Data Structures and Pattern Recognition

Dimensionality reduction plays a vital role in pattern recognition. However, for normalized vector data, existing methods do not utilize the fact that the data is normalized. In this chapter, the authors propose to employ an Angular Decomposition of the normalized vector data which corresponds to embedding them on a unit surface. On graph data for similarity/kernel matrices with constant diagonal elements, the authors propose the Angular Decomposition of the similarity matrices which corresponds to embedding objects on a unit sphere. In these angular embeddings, the Euclidean distance is equivalent to the cosine similarity. Thus data structures best described in the cosine similarity and data structures best captured by the Euclidean distance can both be effectively detected in our angular embedding. The authors provide the theoretical analysis, derive the computational algorithm, and evaluate the angular embedding on several datasets. Experiments on data clustering demonstrate that the method can provide a more discriminative subspace.

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Granule-Based-Classifier (GbC): A Lattice Computing Scheme Applied on Tree Data Structures

Mathematics ◽

10.3390/math9222889 ◽

2021 ◽

Vol 9 (22) ◽

pp. 2889

Author(s):

Vassilis G. Kaburlasos ◽

Chris Lytridis ◽

Eleni Vrochidou ◽

Christos Bazinas ◽

George A. Papakostas ◽

...

Keyword(s):

Pattern Recognition ◽

Data Structures ◽

Real World ◽

Head Orientation ◽

Human Face ◽

Human Face Recognition ◽

Face Representation ◽

Tree Data ◽

Tree Data Structure ◽

Logic Reasoning

Social robots keep proliferating. A critical challenge remains their sensible interaction with humans, especially in real world applications. Hence, computing with real world semantics is instrumental. Recently, the Lattice Computing (LC) paradigm has been proposed with a capacity to compute with semantics represented by partial order in a mathematical lattice data domain. In the aforementioned context, this work proposes a parametric LC classifier, namely a Granule-based-Classifier (GbC), applicable in a mathematical lattice (T,⊑) of tree data structures, each of which represents a human face. A tree data structure here emerges from 68 facial landmarks (points) computed in a data preprocessing step by the OpenFace software. The proposed (tree) representation retains human anonymity during data processing. Extensive computational experiments regarding three different pattern recognition problems, namely (1) head orientation, (2) facial expressions, and (3) human face recognition, demonstrate GbC capacities, including good classification results, and a common human face representation in different pattern recognition problems, as well as data induced granular rules in (T,⊑) that allow for (a) explainable decision-making, (b) tunable generalization enabled also by formal logic/reasoning techniques, and (c) an inherent capacity for modular data fusion extensions. The potential of the proposed techniques is discussed.

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