The use of machine learning techniques better known by its Anglicism "Machine Learning" is becoming more and more popular. It applies to a wide variety of fields, from image processing to processing human language, including computer security and the video game industry [2]. One of the main purposes of applying machine learning techniques is prediction. Any machine learning process can be subdivided into the following steps: data preprocessing, model design and training, and model evaluation. The preprocessing phase is still known as “Pre-processing” very often consists of choosing the most informative variables from the set of incoming vectors and normalizing them if necessary. This technique is also called "feature selection / feature engineering". The purpose of the selection of informative variables is to eliminate nonessential variables which can be considered as noise by the model and thus reduce its accuracy of prediction. Several research studies have been carried out in recent decades to propose either algorithms or criteria for the selection of informative variables.
In [6], authors are offered a technology for extracting informative variables based on the ontology of the field studied. The first phase of this technology consists of a preliminary extraction by the domain expert, of the variables which he deems useful without any other restriction than the variables chosen must be objects or attributes of the ontology. The second phase, still described in [6], consists of aggregating and filtering the preselected variables during the previous phase. The mathematical translation of this procedure is as follows: either Ω = { 𝜔1 ,…… ,𝜔𝑛} - the class labels, 𝑋 = { 𝑋1, …, 𝑋𝑛}- the set of variable identifiers. xis - a value taken by Xi. ℵi - the definition domain of Xi(xis ϵ ℵi). Let ∑ be the set of learning vectors.
For a xis value of Xi: xis ϵ ℵi and in the class ωk an aggregate ℵi(ωk) ϵ ℵi is defined as follows:
xis i(ωk) if and only if for ∀ωv∈Ω, v ≠ k : p(ωk/xis) > p(ωv/ xis)+∆, (1)
Where Δ a positive real number defining the dominance threshold.
At the end of phase 2, the author introduces the unitary predicates Bi (ωk) which take the value 'true' (1) if and only if xis ϵ ℵi(ωk). The final results of the second phase will, therefore, be the aggregates ℵi(ωk), the unitary predicates Bi(ωk) and i ϵ I(ωk): I(ωk) - a subset of the indexes of the variables Xi that passed the test of inequality (1).
During Phase 3 a probabilistic approach was introduced to determine cause-and-effect dependencies in the conjunction of the predicates Bi(ωk) and i ϵ I(ωk), Ω = { 𝜔1 ,…… ,𝜔𝑛 } and ωj ϵ Ω.
Let { ℵi(ωj) }| i ϵ I(ωk), j = 1, ..., m - the set of aggregates where p(ℵi(ωj))=|ℵi(ωj)|/|ℵi|, where | | represents the standard of the corresponding assembly. It is obvious that: p(Bi(ωj)) = p (ℵi(ωj)).
In the following three filters will be introduced to select the predicates:
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)
The authors of [7] in Chap. 6 entitled "Dimensionality reduction" discuss the PCA (Principal Component Analysis [8]) algorithm based on the analysis of linear dependence. The idea is to replace the redundant variables with a new one that sums up the information contained in the original vector space. One of the first concepts to appear is SVD (Singular Value Decomposition) [9]. Let X be a matrix of dimension n * d; n- being the number of lines and d - the dimension of the initial vector space to be reduced. Let x be a column vector (transposed from one of the rows of X) and let v - be one of the new vector entities (main components) that we are looking for. According to the SVD theorem, matrix X can be decomposed sum follows 𝑋 = 𝑈𝛴𝑉𝑇, U and V being orthogonal matrices such that 𝑈𝑇𝑈 = 𝐼 𝑒𝑡 𝑉𝑇𝑉 = 𝐼. ∑ a diagonal matrix containing the singular values of X
In the following, the author develops the main stages of PCA [8]. The first step is to refocus the data in the initial vector space. The second step is the linear projection of the initial data vector x into new vectors v. The third step is to maximize the variance of the coordinates. The equation of the coordinate vector after projection is 𝑧=Xv. |
The objective function for the main components is maxw WTW, where WTW = 1. It appears that the optimal form of W is the eigenvector of XTX.
In [10] the authors based on Bayes' theorem:
![](data:image/png;base64,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)
and on Information theory [11], in particular, the notion of self-information 𝐼(𝑥𝑖)=−𝑙𝑜𝑔2𝑃(𝑥𝑖) proposes an algorithm supposed to improve the forecasting accuracy of the NBC (Naive Bayesian Classifier) model [12].
The algorithm divided into two stages consists of its first phase of calculating the weight of each variable 𝑊𝐹𝑖 = − 𝑙𝑜𝑔2𝑃(𝐶|𝐹𝑖). The second phase consists of selecting the variables whose weight 𝑊𝐹𝑖 would have exceeded a certain threshold δ determined by the user.
A new method called LFE (Learning Feature Engineering) is proposed in [13]. At the heart of the LFE [14], we find a set of multilayer classifying perceptrons. Each perceptron corresponding to a transformation. LFE takes as input a dataset and recommends a set of paradigms allowing reconstructing a subset of the informative variables of the initial dataset. Each paradigm is made up of a transformation and the ordered list of variables for which the transformation was most efficient.
In the following, we will propose a model based on the machine learning methods already mentioned to predict the number of COVID-19 cases in Morocco per day. Through the use of the library dedicated to distributed learning methods Spark ML [3].