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diff --git a/docs/_build/doctrees/environment.pickle b/docs/_build/doctrees/environment.pickle
diff --git a/docs/_build/doctrees/index.doctree b/docs/_build/doctrees/index.doctree
diff --git a/docs/_build/doctrees/nbsphinx/stSME_comparison.ipynb b/docs/_build/doctrees/nbsphinx/stSME_comparison.ipynb
@@ -4,7 +4,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# This tutorial compares clustering performance of three scenarios: \n",
+    "# StSME comparison\n",
+    "\n",
+    "## This tutorial compares clustering performance of three scenarios: \n",
     " (1) normal (without stSME) \n",
     " \n",
     " (2) stSME applied on dimension reduced spaces (PCA) as normalization and \n",

diff --git a/docs/_build/doctrees/stSME_comparison.doctree b/docs/_build/doctrees/stSME_comparison.doctree
diff --git a/docs/_build/html/Pseudo-space-time-tutorial.html b/docs/_build/html/Pseudo-space-time-tutorial.html
@@ -41,7 +41,7 @@
     <link rel="index" title="Index" href="genindex.html" />
     <link rel="search" title="Search" href="search.html" />
     <link rel="next" title="Spatial cell-cell interaction tutorial" href="cci.html" />
-    <link rel="prev" title="This tutorial compares clustering performance of three scenarios:" href="stSME_comparison.html" /> 
+    <link rel="prev" title="StSME comparison" href="stSME_comparison.html" /> 
 </head>
 
 <body class="wy-body-for-nav">
@@ -100,7 +100,7 @@
 <p class="caption"><span class="caption-text">Tutorials:</span></p>
 <ul class="current">
 <li class="toctree-l1"><a class="reference internal" href="stSME_clustering.html">stSME clustering tutorial</a></li>
-<li class="toctree-l1"><a class="reference internal" href="stSME_comparison.html">This tutorial compares clustering performance of three scenarios:</a></li>
+<li class="toctree-l1"><a class="reference internal" href="stSME_comparison.html">StSME comparison</a></li>
 <li class="toctree-l1 current"><a class="current reference internal" href="#">Spatial trajectory inference analysis tutorial</a><ul>
 <li class="toctree-l2"><a class="reference internal" href="#1.-Preparation">1. Preparation</a></li>
 <li class="toctree-l2"><a class="reference internal" href="#2.-Running-the-global-trajectory-inference">2. Running the global trajectory inference</a></li>
@@ -895,7 +895,7 @@ <h2>5. Detect transition markers of clades and branches<a class="headerlink" hre
         <a href="cci.html" class="btn btn-neutral float-right" title="Spatial cell-cell interaction tutorial" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right"></span></a>
 
 
-        <a href="stSME_comparison.html" class="btn btn-neutral float-left" title="This tutorial compares clustering performance of three scenarios:" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left"></span> Previous</a>
+        <a href="stSME_comparison.html" class="btn btn-neutral float-left" title="StSME comparison" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left"></span> Previous</a>
 
     </div>
 

diff --git a/docs/_build/html/Read_MERFISH.html b/docs/_build/html/Read_MERFISH.html
@@ -100,7 +100,7 @@
 <p class="caption"><span class="caption-text">Tutorials:</span></p>
 <ul class="current">
 <li class="toctree-l1"><a class="reference internal" href="stSME_clustering.html">stSME clustering tutorial</a></li>
-<li class="toctree-l1"><a class="reference internal" href="stSME_comparison.html">This tutorial compares clustering performance of three scenarios:</a></li>
+<li class="toctree-l1"><a class="reference internal" href="stSME_comparison.html">StSME comparison</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Pseudo-space-time-tutorial.html">Spatial trajectory inference analysis tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="cci.html">Spatial cell-cell interaction tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="cci_within-spot_single_lr.html">Scenario 1: Cell-cell interaction analysis (single L-R pair, within-spot)</a></li>

diff --git a/docs/_build/html/Read_seqfish.html b/docs/_build/html/Read_seqfish.html
@@ -100,7 +100,7 @@
 <p class="caption"><span class="caption-text">Tutorials:</span></p>
 <ul class="current">
 <li class="toctree-l1"><a class="reference internal" href="stSME_clustering.html">stSME clustering tutorial</a></li>
-<li class="toctree-l1"><a class="reference internal" href="stSME_comparison.html">This tutorial compares clustering performance of three scenarios:</a></li>
+<li class="toctree-l1"><a class="reference internal" href="stSME_comparison.html">StSME comparison</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Pseudo-space-time-tutorial.html">Spatial trajectory inference analysis tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="cci.html">Spatial cell-cell interaction tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="cci_within-spot_single_lr.html">Scenario 1: Cell-cell interaction analysis (single L-R pair, within-spot)</a></li>

diff --git a/docs/_build/html/Read_slideseq.html b/docs/_build/html/Read_slideseq.html
@@ -100,7 +100,7 @@
 <p class="caption"><span class="caption-text">Tutorials:</span></p>
 <ul class="current">
 <li class="toctree-l1"><a class="reference internal" href="stSME_clustering.html">stSME clustering tutorial</a></li>
-<li class="toctree-l1"><a class="reference internal" href="stSME_comparison.html">This tutorial compares clustering performance of three scenarios:</a></li>
+<li class="toctree-l1"><a class="reference internal" href="stSME_comparison.html">StSME comparison</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Pseudo-space-time-tutorial.html">Spatial trajectory inference analysis tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="cci.html">Spatial cell-cell interaction tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="cci_within-spot_single_lr.html">Scenario 1: Cell-cell interaction analysis (single L-R pair, within-spot)</a></li>

diff --git a/docs/_build/html/ST_deconvolution_visualization.html b/docs/_build/html/ST_deconvolution_visualization.html
@@ -99,7 +99,7 @@
 <p class="caption"><span class="caption-text">Tutorials:</span></p>
 <ul class="current">
 <li class="toctree-l1"><a class="reference internal" href="stSME_clustering.html">stSME clustering tutorial</a></li>
-<li class="toctree-l1"><a class="reference internal" href="stSME_comparison.html">This tutorial compares clustering performance of three scenarios:</a></li>
+<li class="toctree-l1"><a class="reference internal" href="stSME_comparison.html">StSME comparison</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Pseudo-space-time-tutorial.html">Spatial trajectory inference analysis tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="cci.html">Spatial cell-cell interaction tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="cci_within-spot_single_lr.html">Scenario 1: Cell-cell interaction analysis (single L-R pair, within-spot)</a></li>

diff --git a/docs/_build/html/Working-with-Old-Spatial-Transcriptomics-data.html b/docs/_build/html/Working-with-Old-Spatial-Transcriptomics-data.html
@@ -100,7 +100,7 @@
 <p class="caption"><span class="caption-text">Tutorials:</span></p>
 <ul class="current">
 <li class="toctree-l1"><a class="reference internal" href="stSME_clustering.html">stSME clustering tutorial</a></li>
-<li class="toctree-l1"><a class="reference internal" href="stSME_comparison.html">This tutorial compares clustering performance of three scenarios:</a></li>
+<li class="toctree-l1"><a class="reference internal" href="stSME_comparison.html">StSME comparison</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Pseudo-space-time-tutorial.html">Spatial trajectory inference analysis tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="cci.html">Spatial cell-cell interaction tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="cci_within-spot_single_lr.html">Scenario 1: Cell-cell interaction analysis (single L-R pair, within-spot)</a></li>

diff --git a/docs/_build/html/_modules/index.html b/docs/_build/html/_modules/index.html
@@ -98,7 +98,7 @@
 <p class="caption"><span class="caption-text">Tutorials:</span></p>
 <ul>
 <li class="toctree-l1"><a class="reference internal" href="../stSME_clustering.html">stSME clustering tutorial</a></li>
-<li class="toctree-l1"><a class="reference internal" href="../stSME_comparison.html">This tutorial compares clustering performance of three scenarios:</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../stSME_comparison.html">StSME comparison</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../Pseudo-space-time-tutorial.html">Spatial trajectory inference analysis tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../cci.html">Spatial cell-cell interaction tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../cci_within-spot_single_lr.html">Scenario 1: Cell-cell interaction analysis (single L-R pair, within-spot)</a></li>

diff --git a/docs/_build/html/_modules/stlearn/adds/add_image.html b/docs/_build/html/_modules/stlearn/adds/add_image.html
@@ -98,7 +98,7 @@
 <p class="caption"><span class="caption-text">Tutorials:</span></p>
 <ul>
 <li class="toctree-l1"><a class="reference internal" href="../../../stSME_clustering.html">stSME clustering tutorial</a></li>
-<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">This tutorial compares clustering performance of three scenarios:</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">StSME comparison</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../Pseudo-space-time-tutorial.html">Spatial trajectory inference analysis tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci.html">Spatial cell-cell interaction tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci_within-spot_single_lr.html">Scenario 1: Cell-cell interaction analysis (single L-R pair, within-spot)</a></li>

diff --git a/docs/_build/html/_modules/stlearn/adds/add_lr.html b/docs/_build/html/_modules/stlearn/adds/add_lr.html
@@ -98,7 +98,7 @@
 <p class="caption"><span class="caption-text">Tutorials:</span></p>
 <ul>
 <li class="toctree-l1"><a class="reference internal" href="../../../stSME_clustering.html">stSME clustering tutorial</a></li>
-<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">This tutorial compares clustering performance of three scenarios:</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">StSME comparison</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../Pseudo-space-time-tutorial.html">Spatial trajectory inference analysis tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci.html">Spatial cell-cell interaction tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci_within-spot_single_lr.html">Scenario 1: Cell-cell interaction analysis (single L-R pair, within-spot)</a></li>

diff --git a/docs/_build/html/_modules/stlearn/adds/add_positions.html b/docs/_build/html/_modules/stlearn/adds/add_positions.html
@@ -98,7 +98,7 @@
 <p class="caption"><span class="caption-text">Tutorials:</span></p>
 <ul>
 <li class="toctree-l1"><a class="reference internal" href="../../../stSME_clustering.html">stSME clustering tutorial</a></li>
-<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">This tutorial compares clustering performance of three scenarios:</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">StSME comparison</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../Pseudo-space-time-tutorial.html">Spatial trajectory inference analysis tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci.html">Spatial cell-cell interaction tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci_within-spot_single_lr.html">Scenario 1: Cell-cell interaction analysis (single L-R pair, within-spot)</a></li>

diff --git a/docs/_build/html/_modules/stlearn/adds/annotation.html b/docs/_build/html/_modules/stlearn/adds/annotation.html
@@ -98,7 +98,7 @@
 <p class="caption"><span class="caption-text">Tutorials:</span></p>
 <ul>
 <li class="toctree-l1"><a class="reference internal" href="../../../stSME_clustering.html">stSME clustering tutorial</a></li>
-<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">This tutorial compares clustering performance of three scenarios:</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">StSME comparison</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../Pseudo-space-time-tutorial.html">Spatial trajectory inference analysis tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci.html">Spatial cell-cell interaction tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci_within-spot_single_lr.html">Scenario 1: Cell-cell interaction analysis (single L-R pair, within-spot)</a></li>

diff --git a/docs/_build/html/_modules/stlearn/adds/parsing.html b/docs/_build/html/_modules/stlearn/adds/parsing.html
@@ -98,7 +98,7 @@
 <p class="caption"><span class="caption-text">Tutorials:</span></p>
 <ul>
 <li class="toctree-l1"><a class="reference internal" href="../../../stSME_clustering.html">stSME clustering tutorial</a></li>
-<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">This tutorial compares clustering performance of three scenarios:</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">StSME comparison</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../Pseudo-space-time-tutorial.html">Spatial trajectory inference analysis tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci.html">Spatial cell-cell interaction tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci_within-spot_single_lr.html">Scenario 1: Cell-cell interaction analysis (single L-R pair, within-spot)</a></li>

diff --git a/docs/_build/html/_modules/stlearn/embedding/diffmap.html b/docs/_build/html/_modules/stlearn/embedding/diffmap.html
@@ -98,7 +98,7 @@
 <p class="caption"><span class="caption-text">Tutorials:</span></p>
 <ul>
 <li class="toctree-l1"><a class="reference internal" href="../../../stSME_clustering.html">stSME clustering tutorial</a></li>
-<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">This tutorial compares clustering performance of three scenarios:</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">StSME comparison</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../Pseudo-space-time-tutorial.html">Spatial trajectory inference analysis tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci.html">Spatial cell-cell interaction tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci_within-spot_single_lr.html">Scenario 1: Cell-cell interaction analysis (single L-R pair, within-spot)</a></li>

diff --git a/docs/_build/html/_modules/stlearn/embedding/fa.html b/docs/_build/html/_modules/stlearn/embedding/fa.html
@@ -98,7 +98,7 @@
 <p class="caption"><span class="caption-text">Tutorials:</span></p>
 <ul>
 <li class="toctree-l1"><a class="reference internal" href="../../../stSME_clustering.html">stSME clustering tutorial</a></li>
-<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">This tutorial compares clustering performance of three scenarios:</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">StSME comparison</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../Pseudo-space-time-tutorial.html">Spatial trajectory inference analysis tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci.html">Spatial cell-cell interaction tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci_within-spot_single_lr.html">Scenario 1: Cell-cell interaction analysis (single L-R pair, within-spot)</a></li>

diff --git a/docs/_build/html/_modules/stlearn/embedding/ica.html b/docs/_build/html/_modules/stlearn/embedding/ica.html
@@ -98,7 +98,7 @@
 <p class="caption"><span class="caption-text">Tutorials:</span></p>
 <ul>
 <li class="toctree-l1"><a class="reference internal" href="../../../stSME_clustering.html">stSME clustering tutorial</a></li>
-<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">This tutorial compares clustering performance of three scenarios:</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">StSME comparison</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../Pseudo-space-time-tutorial.html">Spatial trajectory inference analysis tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci.html">Spatial cell-cell interaction tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci_within-spot_single_lr.html">Scenario 1: Cell-cell interaction analysis (single L-R pair, within-spot)</a></li>

diff --git a/docs/_build/html/_modules/stlearn/embedding/pca.html b/docs/_build/html/_modules/stlearn/embedding/pca.html
@@ -98,7 +98,7 @@
 <p class="caption"><span class="caption-text">Tutorials:</span></p>
 <ul>
 <li class="toctree-l1"><a class="reference internal" href="../../../stSME_clustering.html">stSME clustering tutorial</a></li>
-<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">This tutorial compares clustering performance of three scenarios:</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">StSME comparison</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../Pseudo-space-time-tutorial.html">Spatial trajectory inference analysis tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci.html">Spatial cell-cell interaction tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci_within-spot_single_lr.html">Scenario 1: Cell-cell interaction analysis (single L-R pair, within-spot)</a></li>

diff --git a/docs/_build/html/_modules/stlearn/embedding/umap.html b/docs/_build/html/_modules/stlearn/embedding/umap.html
@@ -98,7 +98,7 @@
 <p class="caption"><span class="caption-text">Tutorials:</span></p>
 <ul>
 <li class="toctree-l1"><a class="reference internal" href="../../../stSME_clustering.html">stSME clustering tutorial</a></li>
-<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">This tutorial compares clustering performance of three scenarios:</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">StSME comparison</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../Pseudo-space-time-tutorial.html">Spatial trajectory inference analysis tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci.html">Spatial cell-cell interaction tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci_within-spot_single_lr.html">Scenario 1: Cell-cell interaction analysis (single L-R pair, within-spot)</a></li>

diff --git a/docs/_build/html/_modules/stlearn/image_preprocessing/feature_extractor.html b/docs/_build/html/_modules/stlearn/image_preprocessing/feature_extractor.html
@@ -98,7 +98,7 @@
 <p class="caption"><span class="caption-text">Tutorials:</span></p>
 <ul>
 <li class="toctree-l1"><a class="reference internal" href="../../../stSME_clustering.html">stSME clustering tutorial</a></li>
-<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">This tutorial compares clustering performance of three scenarios:</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">StSME comparison</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../Pseudo-space-time-tutorial.html">Spatial trajectory inference analysis tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci.html">Spatial cell-cell interaction tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci_within-spot_single_lr.html">Scenario 1: Cell-cell interaction analysis (single L-R pair, within-spot)</a></li>

diff --git a/docs/_build/html/_modules/stlearn/image_preprocessing/image_tiling.html b/docs/_build/html/_modules/stlearn/image_preprocessing/image_tiling.html
@@ -98,7 +98,7 @@
 <p class="caption"><span class="caption-text">Tutorials:</span></p>
 <ul>
 <li class="toctree-l1"><a class="reference internal" href="../../../stSME_clustering.html">stSME clustering tutorial</a></li>
-<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">This tutorial compares clustering performance of three scenarios:</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../../stSME_comparison.html">StSME comparison</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../Pseudo-space-time-tutorial.html">Spatial trajectory inference analysis tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci.html">Spatial cell-cell interaction tutorial</a></li>
 <li class="toctree-l1"><a class="reference internal" href="../../../cci_within-spot_single_lr.html">Scenario 1: Cell-cell interaction analysis (single L-R pair, within-spot)</a></li>