [0,2].

Embeddings on PBMC for different denoise_regul

---

source

HeatGeo

 HeatGeo (knn:int, anisotropy:int=0, decay:int=40, n_pca:int=40,
          tau:int=10, emb_dim:int=2, filter_method:str='mar',
          order:int=32, lap_type:str='normalized', tau_min:float=0.1,
          tau_max:float=200, n_tau:int=1, log_normalize:bool=False,
          scale_factor:float=1.0, denoising:bool=False,
          graph_type:str='alpha', truncation_type:Optional[str]=None,
          truncation_arg:Optional[str]=None,
          treshold_type:Optional[str]=None, harnack_regul:float=0,
          norm_treshold:bool=True, mds_weights_type:Optional[str]=None,
          mds_weights_args:Optional[str]=None, denoise_regul:float=0.0)

Base class for embedding methods.

	Type	Default	Details
knn	int
anisotropy	int	0
decay	int	40
n_pca	int	40
tau	int	10
emb_dim	int	2
filter_method	str	mar
order	int	32
lap_type	str	normalized
tau_min	float	0.1
tau_max	float	200
n_tau	int	1
log_normalize	bool	False
scale_factor	float	1.0
denoising	bool	False
graph_type	str	alpha
truncation_type	Optional	None
truncation_arg	Optional	None
treshold_type	Optional	None	“min” or “max”
harnack_regul	float	0	Harnack regularization parameter, between 0 and 1.
norm_treshold	bool	True
mds_weights_type	Optional	None
mds_weights_args	Optional	None	“heat_kernel”, “inv_dist”,“gaussian_dist”
denoise_regul	float	0.0

---

source

BaseEmb

 BaseEmb (knn:int, anisotropy:int=0, decay:int=40, n_pca:int=40,
          tau:Union[int,str]='auto', emb_dim:int=2, order:int=32,
          random_state:int=42, scale_factor:float=2.0, tau_min:float=0.1,
          tau_max:float=1.0, n_tau:int=1, n_landmarks:Optional[int]=None,
          solver:str='sgd', lap_type:str='normalized',
          filter_method:str='pygsp', graph_type:str='alpha',
          mds_weights:Optional[str]=None)

Base class for embedding methods.

	Type	Default	Details
knn	int		number of nearest neighbors
anisotropy	int	0	anisotropy parameter in the diffusion kernel
decay	int	40	decay parameter in the diffusion kernel
n_pca	int	40	number of principal components to use for knn estimation
tau	Union	auto	diffusion time
emb_dim	int	2	embedding dimension
order	int	32	order of the Chebyshev approximation, or steps in Euler’s method
random_state	int	42	random state for the embedding
scale_factor	float	2.0	power when computing the distance matrix
tau_min	float	0.1	minimum diffusion time
tau_max	float	1.0	maximum diffusion time
n_tau	int	1	number of diffusion times for entropy.
n_landmarks	Optional	None
solver	str	sgd	solver to use for MDS
lap_type	str	normalized	type of Laplacian to use for the graph "normalized" or "combinatorial"
filter_method	str	pygsp	method to use for Heat approx. "pygsp" or "euler", "mar"
graph_type	str	alpha	type of graph to use for the embedding "knn" or "alpha" or scanpy
mds_weights	Optional	None	weights to use for MDS