多维输出分类（MOC）指将单个输入样本与多个维度的离散输出变量进行关联的新学习范式，其广泛存在于计算广告和计算视觉等众多应用领域。MOC涉及多维异质（语义不同）且值域常异的离散输出变量, 比多标签和多分类学习范式更一般，因而研究也更具挑战性。其成功学习的关键在于不仅要达到学习的有效性而且应能揭示出多维输出变量间的维间关系和各维内部输出变量值间的维内关系。目前对此问题的研究不仅远少于多标签学习而且相关工作也仅仅限于单一的维间或单一的维内关系探索，缺乏更本质的两种关系的联合探索。而这些关系的联合学习直觉上可望促进学习性能的同时，更可使结果可解释。本课题旨在已有工作基础上，建立一个能发现维间/维内关系的MOC学习统一框架。为此整个工作将围绕分类和联合关系学习的关键问题开展建模、算法设计、理论分析、实验验证、应用和拓展性等研究，所获成果可望为MOC及相关机器学习研究提供可借鉴的建模理念和方法。

Multi-dimensional Output Classification (MOC) is a new learning paradigm which aims to learn an association between individual inputs and their multiple dimensional discrete output variables and thus can be applied in such practical areas as computational ads and computer vision etc. MOC involves multi-dimensional heterogeneous (different semantics) and discrete output variables with often different ranges, more general than multi-label learning and multi-class learning, thus has stronger challenge for its research. a key to its successful learning lies in not only being required effectiveness in learning but also able to reveal relationships both between dimensions and between values in each dimension. To date, not only is its study much less than multlabel learning but also are related works just limited to the exploration either within-dimension relation or between-dimensional relation, lacking more essential joint exploration of these relations. However, their joint exploration can intuitively promote both learning performance and interpretability of learning results. Our project, based on existing works, aims to establish a unified MOC learning framework which can discover desirable between-/within- dimensional relations. To the end, we will systemically study key problems including modeling for classification and joint relation learning, algorithm design, theoretical analysis, experimental verification,its applications and extensions. our achievements can desirably provide a valuable reference for deeper investigating MOC modeling, learning and other related machine learning problems.