Datasets composed of numerical and categorical attributes (also called mixed data hereinafter) are common in real clustering tasks. Differing from numerical attributes that indicate tendencies between two concepts (e.g., high and low temperature) with their values in well-defined Euclidean distance space, categorical attribute values are different concepts (e.g., different occupations) embedded in an implicit space. Simultaneously exploiting these two very different types of information is an unavoidable but challenging problem, and most advanced attempts either encode the heterogeneous numerical and categorical attributes into one type, or define a unified metric for them for mixed data clustering, leaving their inherent connection unrevealed. This paper, therefore, studies the connection among any-type of attributes and proposes a novel Heterogeneous Attribute Reconstruction and Representation (HARR) learning paradigm accordingly for cluster analysis. The paradigm transforms heterogeneous attributes into a homogeneous status for distance metric learning, and integrates the learning with clustering to automatically adapt the metric to different clustering tasks. Differing from most existing works that directly adopt defined distance metrics or learn attribute weights to search clusters in a subspace. We propose to project the values of each attribute into unified learnable multiple spaces to more finely represent and learn the distance metric for categorical data. HARR is parameter-free, convergence-guaranteed, and can more effectively self-adapt to different sought number of clusters $k$. Extensive experiments illustrate its superiority in terms of accuracy and efficiency.