IncomLDL
--------

IncomLDL refers to *incomplete label distribution learning*. The key differences between IncomLDL and LDL in definition are as follows:

   Let :math:`\Omega = [n] \times [c]` denote the indices of observed entries sampled uniformly at random from the label distribution matrix :math:`\boldsymbol{D}` with an observed rate :math:`\omega`, where :math:`[k] = \lbrace 1,\, 2,\, \dots,\, k \rbrace`. Then, a linear operator :math:`\mathcal{R}_{\Omega}` is defined as

   .. math:: \mathcal{R}_{\Omega}(\boldsymbol{D})_{ij} = \begin{cases} D_{ij} & \text{if } (i, j) \in \Omega \text{,} \\ 0 & \text{otherwise.} \end{cases}

   The given label distribution matrix in the training set is incomplete, i.e., :math:`\tilde{\boldsymbol{D}} = \mathcal{R}_{\Omega}(\boldsymbol{D})`. Under the *incomplete setting*, the performance is evaluated on a test set; under the *transductive setting*, the test data with no supervised information are accompanied by the incomplete training data.

.. toctree::
   :maxdepth: 2

`BaseIncomLDL`
~~~~~~~~~~~~~~

.. autoclass:: pyldl.algorithms.base.BaseIncomLDL
   :members:
   :private-members:

.. jinja:: incomldl_ctx

   {% for class_name in all_incomldl_algs %}
   {{ class_name.replace('_', '-').lstrip('-') }}
   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

   .. autoclass:: pyldl.algorithms.{{ class_name }}
      :members:
      :private-members:

   {% endfor %}

References
~~~~~~~~~~

.. bibliography:: bib/incomldl/references.bib
   :labelprefix: INCOM-LDL-
   :cited:

Further Reading
~~~~~~~~~~~~~~~

.. bibliography:: bib/incomldl/references.bib
   :labelprefix: INCOM-LDL-
   :notcited: