Performance comparison of inference on hematopoiesis dataset

Performance comparison of inference on hematopoiesis dataset#

Comparison of cross-boundary correctness (CBC) and terminal state identification

Library imports#

from tqdm import tqdm

import numpy as np
import pandas as pd
from scipy.stats import ttest_ind

import matplotlib.pyplot as plt
import mplscience
import seaborn as sns
from matplotlib import rcParams

import cellrank as cr
import scanpy as sc
import scvelo as scv

from rgv_tools import DATA_DIR, FIG_DIR
from rgv_tools.benchmarking import get_tsi_score, plot_tsi
from rgv_tools.core import METHOD_PALETTE_TSI
from rgv_tools.plotting._significance import add_significance, get_significance
from rgv_tools.utils._stools import reverse_cluster, reverse_cluster_dict

/home/icb/weixu.wang/miniconda3/envs/regvelo_test/lib/python3.10/site-packages/anndata/utils.py:429: FutureWarning: Importing read_csv from `anndata` is deprecated. Import anndata.io.read_csv instead.
  warnings.warn(msg, FutureWarning)
/home/icb/weixu.wang/miniconda3/envs/regvelo_test/lib/python3.10/site-packages/anndata/utils.py:429: FutureWarning: Importing read_excel from `anndata` is deprecated. Import anndata.io.read_excel instead.
  warnings.warn(msg, FutureWarning)
/home/icb/weixu.wang/miniconda3/envs/regvelo_test/lib/python3.10/site-packages/anndata/utils.py:429: FutureWarning: Importing read_hdf from `anndata` is deprecated. Import anndata.io.read_hdf instead.
  warnings.warn(msg, FutureWarning)
/home/icb/weixu.wang/miniconda3/envs/regvelo_test/lib/python3.10/site-packages/anndata/utils.py:429: FutureWarning: Importing read_loom from `anndata` is deprecated. Import anndata.io.read_loom instead.
  warnings.warn(msg, FutureWarning)
/home/icb/weixu.wang/miniconda3/envs/regvelo_test/lib/python3.10/site-packages/anndata/utils.py:429: FutureWarning: Importing read_mtx from `anndata` is deprecated. Import anndata.io.read_mtx instead.
  warnings.warn(msg, FutureWarning)
/home/icb/weixu.wang/miniconda3/envs/regvelo_test/lib/python3.10/site-packages/anndata/utils.py:429: FutureWarning: Importing read_text from `anndata` is deprecated. Import anndata.io.read_text instead.
  warnings.warn(msg, FutureWarning)
/home/icb/weixu.wang/miniconda3/envs/regvelo_test/lib/python3.10/site-packages/anndata/utils.py:429: FutureWarning: Importing read_umi_tools from `anndata` is deprecated. Import anndata.io.read_umi_tools instead.
  warnings.warn(msg, FutureWarning)

General settings#

plt.rcParams["svg.fonttype"] = "none"
sns.reset_defaults()
sns.reset_orig()
scv.settings.set_figure_params("scvelo", dpi_save=400, dpi=80, transparent=True, fontsize=14, color_map="viridis")

Constants#

DATASET = "hematopoiesis"

SAVE_FIGURES = False
if SAVE_FIGURES:
    (FIG_DIR / DATASET).mkdir(parents=True, exist_ok=True)

FIGURE_FORMATE = "svg"

VELOCITY_METHODS = ["regvelo_unregularized", "regvelo", "scvelo", "velovi"]

TERMINAL_STATES = ["Ery", "Mon", "Bas", "Neu", "Meg"]

STATE_TRANSITIONS = [
    ("HSC", "GMP-like"),
    ("GMP-like", "Mon"),
    ("HSC", "MEP-like"),
    ("MEP-like", "Ery"),
    ("MEP-like", "Meg"),
    ("MEP-like", "Bas"),
]

STATE_TRANSITIONS_REVERSE = [
    ("GMP-like", "HSC"),
    ("Mon", "GMP-like"),
    ("MEP-like", "HSC"),
    ("Ery", "MEP-like"),
    ("Meg", "MEP-like"),
    ("Bas", "MEP-like"),
]

Data loading#

vks = {}

for method in VELOCITY_METHODS:
    adata = sc.read_h5ad(DATA_DIR / DATASET / "processed" / f"adata_run_{method}.h5ad")

    del adata.var["velocity_genes"]
    ## Visualize velocity on UMAP
    with mplscience.style_context():
        fig, ax = plt.subplots(figsize=(6, 4))
        scv.tl.velocity_graph(adata)
        scv.pl.velocity_embedding_stream(
            adata, basis="umap", color="cell_type", title="", legend_loc="lower right", ax=ax
        )

        if SAVE_FIGURES:
            fig.savefig(
                FIG_DIR / DATASET / f"vector_field_{method}.svg", format="svg", transparent=True, bbox_inches="tight"
            )
        plt.show()

    ## construct graph
    vk = cr.kernels.VelocityKernel(adata)
    vk.compute_transition_matrix()
    vks[method] = vk

computing velocity graph (using 1/128 cores)

    finished (0:00:01) --> added 
    'velocity_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity embedding
    finished (0:00:00) --> added
    'velocity_umap', embedded velocity vectors (adata.obsm)
../_images/927cf376f5da5e4af5823cc942e50e75518d148833b6d838d70d91cb3faea1cd.png 
computing velocity graph (using 1/128 cores)

    finished (0:00:01) --> added 
    'velocity_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity embedding
    finished (0:00:00) --> added
    'velocity_umap', embedded velocity vectors (adata.obsm)
../_images/8cea172dbad92b1be586e5733d1c034c1cc346681a0b3edc95ce27578b307cda.png 
computing velocity graph (using 1/128 cores)

    finished (0:00:01) --> added 
    'velocity_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity embedding
    finished (0:00:00) --> added
    'velocity_umap', embedded velocity vectors (adata.obsm)
../_images/506b5802cba3000feece2dee602e16a8966b4f2ecd56d3f63e2fcce5898c8306.png 
computing velocity graph (using 1/128 cores)

    finished (0:00:01) --> added 
    'velocity_graph', sparse matrix with cosine correlations (adata.uns)
computing velocity embedding
    finished (0:00:00) --> added
    'velocity_umap', embedded velocity vectors (adata.obsm)
../_images/3de6a11c15867bb00d56ad1209e7bc324c78e2827444c4c48c5b4db0d3701811.png

Comparing RegVelo and scVelo#

Measuring forward CBC#

cluster_key = "cell_type"
rep = "X_pca"

score_df = []
for source, target in tqdm(STATE_TRANSITIONS):
    cbc_rgv = vks["regvelo"].cbc(source=source, target=target, cluster_key=cluster_key, rep=rep)
    cbc_rgv_wo = vks["regvelo_unregularized"].cbc(source=source, target=target, cluster_key=cluster_key, rep=rep)

    score_df.append(
        pd.DataFrame(
            {
                "State transition": [f"{source} - {target}"] * len(cbc_rgv),
                "Log ratio": np.log((cbc_rgv + 1) / (cbc_rgv_wo + 1)),
            }
        )
    )
score_df_forward = pd.concat(score_df)

100%|██████████| 6/6 [00:01<00:00,  5.96it/s]

dfs = []

ttest_res = {}
significances = {}

for source, target in STATE_TRANSITIONS:
    obs_mask = score_df_forward["State transition"].isin([f"{source} - {target}"])
    a = score_df_forward.loc[obs_mask, "Log ratio"].values
    b = np.zeros(len(a))

    ttest_res[f"{source} - {target}"] = ttest_ind(a, b, equal_var=False, alternative="greater")
    significances[f"{source} - {target}"] = get_significance(ttest_res[f"{source} - {target}"].pvalue)

significances_forward = significances.copy()
significances_forward

{'HSC - GMP-like': '***',
 'GMP-like - Mon': '***',
 'HSC - MEP-like': '***',
 'MEP-like - Ery': '***',
 'MEP-like - Meg': 'n.s.',
 'MEP-like - Bas': '***'}

Measuring backward CBC#

score_df = []
for source, target in tqdm(STATE_TRANSITIONS_REVERSE):
    cbc_rgv = -vks["regvelo"].cbc(source=source, target=target, cluster_key=cluster_key, rep=rep)
    cbc_rgv_wo = -vks["regvelo_unregularized"].cbc(source=source, target=target, cluster_key=cluster_key, rep=rep)

    score_df.append(
        pd.DataFrame(
            {
                "State transition": [f"{source} - {target}"] * len(cbc_rgv),
                "Log ratio": np.log((cbc_rgv + 1) / (cbc_rgv_wo + 1)),
            }
        )
    )
score_df_backward = pd.concat(score_df)

100%|██████████| 6/6 [00:00<00:00,  6.58it/s]

dfs = []

ttest_res = {}
significances = {}

for source, target in STATE_TRANSITIONS_REVERSE:
    obs_mask = score_df_backward["State transition"].isin([f"{source} - {target}"])
    a = score_df_backward.loc[obs_mask, "Log ratio"].values
    b = np.zeros(len(a))

    ttest_res[f"{source} - {target}"] = ttest_ind(a, b, equal_var=False, alternative="greater")
    significances[f"{source} - {target}"] = get_significance(ttest_res[f"{source} - {target}"].pvalue)

significances_backward = significances.copy()
significances_backward

{'GMP-like - HSC': '***',
 'Mon - GMP-like': '***',
 'MEP-like - HSC': '***',
 'Ery - MEP-like': '***',
 'Meg - MEP-like': '*',
 'Bas - MEP-like': 'n.s.'}

score_df_backward["State transition"] = score_df_backward["State transition"].apply(reverse_cluster)

score_df_forward.loc[:, "Direction"] = "Forward"
score_df_backward.loc[:, "Direction"] = "Backward"
score_df = pd.concat([score_df_forward, score_df_backward])

significances_backward = reverse_cluster_dict(significances_backward)
significances_backward

{'HSC - GMP-like': '***',
 'GMP-like - Mon': '***',
 'HSC - MEP-like': '***',
 'MEP-like - Ery': '***',
 'MEP-like - Meg': '*',
 'MEP-like - Bas': 'n.s.'}

Plot CBC#

score_forward = []
for i in list(significances_forward.keys()):
    score_forward.append(significances_forward[i])

score_backward = []
for i in list(significances_backward.keys()):
    score_backward.append(significances_backward[i])

sig_m = pd.DataFrame(
    {
        "State transition": list(significances_forward.keys()) + list(significances_backward.keys()),
        "Direction": ["Forward"] * 6 + ["Backward"] * 6,
        "Sign": score_forward + score_backward,
    }
)

with mplscience.style_context():
    sns.set_style(style="whitegrid")
    fig, ax = plt.subplots(1, 1, figsize=(12, 4), sharey=True)
    flierprops = {"marker": "D", "markerfacecolor": "grey", "linestyle": "none", "markersize": 2}
    sns.boxplot(x="State transition", y="Log ratio", hue="Direction", data=score_df, flierprops=flierprops, ax=ax)

    # Calculate the maximum Y value from the data to set a uniform height for significance indicators
    y_max = score_df["Log ratio"].max()

    # Add significance indicators
    cell_types = score_df["State transition"].unique()
    categories = score_df["Direction"].unique()

    for i, cell_type in enumerate(cell_types):
        for j, category in enumerate(categories):
            star = sig_m[(sig_m["State transition"].isin([cell_type])) & (sig_m["Direction"].isin([category]))][
                "Sign"
            ].tolist()[0]

            # Calculate the position of the asterisk
            x = i + (j - 0.5) * 0.4  # Adjust the position of the asterisk
            y = y_max + 0.05  # Uniform height for all asterisks

            ax.text(x, y, star, ha="center", va="bottom", color="black")

    plt.ylim(score_df["Log ratio"].min() - 0.1, score_df["Log ratio"].max() + 0.8)
    plt.legend(loc="lower center", bbox_to_anchor=(0.5, -0.3), ncol=len(categories))
    # Apply tight layout
    plt.tight_layout()

    if SAVE_FIGURES:
        fig.savefig(
            FIG_DIR / DATASET / "transition_benchmark_velocity.svg", format="svg", transparent=True, bbox_inches="tight"
        )
    plt.show()
../_images/91d60a2363004c56c8993eb9cd044bbbb133d792d541e11719a257e89355897e.png

Comparing RegVelo and scVelo#

Measuring forward CBC#

cluster_key = "cell_type"
rep = "X_pca"

score_df = []
for source, target in tqdm(STATE_TRANSITIONS):
    cbc_rgv = vks["regvelo"].cbc(source=source, target=target, cluster_key=cluster_key, rep=rep)
    cbc_scv = vks["scvelo"].cbc(source=source, target=target, cluster_key=cluster_key, rep=rep)

    score_df.append(
        pd.DataFrame(
            {
                "State transition": [f"{source} - {target}"] * len(cbc_rgv),
                "Log ratio": np.log((cbc_rgv + 1) / (cbc_scv + 1)),
            }
        )
    )
score_df_forward = pd.concat(score_df)

100%|██████████| 6/6 [00:00<00:00,  6.02it/s]

dfs = []

ttest_res = {}
significances = {}

for source, target in STATE_TRANSITIONS:
    obs_mask = score_df_forward["State transition"].isin([f"{source} - {target}"])
    a = score_df_forward.loc[obs_mask, "Log ratio"].values
    b = np.zeros(len(a))

    ttest_res[f"{source} - {target}"] = ttest_ind(a, b, equal_var=False, alternative="greater")
    significances[f"{source} - {target}"] = get_significance(ttest_res[f"{source} - {target}"].pvalue)

significances_forward = significances.copy()
significances_forward

{'HSC - GMP-like': '***',
 'GMP-like - Mon': '***',
 'HSC - MEP-like': 'n.s.',
 'MEP-like - Ery': '***',
 'MEP-like - Meg': 'n.s.',
 'MEP-like - Bas': '**'}

Measuring backward CBC#

score_df = []
for source, target in tqdm(STATE_TRANSITIONS_REVERSE):
    cbc_rgv = -vks["regvelo"].cbc(source=source, target=target, cluster_key=cluster_key, rep=rep)
    cbc_scv = -vks["scvelo"].cbc(source=source, target=target, cluster_key=cluster_key, rep=rep)

    score_df.append(
        pd.DataFrame(
            {
                "State transition": [f"{source} - {target}"] * len(cbc_rgv),
                "Log ratio": np.log((cbc_rgv + 1) / (cbc_scv + 1)),
            }
        )
    )
score_df_backward = pd.concat(score_df)

100%|██████████| 6/6 [00:00<00:00,  6.63it/s]

dfs = []

ttest_res = {}
significances = {}

for source, target in STATE_TRANSITIONS_REVERSE:
    obs_mask = score_df_backward["State transition"].isin([f"{source} - {target}"])
    a = score_df_backward.loc[obs_mask, "Log ratio"].values
    b = np.zeros(len(a))

    ttest_res[f"{source} - {target}"] = ttest_ind(a, b, equal_var=False, alternative="greater")
    significances[f"{source} - {target}"] = get_significance(ttest_res[f"{source} - {target}"].pvalue)

significances_backward = significances.copy()
significances_backward

{'GMP-like - HSC': 'n.s.',
 'Mon - GMP-like': 'n.s.',
 'MEP-like - HSC': 'n.s.',
 'Ery - MEP-like': '**',
 'Meg - MEP-like': '***',
 'Bas - MEP-like': '***'}

score_df_backward["State transition"] = score_df_backward["State transition"].apply(reverse_cluster)

score_df_forward.loc[:, "Direction"] = "Forward"
score_df_backward.loc[:, "Direction"] = "Backward"
score_df = pd.concat([score_df_forward, score_df_backward])

significances_backward = reverse_cluster_dict(significances_backward)
significances_backward

{'HSC - GMP-like': 'n.s.',
 'GMP-like - Mon': 'n.s.',
 'HSC - MEP-like': 'n.s.',
 'MEP-like - Ery': '**',
 'MEP-like - Meg': '***',
 'MEP-like - Bas': '***'}

Plot CBC#

score_forward = []
for i in list(significances_forward.keys()):
    score_forward.append(significances_forward[i])

score_backward = []
for i in list(significances_backward.keys()):
    score_backward.append(significances_backward[i])

sig_m = pd.DataFrame(
    {
        "State transition": list(significances_forward.keys()) + list(significances_backward.keys()),
        "Direction": ["Forward"] * 6 + ["Backward"] * 6,
        "Sign": score_forward + score_backward,
    }
)

with mplscience.style_context():
    sns.set_style(style="whitegrid")
    fig, ax = plt.subplots(1, 1, figsize=(12, 4), sharey=True)
    flierprops = {"marker": "D", "markerfacecolor": "grey", "linestyle": "none", "markersize": 2}
    sns.boxplot(x="State transition", y="Log ratio", hue="Direction", data=score_df, flierprops=flierprops, ax=ax)

    # Calculate the maximum Y value from the data to set a uniform height for significance indicators
    y_max = score_df["Log ratio"].max()

    # Add significance indicators
    cell_types = score_df["State transition"].unique()
    categories = score_df["Direction"].unique()

    for i, cell_type in enumerate(cell_types):
        for j, category in enumerate(categories):
            star = sig_m[(sig_m["State transition"].isin([cell_type])) & (sig_m["Direction"].isin([category]))][
                "Sign"
            ].tolist()[0]

            # Calculate the position of the asterisk
            x = i + (j - 0.5) * 0.4  # Adjust the position of the asterisk
            y = y_max + 0.05  # Uniform height for all asterisks

            ax.text(x, y, star, ha="center", va="bottom", color="black")

    plt.ylim(score_df["Log ratio"].min() - 0.2, score_df["Log ratio"].max() + 0.8)
    plt.legend(loc="lower center", bbox_to_anchor=(0.5, -0.3), ncol=len(categories))
    # Apply tight layout
    plt.tight_layout()

    if SAVE_FIGURES:
        fig.savefig(FIG_DIR / DATASET / "rgv_scv.svg", format="svg", transparent=True, bbox_inches="tight")
    plt.show()
../_images/e4bc42d6b872f81e35fe6886e92fb7e34d0ff617560ecfc19b1f69c4e9909703.png

Comparing RegVelo and veloVI#

Measuring forward CBC#

cluster_key = "cell_type"
rep = "X_pca"

score_df = []
for source, target in tqdm(STATE_TRANSITIONS):
    cbc_rgv = vks["regvelo"].cbc(source=source, target=target, cluster_key=cluster_key, rep=rep)
    cbc_vi = vks["velovi"].cbc(source=source, target=target, cluster_key=cluster_key, rep=rep)

    score_df.append(
        pd.DataFrame(
            {
                "State transition": [f"{source} - {target}"] * len(cbc_rgv),
                "Log ratio": np.log((cbc_rgv + 1) / (cbc_vi + 1)),
            }
        )
    )
score_df_forward = pd.concat(score_df)

100%|██████████| 6/6 [00:01<00:00,  5.98it/s]

dfs = []

ttest_res = {}
significances = {}

for source, target in STATE_TRANSITIONS:
    obs_mask = score_df_forward["State transition"].isin([f"{source} - {target}"])
    a = score_df_forward.loc[obs_mask, "Log ratio"].values
    b = np.zeros(len(a))

    ttest_res[f"{source} - {target}"] = ttest_ind(a, b, equal_var=False, alternative="greater")
    significances[f"{source} - {target}"] = get_significance(ttest_res[f"{source} - {target}"].pvalue)

significances_forward = significances.copy()
significances_forward

{'HSC - GMP-like': 'n.s.',
 'GMP-like - Mon': '***',
 'HSC - MEP-like': 'n.s.',
 'MEP-like - Ery': 'n.s.',
 'MEP-like - Meg': 'n.s.',
 'MEP-like - Bas': 'n.s.'}

Measuring backward CBC#

score_df = []
for source, target in tqdm(STATE_TRANSITIONS_REVERSE):
    cbc_rgv = -vks["regvelo"].cbc(source=source, target=target, cluster_key=cluster_key, rep=rep)
    cbc_vi = -vks["velovi"].cbc(source=source, target=target, cluster_key=cluster_key, rep=rep)

    score_df.append(
        pd.DataFrame(
            {
                "State transition": [f"{source} - {target}"] * len(cbc_rgv),
                "Log ratio": np.log((cbc_rgv + 1) / (cbc_vi + 1)),
            }
        )
    )
score_df_backward = pd.concat(score_df)

100%|██████████| 6/6 [00:00<00:00,  6.59it/s]

dfs = []

ttest_res = {}
significances = {}

for source, target in STATE_TRANSITIONS_REVERSE:
    obs_mask = score_df_backward["State transition"].isin([f"{source} - {target}"])
    a = score_df_backward.loc[obs_mask, "Log ratio"].values
    b = np.zeros(len(a))

    ttest_res[f"{source} - {target}"] = ttest_ind(a, b, equal_var=False, alternative="greater")
    significances[f"{source} - {target}"] = get_significance(ttest_res[f"{source} - {target}"].pvalue)

significances_backward = significances.copy()
significances_backward

{'GMP-like - HSC': '***',
 'Mon - GMP-like': '***',
 'MEP-like - HSC': '***',
 'Ery - MEP-like': '***',
 'Meg - MEP-like': '**',
 'Bas - MEP-like': '***'}

score_df_backward["State transition"] = score_df_backward["State transition"].apply(reverse_cluster)

score_df_forward.loc[:, "Direction"] = "Forward"
score_df_backward.loc[:, "Direction"] = "Backward"
score_df = pd.concat([score_df_forward, score_df_backward])

significances_backward = reverse_cluster_dict(significances_backward)
significances_backward

{'HSC - GMP-like': '***',
 'GMP-like - Mon': '***',
 'HSC - MEP-like': '***',
 'MEP-like - Ery': '***',
 'MEP-like - Meg': '**',
 'MEP-like - Bas': '***'}

Plot CBC#

score_forward = []
for i in list(significances_forward.keys()):
    score_forward.append(significances_forward[i])

score_backward = []
for i in list(significances_backward.keys()):
    score_backward.append(significances_backward[i])

sig_m = pd.DataFrame(
    {
        "State transition": list(significances_forward.keys()) + list(significances_backward.keys()),
        "Direction": ["Forward"] * 6 + ["Backward"] * 6,
        "Sign": score_forward + score_backward,
    }
)

with mplscience.style_context():
    sns.set_style(style="whitegrid")
    fig, ax = plt.subplots(1, 1, figsize=(12, 4), sharey=True)
    flierprops = {"marker": "D", "markerfacecolor": "grey", "linestyle": "none", "markersize": 2}
    sns.boxplot(x="State transition", y="Log ratio", hue="Direction", data=score_df, flierprops=flierprops, ax=ax)

    # Calculate the maximum Y value from the data to set a uniform height for significance indicators
    y_max = score_df["Log ratio"].max()

    # Add significance indicators
    cell_types = score_df["State transition"].unique()
    categories = score_df["Direction"].unique()

    for i, cell_type in enumerate(cell_types):
        for j, category in enumerate(categories):
            star = sig_m[(sig_m["State transition"].isin([cell_type])) & (sig_m["Direction"].isin([category]))][
                "Sign"
            ].tolist()[0]

            # Calculate the position of the asterisk
            x = i + (j - 0.5) * 0.4  # Adjust the position of the asterisk
            y = y_max + 0.05  # Uniform height for all asterisks

            ax.text(x, y, star, ha="center", va="bottom", color="black")

    plt.ylim(score_df["Log ratio"].min() - 0.2, score_df["Log ratio"].max() + 0.8)
    plt.legend(loc="lower center", bbox_to_anchor=(0.5, -0.3), ncol=len(categories))
    # Apply tight layout
    plt.tight_layout()
    plt.show()

    if SAVE_FIGURES:
        fig.savefig(FIG_DIR / DATASET / "rgv_velovi.svg", format="svg", transparent=True, bbox_inches="tight")
    plt.show()
../_images/2a16b29d476d64a6b753365cff7f561458fd47549c80edabe94cd4378e49d89e.png

Terminal state identification#

ks = {}

for method in VELOCITY_METHODS:
    adata = sc.read_h5ad(DATA_DIR / DATASET / "processed" / f"adata_run_{method}.h5ad")
    ## construct graph
    ck = cr.kernels.ConnectivityKernel(adata).compute_transition_matrix()
    vk = cr.kernels.VelocityKernel(adata)
    vk.compute_transition_matrix()
    ks[method] = 0.8 * vk + 0.2 * ck

thresholds = np.linspace(0.1, 1, 21)[:20]
estimators = {}
tsi = {}

for method in VELOCITY_METHODS[1:]:
    estimators[method] = cr.estimators.GPCCA(vks[method])
    tsi[method] = get_tsi_score(adata, thresholds, "cell_type", TERMINAL_STATES, estimators[method])

WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Requested more macrostates `3` than available Schur vectors `2`. Recomputing the decomposition
WARNING: Requested more macrostates `4` than available Schur vectors `3`. Recomputing the decomposition
WARNING: Requested more macrostates `5` than available Schur vectors `4`. Recomputing the decomposition
WARNING: Requested more macrostates `6` than available Schur vectors `5`. Recomputing the decomposition
WARNING: Requested more macrostates `7` than available Schur vectors `6`. Recomputing the decomposition
WARNING: Requested more macrostates `8` than available Schur vectors `7`. Recomputing the decomposition
WARNING: Requested more macrostates `9` than available Schur vectors `8`. Recomputing the decomposition
WARNING: Requested more macrostates `10` than available Schur vectors `9`. Recomputing the decomposition
WARNING: Requested more macrostates `11` than available Schur vectors `10`. Recomputing the decomposition
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Requested more macrostates `3` than available Schur vectors `2`. Recomputing the decomposition
WARNING: Requested more macrostates `4` than available Schur vectors `3`. Recomputing the decomposition
WARNING: Requested more macrostates `5` than available Schur vectors `4`. Recomputing the decomposition
WARNING: Requested more macrostates `6` than available Schur vectors `5`. Recomputing the decomposition
WARNING: Requested more macrostates `7` than available Schur vectors `6`. Recomputing the decomposition
WARNING: Requested more macrostates `8` than available Schur vectors `7`. Recomputing the decomposition
WARNING: Requested more macrostates `9` than available Schur vectors `8`. Recomputing the decomposition
WARNING: Requested more macrostates `10` than available Schur vectors `9`. Recomputing the decomposition
WARNING: Requested more macrostates `11` than available Schur vectors `10`. Recomputing the decomposition
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: The following terminal states have different number of cells than requested (30): {'GMP-like': 29, 'HSC': 29}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: The following terminal states have different number of cells than requested (30): {'GMP-like': 29, 'HSC': 29}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: The following terminal states have different number of cells than requested (30): {'GMP-like': 29, 'HSC': 29}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: The following terminal states have different number of cells than requested (30): {'GMP-like': 29, 'HSC': 29}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: The following terminal states have different number of cells than requested (30): {'GMP-like': 29, 'HSC': 29}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: The following terminal states have different number of cells than requested (30): {'GMP-like': 29, 'HSC': 29}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: The following terminal states have different number of cells than requested (30): {'GMP-like': 29, 'HSC': 29}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: The following terminal states have different number of cells than requested (30): {'GMP-like': 29, 'HSC': 29}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: The following terminal states have different number of cells than requested (30): {'GMP-like': 29, 'HSC': 29}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: The following terminal states have different number of cells than requested (30): {'GMP-like': 29, 'HSC': 29}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: The following terminal states have different number of cells than requested (30): {'GMP-like': 29, 'HSC': 29}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: The following terminal states have different number of cells than requested (30): {'GMP-like': 29, 'HSC': 29}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: The following terminal states have different number of cells than requested (30): {'GMP-like': 29, 'HSC': 29}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: The following terminal states have different number of cells than requested (30): {'GMP-like': 29, 'HSC': 29}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: The following terminal states have different number of cells than requested (30): {'GMP-like': 29, 'HSC': 29}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: The following terminal states have different number of cells than requested (30): {'GMP-like': 29, 'HSC': 29}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: The following terminal states have different number of cells than requested (30): {'GMP-like': 29, 'HSC': 29}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: The following terminal states have different number of cells than requested (30): {'GMP-like': 29, 'HSC': 29}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: The following terminal states have different number of cells than requested (30): {'GMP-like': 29, 'HSC': 29}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: The following terminal states have different number of cells than requested (30): {'GMP-like': 29, 'HSC': 29}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Requested more macrostates `3` than available Schur vectors `2`. Recomputing the decomposition
WARNING: Requested more macrostates `4` than available Schur vectors `3`. Recomputing the decomposition
WARNING: Unable to compute macrostates with `n_states=4` because it will split complex conjugate eigenvalues. Using `n_states=5`
WARNING: Requested more macrostates `6` than available Schur vectors `5`. Recomputing the decomposition
WARNING: Requested more macrostates `7` than available Schur vectors `6`. Recomputing the decomposition
WARNING: Requested more macrostates `8` than available Schur vectors `7`. Recomputing the decomposition
WARNING: Unable to compute macrostates with `n_states=8` because it will split complex conjugate eigenvalues. Using `n_states=9`
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: Requested more macrostates `10` than available Schur vectors `9`. Recomputing the decomposition
WARNING: Requested more macrostates `11` than available Schur vectors `10`. Recomputing the decomposition
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=4` because it will split complex conjugate eigenvalues. Using `n_states=5`
WARNING: Unable to compute macrostates with `n_states=8` because it will split complex conjugate eigenvalues. Using `n_states=9`
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=4` because it will split complex conjugate eigenvalues. Using `n_states=5`
WARNING: Unable to compute macrostates with `n_states=8` because it will split complex conjugate eigenvalues. Using `n_states=9`
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=4` because it will split complex conjugate eigenvalues. Using `n_states=5`
WARNING: Unable to compute macrostates with `n_states=8` because it will split complex conjugate eigenvalues. Using `n_states=9`
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=4` because it will split complex conjugate eigenvalues. Using `n_states=5`
WARNING: Unable to compute macrostates with `n_states=8` because it will split complex conjugate eigenvalues. Using `n_states=9`
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=4` because it will split complex conjugate eigenvalues. Using `n_states=5`
WARNING: Unable to compute macrostates with `n_states=8` because it will split complex conjugate eigenvalues. Using `n_states=9`
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=4` because it will split complex conjugate eigenvalues. Using `n_states=5`
WARNING: Unable to compute macrostates with `n_states=8` because it will split complex conjugate eigenvalues. Using `n_states=9`
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=4` because it will split complex conjugate eigenvalues. Using `n_states=5`
WARNING: Unable to compute macrostates with `n_states=8` because it will split complex conjugate eigenvalues. Using `n_states=9`
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=4` because it will split complex conjugate eigenvalues. Using `n_states=5`
WARNING: Unable to compute macrostates with `n_states=8` because it will split complex conjugate eigenvalues. Using `n_states=9`
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=4` because it will split complex conjugate eigenvalues. Using `n_states=5`
WARNING: Unable to compute macrostates with `n_states=8` because it will split complex conjugate eigenvalues. Using `n_states=9`
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=4` because it will split complex conjugate eigenvalues. Using `n_states=5`
WARNING: Unable to compute macrostates with `n_states=8` because it will split complex conjugate eigenvalues. Using `n_states=9`
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=4` because it will split complex conjugate eigenvalues. Using `n_states=5`
WARNING: Unable to compute macrostates with `n_states=8` because it will split complex conjugate eigenvalues. Using `n_states=9`
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=4` because it will split complex conjugate eigenvalues. Using `n_states=5`
WARNING: Unable to compute macrostates with `n_states=8` because it will split complex conjugate eigenvalues. Using `n_states=9`
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=4` because it will split complex conjugate eigenvalues. Using `n_states=5`
WARNING: Unable to compute macrostates with `n_states=8` because it will split complex conjugate eigenvalues. Using `n_states=9`
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=4` because it will split complex conjugate eigenvalues. Using `n_states=5`
WARNING: Unable to compute macrostates with `n_states=8` because it will split complex conjugate eigenvalues. Using `n_states=9`
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=4` because it will split complex conjugate eigenvalues. Using `n_states=5`
WARNING: Unable to compute macrostates with `n_states=8` because it will split complex conjugate eigenvalues. Using `n_states=9`
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=4` because it will split complex conjugate eigenvalues. Using `n_states=5`
WARNING: Unable to compute macrostates with `n_states=8` because it will split complex conjugate eigenvalues. Using `n_states=9`
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=4` because it will split complex conjugate eigenvalues. Using `n_states=5`
WARNING: Unable to compute macrostates with `n_states=8` because it will split complex conjugate eigenvalues. Using `n_states=9`
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=4` because it will split complex conjugate eigenvalues. Using `n_states=5`
WARNING: Unable to compute macrostates with `n_states=8` because it will split complex conjugate eigenvalues. Using `n_states=9`
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=4` because it will split complex conjugate eigenvalues. Using `n_states=5`
WARNING: Unable to compute macrostates with `n_states=8` because it will split complex conjugate eigenvalues. Using `n_states=9`
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}

df = pd.DataFrame(
    {
        "TSI": tsi["regvelo"] + tsi["velovi"] + tsi["scvelo"],
        "Model": ["RegVelo"] * 20 + ["veloVI"] * 20 + ["scVelo"] * 20,
    }
)
with mplscience.style_context():
    sns.set_style(style="whitegrid")
    fig, ax = plt.subplots(figsize=(3, 4))

    sns.barplot(data=df, x="Model", y="TSI", palette="colorblind", ax=ax)

    ttest_res = ttest_ind(tsi["regvelo"], tsi["velovi"], alternative="greater")
    significance = get_significance(ttest_res.pvalue)
    add_significance(
        ax=ax,
        left=0,
        right=1,
        significance=significance,
        lw=1,
        bracket_level=1.05,
        c="k",
        level=0,
    )

    ttest_res = ttest_ind(tsi["regvelo"], tsi["scvelo"], alternative="greater")
    significance = get_significance(ttest_res.pvalue)
    add_significance(ax=ax, left=0, right=2, significance=significance, lw=1, c="k", level=2, bracket_level=0.9)

    y_min, y_max = ax.get_ylim()
    ax.set_ylim([y_min, y_max + 0.02])

    if SAVE_FIGURES:
        fig.savefig(FIG_DIR / DATASET / "TSI_benchmark_update.svg", format="svg", transparent=True, bbox_inches="tight")
    plt.show()
../_images/81a8bae2588dff6872944a1f4c521a689ba9fbe866ef331d5242390607321721.png

Show the stair plot#

tsi_rgv_curve = plot_tsi(adata, estimators["regvelo"], 0.8, TERMINAL_STATES, "cell_type")
tsi_scv_curve = plot_tsi(adata, estimators["scvelo"], 0.8, TERMINAL_STATES, "cell_type")
tsi_vi_curve = plot_tsi(adata, estimators["velovi"], 0.8, TERMINAL_STATES, "cell_type")

WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=11` because it will split complex conjugate eigenvalues. Using `n_states=12`
WARNING: The following terminal states have different number of cells than requested (30): {'GMP-like': 29, 'HSC': 29}
WARNING: Found only one macrostate, making it the singular terminal state
WARNING: Unable to compute macrostates with `n_states=4` because it will split complex conjugate eigenvalues. Using `n_states=5`
WARNING: Unable to compute macrostates with `n_states=8` because it will split complex conjugate eigenvalues. Using `n_states=9`
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}
WARNING: The following terminal states have different number of cells than requested (30): {'Mon_2': 27}

### plot the recovery figure
df = pd.DataFrame(
    {
        "number_macrostate": range(0, 12),
        "RegVelo": [0] + tsi_rgv_curve,
        "veloVI": [0] + tsi_vi_curve,
        "scVelo": [0] + tsi_scv_curve,
    }
)
df = pd.melt(df, ["number_macrostate"])

# Set figure size
with mplscience.style_context():
    sns.set_style(style="whitegrid")

    rcParams["figure.figsize"] = 4, 3

    # Plot the grid plot
    ax = sns.lineplot(
        x="number_macrostate",
        y="value",
        hue="variable",
        style="variable",
        palette=METHOD_PALETTE_TSI,
        drawstyle="steps-post",
        data=df,
        linewidth=3,
    )

    # Set labels and titles
    ax.set(ylabel="Number of correct predictions")
    plt.xlabel("Number of macrostates", fontsize=14)
    plt.ylabel("Identified terminal states", fontsize=14)

    # Customize tick parameters for better readability
    ax.set_xticks([0, 2, 4, 6, 8, 10])
    ax.set_xticklabels([0, 2, 4, 6, 8, 10])
    plt.xticks(fontsize=14)
    plt.yticks(fontsize=14)
    plt.legend(loc="upper center", bbox_to_anchor=(0.5, -0.18), shadow=True, ncol=4, fontsize=14)

    if SAVE_FIGURES:
        plt.savefig(FIG_DIR / DATASET / "state_identification.svg", format="svg", transparent=True, bbox_inches="tight")
    plt.show()
../_images/fd2be03eec10f86a8fba917f3b548e4e80241ba8345a279e084637367c343333.png