Hence, dimensionality reduction is applied to transform the multi-dimensional feature space to two or three numeric features while trying to preserve the data structure [15].
Firstly, a multi-dimensional feature vector is constructed using local spatial information.
To utilize linear regressions for nonlinear models, nonlinear maps that transform data into a multi-dimensional feature space are engaged.
Non-linear problems are tackled by transforming them into linear ones in multi-dimensional feature space using Kernel functions.
After quantization and normalisation, our goal now is to generate a multidimensional normalization map – a multidimensional normalization map is a multi-dimensional feature value space.
To address this, we introduce a multi-dimensional key generation technology which maps from multi-dimensional feature space directly to a key space.
Due to the multi-dimensional feature of sustainability, how to account for the impacts of various design factors and the cause-and-effect relationships can be very difficult.
However, some of the recently reported shape representations are embedded in arbitrary metric spaces, i.e. distance spaces, rather than in multi-dimensional feature space.
Different from classical criteria (e.g., Fisher criterion, r2 coefficient) used for ranking one-dimensional observations [20], the proposed criteria are more suitable to quantify how informative a multi-dimensional feature vector is for distinguishing two classes.
However, those measures are typically used for quantifying the discriminative power of one-dimensional feature and are not appropriate for multi-dimensional feature vector evaluation, in particular for our time-frequency optimization.
F score is based on the popular Fisher's discriminant and purely data driven; however, it differs from traditional measures since it provides a simple and effective measure for quantifying the discriminative power of a multi-dimensional feature vector.
