  In this paper, we introduce a new family of descriptors for persistence
diagrams. Our approach transforms these diagrams into elements of a
finite-dimensional vector space using functionals based on the discrete
measures they induce. While our focus is primarily on identity and
frequency-based transformations, we do not restrict our approach exclusively to
this types of techniques. We term this family of transformations as LITE
(Lattice Integrated Topological Embedding) and prove stability for some members
of this family against the 1-$Kantorovitch$-$Rubinstein$ metric, ensuring its
responsiveness to subtle data variations. Extensive comparative analysis
reveals that our descriptor performs competitively with the current
state-of-art from the topological data analysis literature, and often
surpasses, the existing methods. This research not only introduces an
innovative perspective for data scientists but also critiques the current
trajectory of literature on methodologies for vectorizing diagrams. It
establishes a foundation for future progress in applying persistence diagrams
to data analysis and machine learning under a more simple and effective lens.
