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README.md

@@ -1,45 +1,62 @@
 ![Logo](https://github.com/lucasimi/tda-mapper-python/raw/main/docs/source/logos/tda-mapper-logo-horizontal.png)
 
-[![Source Code](https://img.shields.io/badge/lucasimi-tda--mapper--python-blue?logo=github&logoColor=silver)](https://github.com/lucasimi/tda-mapper-python)
 [![PyPI version](https://img.shields.io/pypi/v/tda-mapper?logo=python&logoColor=silver)](https://pypi.python.org/pypi/tda-mapper)
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 [![DOI](https://img.shields.io/badge/DOI-10.5281/zenodo.10642381-blue?logo=doi&logoColor=silver)](https://doi.org/10.5281/zenodo.10642381)
-[![Streamlit App](https://img.shields.io/badge/Streamlit-App-blue?logo=streamlit&logoColor=silver)](https://tda-mapper-app.streamlit.app/)
 
 # tda-mapper
 
-**tda-mapper** is a Python library based on the Mapper algorithm, a key tool in
-Topological Data Analysis (TDA). Designed for efficient computations and backed
-by advanced spatial search techniques, it scales seamlessly to high dimensional
-data, making it suitable for applications in machine learning, data mining, and
-exploratory data analysis.
+**tda-mapper** is a Python library built around the Mapper algorithm, a core
+technique in Topological Data Analysis (TDA) for extracting topological
+structure from complex data. Designed for computational efficiency and
+scalability, it leverages optimized spatial search methods to support
+high-dimensional datasets. The library is well-suited for integration into
+machine learning pipelines, unsupervised learning tasks, and exploratory data
+analysis.
 
 Further details in the
 [documentation](https://tda-mapper.readthedocs.io/en/main/)
 and in the
 [paper](https://openreview.net/pdf?id=lTX4bYREAZ).
 
-## Main Features
+### Core Features
+
+- **Efficient construction**
+
+    Leverages optimized spatial search techniques and parallelization to
+    accelerate the construction of Mapper graphs, supporting the analysis of
+    high-dimensional datasets.
+
+- **Scikit-learn integration**
 
-- **Fast Mapper graph construction**: Accelerates computations with efficient spatial search, enabling analysis of large, high-dimensional datasets.
+    Provides custom estimators that are fully compatible with scikit-learn's
+    API, enabling seamless integration into scikit-learn pipelines for tasks
+    such as dimensionality reduction, clustering, and feature extraction.
 
-- **Scikit-learn compatibility**: Easily integrate Mapper as a part of your machine learning workflows.
+- **Flexible visualization**
 
-- **Flexible visualization options**: Visualize Mapper graphs with multiple supported backends, tailored to your needs.
+    Multiple visualization backends supported (e.g., Plotly, Matplotlib) for
+    generating high-quality Mapper graph representations with adjustable 
+    layouts and styling.
 
-- **Interactive exploration**: Explore data interactively through a user-friendly app.
+- **Interactive app**
+
+    Provides an interactive web-based interface (via Streamlit) for dynamic
+    exploration of Mapper graph structures, offering real-time adjustments to
+    parameters and visualizations.
 
 ## Background
 
-The Mapper algorithm transforms complex datasets into graph representations
-that highlight clusters, transitions, and topological features. These insights
-reveal hidden patterns in data, applicable across fields like social sciences,
-biology, and machine learning. For an in-depth coverage of Mapper, including
-its mathematical foundations and applications, read the 
+The Mapper algorithm extracts topological features from complex datasets,
+representing them as graphs that highlight clusters, transitions, and key
+structural patterns. These insights reveal hidden data relationships and are
+applicable across diverse fields, including social sciences, biology, and
+machine learning. For an in-depth overview of Mapper, including its
+mathematical foundations and practical applications, read 
 [the original paper](https://research.math.osu.edu/tgda/mapperPBG.pdf).
 
 | Step 1 | Step 2 | Step 3 | Step 4 |
@@ -52,13 +69,11 @@ its mathematical foundations and applications, read the
 If you use **tda-mapper** in your work, please consider citing both the
 [library](https://doi.org/10.5281/zenodo.10642381), archived in a permanent
 Zenodo record, and the [paper](https://openreview.net/pdf?id=lTX4bYREAZ),
-which provides a broader methodological overview.
-We recommend citing the specific version of the library used in your research,
-as well as the paper.
-For citation examples, refer to the
+which provides a broader methodological overview. We recommend citing the
+specific version of the library used in your research, along with the paper.
+For citation examples, please refer to the
 [documentation](https://tda-mapper.readthedocs.io/en/main/#citations).
 
-
 ## Quick Start
 
 ### Installation
@@ -71,12 +86,11 @@ pip install tda-mapper
 
 ### How to Use
 
-Here's a minimal example using the **circles dataset** from `scikit-learn` to demonstrate how to use **tda-mapper**.
-We start by generating the data and visualizing it.
-The dataset consists of two concentric circles.
-The goal is to compute a Mapper graph that summarizes this structure while preserving topological features.
-We proceed as follows:
-
+Here's a minimal example using the **circles dataset** from `scikit-learn` to
+demonstrate how to use **tda-mapper**. This example demonstrates how to apply
+the Mapper algorithm on a synthetic dataset (concentric circles). The goal is
+to extract a topological graph representation using `PCA` as a lens and
+`DBSCAN` for clustering. We proceed as follows:
 
 ```python
 import matplotlib.pyplot as plt
@@ -114,7 +128,10 @@ fig.show(config={"scrollZoom": True})
 | ---------------- | ------------ |
 | ![Original Dataset](https://github.com/lucasimi/tda-mapper-python/raw/main/resources/circles_dataset_v2.png) | ![Mapper Graph](https://github.com/lucasimi/tda-mapper-python/raw/main/resources/circles_mean_v2.png) |
 
-Left: the original dataset consisting of two concentric circles with noise, colored by class label. Right: the resulting Mapper graph, built from the PCA projection and clustered using DBSCAN. The two concentric circles are well identified by the connected components in the Mapper graph.
+Left: the original dataset consisting of two concentric circles with noise,
+colored by class label. Right: the resulting Mapper graph, built from the PCA
+projection and clustered using DBSCAN. The two concentric circles are well
+identified by the connected components in the Mapper graph.
 
 More examples can be found in the
 [documentation](https://tda-mapper.readthedocs.io/en/main/examples.html).
@@ -124,10 +141,18 @@ More examples can be found in the
 Use our Streamlit app to visualize and explore your data without writing code.
 You can run a live demo directly on
 [Streamlit Cloud](https://tda-mapper-app.streamlit.app/),
-or locally on your machine using the following:
+or locally on your machine. The first time you run the app locally, you may
+need to install the required dependencies from the `requirements.txt` file by
+running 
 
-```
+```bash
 pip install -r app/requirements.txt
+```
+
+then run the app locally with 
+
+```bash
 streamlit run app/streamlit_app.py
 ```
-![tda-mapper-app](https://github.com/lucasimi/tda-mapper-python/raw/main/resources/tda-mapper-app.png)
+
+![tda-mapper-app](https://github.com/lucasimi/tda-mapper-python/raw/main/resources/tda-mapper-app.png)

docs/source/index.rst

@@ -25,47 +25,56 @@
    https://github.com/lucasimi/tda-mapper-python/raw/main/docs/source/logos/tda-mapper-logo-horizontal.png
    :alt: Logo
 
-|Source Code| |PyPI version| |downloads| |test| |publish| |docs| |codecov| |DOI|
-|Streamlit App|
+|PyPI version| |downloads| |codecov| |test| |publish| |docs|  |DOI|
+
+|Source Code|
 
 tda-mapper
 ==========
 
-**tda-mapper** is a Python library based on the Mapper algorithm, a key tool in
-Topological Data Analysis (TDA). Designed for efficient computations and backed
-by advanced spatial search techniques, it scales seamlessly to high dimensional
-data, making it suitable for applications in machine learning, data mining, and
-exploratory data analysis.
+**tda-mapper** is a Python library built around the Mapper algorithm, a core
+technique in Topological Data Analysis (TDA) for extracting topological 
+structure from complex data. Designed for computational efficiency and
+scalability, it leverages optimized spatial search methods to support 
+high-dimensional datasets. The library is well-suited for integration into
+machine learning pipelines, unsupervised learning tasks, and exploratory data
+analysis.
 
 Further details in the
 `documentation <https://tda-mapper.readthedocs.io/en/main/>`__
 and in the
 `paper <https://openreview.net/pdf?id=lTX4bYREAZ>`__.
 
-Main features
+Core features
 -------------
 
-- **Fast Mapper graph construction**: Accelerates computations with efficient
-  spatial search, enabling analysis of large, high-dimensional datasets.
+- **Efficient construction**
+
+    Leverages optimized spatial search techniques and parallelization to accelerate the construction of Mapper graphs, supporting the analysis of high-dimensional datasets.
+
+- **Scikit-learn integration**
+
+    Provides custom estimators that are fully compatible with scikit-learn's API, enabling seamless integration into scikit-learn pipelines for tasks such as dimensionality reduction, clustering, and feature extraction.
+
+- **Flexible visualization**
+
+    Multiple visualization backends supported (e.g., Plotly, Matplotlib) for generating high-quality Mapper graph representations with adjustable layouts and styling.
 
-- **Scikit-learn compatibility**: Easily integrate Mapper as a part of your
-  machine learning workflows.
+- **Interactive app**
 
-- **Flexible visualization options**: Visualize Mapper graphs with multiple
-  supported backends, tailored to your needs.
+    Provides an interactive web-based interface (via Streamlit) for dynamic exploration of Mapper graph structures, offering real-time adjustments to parameters and visualizations.
 
-- **Interactive exploration**: Explore data interactively through a
-  user-friendly app.
 
 Background
 ----------
 
-The Mapper algorithm transforms complex datasets into graph representations
-that highlight clusters, transitions, and topological features. These insights
-reveal hidden patterns in data, applicable across fields like social sciences,
-biology, and machine learning. For an in-depth coverage of Mapper, including
-its mathematical foundations and applications, read the 
-`original paper <https://research.math.osu.edu/tgda/mapperPBG.pdf>`__.
+The Mapper algorithm extracts topological features from complex datasets,
+representing them as graphs that highlight clusters, transitions, and key
+structural patterns. These insights reveal hidden data relationships and are
+applicable across diverse fields, including social sciences, biology, and
+machine learning. For an in-depth overview of Mapper, including its
+mathematical foundations and practical applications, read 
+`the original paper <https://research.math.osu.edu/tgda/mapperPBG.pdf>`__.
 
 +-----------------+-----------------+-----------------+-----------------+
 | Step 1          | Step 2          | Step 3          | Step 4          |
@@ -78,12 +87,12 @@ its mathematical foundations and applications, read the
 Citations
 ---------
 
-If you use **tda-mapper** in your work, please consider citing both the 
+If you use **tda-mapper** in your work, please consider citing both the
 `library <https://doi.org/10.5281/zenodo.10642381>`__,
-archived in a permanent Zenodo record, and the 
+archived in a permanent Zenodo record, and the
 `paper <https://openreview.net/pdf?id=lTX4bYREAZ>`__,
-which provides a broader methodological overview.
-We recommend citing the specific version of the library used in your research, as well as the paper.
+which provides a broader methodological overview. We recommend citing the
+specific version of the library used in your research, along with the paper.
 
 - **tda-mapper**: For example to cite version 0.8.0 you can use:
 

docs/source/quickstart.rst

@@ -37,8 +37,11 @@ Development
 How To Use
 ----------
 
-Here's a minimal example using the **circles dataset** from
-``scikit-learn`` to demonstrate how to use **tda-mapper**:
+Here's a minimal example using the **circles dataset** from `scikit-learn` to
+demonstrate how to use **tda-mapper**. This example demonstrates how to apply
+the Mapper algorithm on a synthetic dataset (concentric circles). The goal is
+to extract a topological graph representation using `PCA` as a lens and
+`DBSCAN` for clustering. We proceed as follows:
 
 .. code:: python
 
@@ -78,6 +81,11 @@ Here's a minimal example using the **circles dataset** from
 | |Original Dataset|                     | |Mapper Graph|              |
 +----------------------------------------+-----------------------------+
 
+Left: the original dataset consisting of two concentric circles with noise,
+colored by class label. Right: the resulting Mapper graph, built from the `PCA`
+projection and clustered using `DBSCAN`. The two concentric circles are well
+identified by the connected components in the Mapper graph.
+
 More examples can be found in the
 `documentation <https://tda-mapper.readthedocs.io/en/main/>`__.
 
@@ -89,13 +97,25 @@ You can run a live demo directly on
 `Streamlit Cloud <https://tda-mapper-app.streamlit.app/>`__,
 or locally on your machine using the following:
 
+Use our Streamlit app to visualize and explore your data without writing code.
+You can run a live demo directly on
+`Streamlit Cloud <https://tda-mapper-app.streamlit.app/>`__,
+or locally on your machine. The first time you run the app locally, you may
+need to install the required dependencies from the `requirements.txt` file by
+running
+
 .. code:: bash
 
    pip install -r app/requirements.txt
+
+then run the app locally with 
+
+.. code:: bash
+
    streamlit run app/streamlit_app.py
 
 |Interactive App|
 
 .. |Original Dataset| image:: https://github.com/lucasimi/tda-mapper-python/raw/main/resources/circles_dataset_v2.png
 .. |Mapper Graph| image:: https://github.com/lucasimi/tda-mapper-python/raw/main/resources/circles_mean_v2.png
-.. |Interactive App| image :: https://github.com/lucasimi/tda-mapper-python/raw/main/resources/tda-mapper-app.png
+.. |Interactive App| image:: https://github.com/lucasimi/tda-mapper-python/raw/main/resources/tda-mapper-app.png