# Data Analysis for Information Discovery
###### Abstract  
Artificial intelligence applications are becoming increasingly popular and are producing better results in many areas of research. The quality of the results depends on the quantity of data and its information content. In recent years, the amount of data available has increased significantly, but this does not always mean more information and therefore better results. The aim of this work is to evaluate the effects of a new data preprocessing method for machine learning. This method was designed for space matrix approximation, and it is called semi-pivoted QR approximation (SPQR). To best of our knowledge, it has never been applied to data preprocessing in machine learning algorithms. This method works as a feature selection algorithm, and in this work, an evaluation of its effects on the performance of an unsupervised clustering algorithm is proposed. The obtained results are compared to those obtained using, as preprocessing algorithm, principal component analysis (PCA). These two methods have been applied to various publicly available datasets. The obtained results show that the SPQR algorithm can achieve results comparable to those obtained using PCA without introducing any transformation of the original dataset. data analysis; PCA; SPQR; FCM +
Footnote †: journal: Medical  
The relevance of variance in the study of models is widely used, for example, think of KLT (Karhunen-Loeve transform) [1], PCA, and its variants. PCA is often used for dimensionality reduction. This process aims to reduce a large number of variables describing a dataset to a smaller number of latent variables, limiting the loss of information as much as possible [2]. In [3], authors used PCA in a computational chain to identify and remove noisy data from a dataset before addressing the classification problem of an artificial neural network (ANN). In [4] authors used PCA in a method to improve image classification performance by exploring the utilization of collective class characteristics to establish a statistically weighted algorithm and combined this weight with PCA to enhance the discrimination ability. From this point of view, it is possible to say that giving input to a model original dataset and a dataset reduced using PCA, the model will produce almost the same results. To test this hypothesis, in this work, a widely used algorithm (PCA) and an algorithm under our evaluation (semi-pivoted QR approximation SPQR [5; 6]) have been used to reduce the dimensionality of the original data of various publicly available databases [7]. On the other hand, manipulating input data is one of the factors that can introduce uncertainty in numerical models. This is an interesting problem that is studied in the field of uncertainty analysis. Uncertainty analysis aims at quantifying the variability of the output that is due to the variability of the input. Some interesting approaches to this problem can be found in [8; 9]. The SPQR method was presented in [5] and, to best of our knowledge, it has never been applied to dataset dimensionality reduction for machine learning algorithms. Fuzzy clustering and silhouette analysis were used to compare the results. The performances obtained were compared among them, showing strong variations among the methods, highlighting the strong impact that preprocessing techniques can have on the performances of machine learning algorithms. In further development of this, the information loss in the case of using the well-known PCA compared to the SPQR algorithm will be evaluated. This analysis was carried out on 10 public databases from the UCI site [7], and for each database, the following procedure was run:  
* Fuzzy clustering on the raw database and performance evaluation with silhouette analysis;
* Fuzzy clustering on the preprocessed database with PCA and performance evaluation with silhouette analysis;
* Fuzzy clustering on the preprocessed database with SPQR and performance evaluation with silhouette analysis;
* All the previous tests performed on normalized data.