anouncement NIPH

_bibliography/papers.bib

@@ -30,14 +30,27 @@ @article{esparza2023blackbox
   preview       = {RestartingTeaser.png},
   code          = {https://git.rwth-aachen.de/netsci/restarting-markov-chains-experiments}
 }
+@article{grande2023nonisotropic,
+  title         = {Non-isotropic Persistent Homology: Leveraging the Metric Dependency of PH},
+  author        = {Vincent P. Grande and Michael T. Schaub},
+  year          = {2023},
+  eprint        = {},
+  arxiv         = {2310.16437},
+  note          = {Preprint.},
+  archiveprefix = {arXiv},
+  primaryclass  = {math.AT},
+  selected      = {true},
+  preview       = {ChangingPhi.gif},
+  code          = {https://git.rwth-aachen.de/netsci/publication-2023-non-isotropic-persistent-homology}
+}
 @inproceedings{roddenberry2023signal,
   title         = {Signal Processing on Product Spaces},
   author        = {T. Mitchell Roddenberry and Vincent P. Grande and Florian Frantzen and Michael T. Schaub and Santiago Segarra},
   year          = {2023},
   arxiv         = {2303.10495},
   archiveprefix = {arXiv},
   primaryclass  = {eess.SP},
-  selected      = {true},
+  selected      = {false},
   preview       = {ProductSpacesTeaser.png},
   booktitle     = {ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
   title         = {Signal Processing On Product Spaces},

_includes/news.html

@@ -1,30 +1,29 @@
-
-          <div class="news">
-            {% if site.news != blank -%} 
-            {%- assign news_size = site.news | size -%}
-            <div class="table-responsive" {% if site.news_scrollable and news_size > 3 %}style="max-height: 10vw"{% endif %}>
-              <table class="table table-sm table-borderless">
-              {%- assign news = site.news | reverse -%}
-              {% if site.news_limit %}
-              {% assign news_limit = site.news_limit %}
-              {% else %}
-              {% assign news_limit = news_size %}
-              {% endif %}
-              {% for item in news limit: news_limit %} 
-                <tr>
-                  <th scope="row">{{ item.date | date: "%b %-d, %Y" }}</th>
-                  <td>
-                    {% if item.inline -%} 
-                      {{ item.content | remove: '<p>' | remove: '</p>' | emojify }}
-                    {%- else -%} 
-                      <a class="news-title" href="{{ item.url | relative_url }}">{{ item.title }}</a>
-                    {%- endif %} 
-                  </td>
-                </tr>
-              {%- endfor %} 
-              </table>
-            </div>
-          {%- else -%} 
-            <p>No news so far...</p>
-          {%- endif %} 
-          </div>
+<div class="news">
+  {% if site.news != blank -%}
+  {%- assign news_size = site.news | size -%}
+  <div class="table-responsive" {% if site.news_scrollable and news_size> 3 %}style="max-height: 20vw"{% endif %}>
+    <table class="table table-sm table-borderless">
+      {%- assign news = site.news | reverse -%}
+      {% if site.news_limit %}
+      {% assign news_limit = site.news_limit %}
+      {% else %}
+      {% assign news_limit = news_size %}
+      {% endif %}
+      {% for item in news limit: news_limit %}
+      <tr>
+        <th scope="row">{{ item.date | date: "%b %-d, %Y" }}</th>
+        <td>
+          {% if item.inline -%}
+          {{ item.content | remove: '<p>' | remove: '</p>' | emojify }}
+          {%- else -%}
+          <a class="news-title" href="{{ item.url | relative_url }}">{{ item.title }}</a>
+          {%- endif %}
+        </td>
+      </tr>
+      {%- endfor %}
+    </table>
+  </div>
+  {%- else -%}
+  <p>No news so far...</p>
+  {%- endif %}
+</div>

_news/announcementArxivNIPH.md

@@ -0,0 +1,7 @@
+---
+layout: post
+date: 2023-10-26 08:00:00+0100
+inline: true
+---
+
+Is there one 'correct' metric for Persistent Homology, or should we rather analyse and compare multiple metrics on point clouds at once? We change the metric, track the effects on the persistence diagrams and extract new information on orientation and orientational variance and strength of point clouds! A preprint of my joint article with <a href='https://michaelschaub.github.io'>Michael Schaub</a> on <a href='https://arxiv.org/abs/2310.16437'>Non-isotropic Homology</a> is now available on arXiv. :blush:

_pages/NIPH.md

@@ -1,15 +1,14 @@
 ---
 layout: page
 permalink: /NIPH/
-title: NIPH
-description: Non-isotropic Persistent Homology.
+title: Non-isotropic Persistent Homology.
+description: Leveraging the metric dependency of PH
 nav: false
 nav_order: 
 ---
-This is an ongoing project. Here is a link to the <a href='../../assets/pdf/NIPHmainTAGML.pdf'>extended abstract</a>. I would be very happy about any comments, ideas, and feedback!
+Click here for the <a href='https://arxiv.org/abs/2310.16437'>arxiv version</a>! I would be very happy about any comments, ideas, and feedback!
 ## Abstract
-Persistent Homology is a widely used topological data analysis  tool that creates a concise description of the topological properties of a point cloud based on a specified filtration. Most filtrations used for persistent homology depend (implicitly) on a chosen metric, which is typically agnostically chosen as the standard euclidean metric on $$\mathbb{R}^n$$. Recent work has tried to uncover the “true” metric on the point cloud using distance-to-measure functions, in order to obtain more meaningful per- sistent homology results. Here we propose an alternative look at this problem: we posit that information on the point cloud is lost when restricting persistent homology to a single (correct) distance function. Instead we show how by varying the distance function on the underlying space and analysing the corresponding shifts in the persistence diagrams, we can extract additional topological and geometrical information. Finally, we numerically show that non-isotropic persistent homology can extract information on orientation, orientational variance, and scaling of randomly generated point clouds with good accuracy.
-
+Persistent Homology is a widely used topological data analysis tool that creates a concise description of the topological properties of a point cloud based on a specified filtration. Most filtrations used for persistent homology depend (implicitly) on a chosen metric, which is typically agnostically chosen as the standard Euclidean metric on $$\mathbb{R}^n$$. Recent work has tried to uncover the 'true' metric on the point cloud using distance-to-measure functions, in order to obtain more meaningful persistent homology results. Here we propose an alternative look at this problem: we posit that information on the point cloud is lost when restricting persistent homology to a single (correct) distance function. Instead, we show how by varying the distance function on the underlying space and analysing the corresponding shifts in the persistence diagrams, we can extract additional topological and geometrical information. Finally, we numerically show that non-isotropic persistent homology can extract information on orientation, orientational variance, and scaling of randomly generated point clouds with good accuracy and conduct some experiments on real-world data.
 <div class="row mt-3">
     <div class="col-sm mt-3 mt-md-0">
         {% include figure.html path="assets/img/ChangingPhi.gif" class="img-fluid rounded z-depth-1" zoomable=true %}

_pages/code.md

@@ -16,6 +16,13 @@ TPCC was accepted for publication at the International Conference on Machine Lea
 <a href='https://git.rwth-aachen.de/netsci/publication-2023-topological-point-cloud-clustering'>Code</a>
 <a href='https://arxiv.org/abs/2303.16716'>Paper</a>
 
+### Non-Isotropic Persistent Homology (NIPH)
+
+NIPH tracks changes in the PH diagram induced by changing the underlying metric of the point cloud to extract information on local orientations of point clouds.
+
+<a href='https://git.rwth-aachen.de/netsci/publication-2023-non-isotropic-persistent-homology'>Code</a>
+<a href='https://arxiv.org/abs/2310.16437'>Paper</a>
+
 ### Black-box Testing Liveness Properties of Partially Observable Stochastic Systems
 
 We study black-box testing for stochastic systems and arbitrary ω-regular specifications, explicitly including liveness properties. We are given a finite-state probabilistic system that we can only execute from the initial state. We have no information on the number of reachable states, or on the probabilities; further, we can only partially observe the states. The only action we can take is to restart the system.
@@ -25,3 +32,4 @@ Languages and Programming, 2023.
 
 <a href='https://git.rwth-aachen.de/netsci/restarting-markov-chains-experiments'>Code</a>
 <a href='https://arxiv.org/pdf/2303.03292.pdf'>Paper</a>
+