Sparse Data Observers (SDO) is an unsupervised learning approach developed to cover the need for fast, highly interpretable and intuitively parameterizable anomaly detection. Its extension, SDOclust, performs clustering while preserving the simplicity and applicability of the original approach.

SDO and SDOclust are powerful options when statistical estimates are representative and feature spaces conform distance-based analysis. Their main characteristics are: lightweight, intuitive, self-adjusted, noise- resistant, able to extract non-convex clusters (SDOclust), and built on robust parameters and interpretable models.

Feasibility and rapid integration into real-world applications are the core goals behind SDO and SDOclust, which can work on most data scenarios without parameter adjustment (simply using the default parameterization).

Installation and dependecies

sdo can be installed from PyPI using

    pip install sdoclust

or directly from our GitHub repository:

    pip install git+https://github.com/CN-TU/pysdoclust

sdo requires de following packages:

• numpy
• math
• scipy
• sklearn

By default, SDO uses distance.cdist (from the scipy package) for calculating point distances and distance matrices (default method or method="brute"). Instead, you can use approximate neighbor search with:

• FAISS
• pyNNdescent

In such a case you will need to install the respective packages when calling SDO or SDOclust with method="faiss" or method="pynndescent", e.g.:

    import sdoclust as sdo
    mdl = sdo.SDO(method='faiss')

However, note that, rather than the dataset X, the dominant factor in searching is the set of observers O, which is typically within a few hundred to a few thousand data points. This means that the default "brute" method is going to obtain better accuracy with equivalent runtimes to "faiss" or "pynndescent". Therefore, these alternatives are suitable when setting pretty large values of k. For default or low, k use the default approach.

Examples of usage

SDO

    import numpy as np
    np.random.seed(1)

    # Generate data
    from sklearn import datasets
    x, y = datasets.make_circles(n_samples=5000, factor=0.3, noise=0.1)

    # SDO outlier scoring
    import sdoclust as sdo
    s = sdo.SDO().fit_predict(x)

    # plotting results
    import matplotlib.pyplot as plt
    fig = plt.figure()
    plt.scatter(x[:,0],x[:,1], s=10, cmap='coolwarm', c=s)
    plt.colorbar(ticks=[np.min(s), np.max(s)])
    plt.title('SDO outlierness scores')
    plt.show()

SDOclust

    import numpy as np
    np.random.seed(1)

    # Generate data
    from sklearn import datasets
    x, y = datasets.make_circles(n_samples=5000, factor=0.3, noise=0.1)

    # SDOclust clustering
    import sdoclust as sdo
    p = sdo.SDOclust().fit_predict(x)

    # plotting results
    import matplotlib.pyplot as plt
    fig = plt.figure()
    plt.scatter(x[:,0],x[:,1], s=10, cmap='coolwarm', c=p)
    plt.title('SDOclust clustering')
    plt.show()

Application notes

SDO and SDOclust obtain good performances without modifying the default parameterization in most applications, but may require adjustment in some cases: typically, when datasets have very few elements, when clusters are overlapping or in cases with many under-represented clusters.

Main SDO parameters are:

• x, which establishes the number of closest observers to evaluate each data point.
• qv, which sets a robust threshold for removing idle observers.

• k, which fixes de number of observers in the model

  mdl = sdo.SDO(x=5, qv=0.3, k=500)
  

Additionally, SDOclust also incorporates:

• zeta, which sets a trade-off between locality and globality for cutting-off graph edges thresholds.
• chi, which defines the chi-closest observer of any given observer to decide cutting-off graph edges thresholds.

• e sets the minimum number of observers that a cluster can have.

  mdl = sdo.SDOclust(zeta=0.6, chi=10, e=3)
  

[1] and [2] provide further explanations on SDO and SDOclust parameters. SDOclust with default parameters tend to find fundamental partitions, i.e. a low number of clusters. If your scenario contains many clusters, or you detect underclustering, try, for example, by increasing k and/or reducing chi.

Citation

If you use SDO or SDOclust in your research, please cite our publications:

SDO

[2] Iglesias, F., Zseby, T., Zimek, A., "Outlier Detection Based on Low Density Models," 2018 IEEE International Conference on Data Mining Workshops (ICDMW), Singapore, 2018, pp. 970-979, doi: 10.1109/ICDMW.2018.00140.,

    @INPROCEEDINGS{SDO2018,
        author    = {F{\'e}lix Iglesias and Tanja Zseby and Alexander Hartl and Arthur Zimek},
        booktitle={2018 IEEE International Conference on Data Mining Workshops (ICDMW)}, 
        title={Outlier Detection Based on Low Density Models}, 
        year={2018},
        volume={},
        number={},
        pages={970-979},
        doi={10.1109/ICDMW.2018.00140}} 
    }

SDOclust

[1] Iglesias, F., Zseby, T., Hartl, A., Zimek, A. (2023). SDOclust: Clustering with Sparse Data Observers. In: Pedreira, O., Estivill-Castro, V. (eds) Similarity Search and Applications. SISAP 2023. Lecture Notes in Computer Science, vol 14289. Springer, Cham. https://doi.org/10.1007/978-3-031-46994-7_16

    @InProceedings{SDOclust2023,
        title     = {SDOclust: Clustering with Sparse Data Observers},
        author    = {F{\'e}lix Iglesias and Tanja Zseby and Arthur Zimek},
        editor    = {{\'O}scar Pedreira and Vladimir Estivill-Castro",
        booktitle = {Similarity Search and Applications},
        year      = {2023},
        publisher = {Springer Nature Switzerland},
        address   = {Cham},
        pages     = {185--199},
        doi       = {https://doi.org/10.1007/978-3-031-46994-7\_16}
    }

Others

• Experiments conducted in [2] are available to download in: Iglesias Vázquez, F.: SDOclust Evaluation Tests (Jun 2023). https://doi.org/10.48436/3q7jp-mg161

• The observers-partitioning task in SDOclust is based on the Graph-Based clustering work of Dani El-Ayyass: https://github.com/dayyass/graph-based-clustering

• An alternative implementation of SDO (only for outlier detection) by Alexander Hartl is in: https://github.com/CN-TU/pysdo

• A version of SDO for streaming data (SDOstream) is included in the dSalmon package: https://pypi.org/project/dSalmon/

• Outlier thresholding (i.e., binary/crips labels for outlier/inlier) can be performed externally with multiple algorithms. The pythresh package offers multiple options: https://github.com/KulikDM/pythresh