Studies on various facets of pattern classification is often imperative while working with multi - dimensional samples pertaining to diverse application scenarios. In this notion, w eighted dimension - based distance measure has been one of the vital considerat ions in pattern analysis as it reflects the degree of similarity between samples . Though it is often presumed to be settled with the pervasive use of Euclidean distance, plethora of issues often surface. In this paper, we present (a) a detail analysis on t he impact of distance measure norms and weights of dimensions along with visualization, (b) a novel weighting scheme for each dimension, (c) incorporation of this dimensional weighting schema in to a KNN classifier, and (d) pattern classification on a varie ty of synthetic as well as realistic datasets with the developed model . It has perform ed well across diverse experiments in comparison to the traditional KNN under the same experimental setups. Specifically, for gene expression datasets, it yields signific ant and consistent gain in classification accuracy (around 10%) in all cross - validation experiments with different values of k. As such datasets contain limited number of samples of high dimensions, meaningful selection of nearest neighbours is desirable, and this requirement is reasonably met by regulat ing the shape and size of the region enclos ing the k number of reference samples with the developed weighting schema and appropriate norm . I t, therefore, stands as an important generalization of K NN classifier powered by weighted Minkowski distance with the present weighting schema .

Thalassemia is a heritable blood disorder which is the outcome of a genetic defect causing lack of production of hemoglobin polypeptide chains. However, there is less understanding of the precise frequency as well as sharing in these areas. Knowing about the frequency of thalassemia occurrence and dependable mutations is thus a significant step in preventing, controlling, and treatment planning. Here, Political Tangent Search Optimizer based Transfer Learning (PTSO_TL) is introduced for thalassemia detection. Initially, input data obtained from a particular dataset is normalized in the data normalization stage. Quantile normalization is utilized in the data normalization stage, and the data are then passed to the feature fusion phase, in which Weighted Euclidean Distance with Deep Maxout Network (DMN) is utilized. Thereafter, data augmentation is performed using the oversampling method to increase data dimensionality. Lastly, thalassemia detection is carried out by TL, wherein a convolutional neural network (CNN) is utilized with hyperparameters from a trained model such as Xception. TL is tuned by PTSO, and the training algorithm PTSO is presented by merging of Political Optimizer (PO) and Tangent Search Algorithm (TSA). Furthermore, PTSO_TL obtained maximal precision, recall, and f-measure values of about 94.3%, 96.1%, and 95.2%, respectively.

Abstract: The weighted Euclidean distance between two vectors is a Euclidean distance where the contribution of each dimension is scaled by a given non-negative weight. The Johnson-Lindenstrauss (JL) lemma can be easily adapted to the weighted Euclidean distance if weights are known at construction time. Given a set of n vectors with dimension d, it suffices to scale each dimension of the input vectors according to the weights, and then apply any standard JL reduction: the weighted Euclidean distance between pairs of vectors is preserved within a multiplicative factor ε with high probability. However, this is not the case when weights are provided after the dimensionality reduction. In this paper, we show that by applying a linear map from real vectors to a complex vector space, it is possible to update the compressed vectors so that the weighted Euclidean distances between pairs of points can be computed within a multiplicative factor ε, even when weights are provided after the dimensionality reduction.