Starting from dimensionality reduction
Feature selection is a part technique of data dimensional reduction.
According to the book
Data minging: concepts and techniques, the most ubiquitous methods are:
- wavelet transforms
- principal components analysis (PCA)
- attribute subset selection(or feature selection)
It is worth mentioning, that PCA, Exploratory Factor Analysis (EFA), SVD, etc are all methods which reconstruct our original attributes. PCA is essentially creates new variables that are linear combinations of the original variables.
However, if we want to reserve the original attributes, then take a look at Feature selection.
Overview of Feature Selection
Yet From the problem solving prospective,I divide the part of techniques into those ways:
- Supervised(regression): LASSO, REF, Autoencoder, etc. The regression area has been investigated extensively more information
- Unsupervised: principal feature analysis(PFA)
Concepts of unsupervised method(PFA)
- Compute the sample covariance matrix or correlation matrix,
- Compute the Principal components and eigenvalues of the Covariance or Correlation matrix A.
- Choose the subspace dimension n, we get new matrix A_n, the vectors Vi are the rows of A_n.
- Cluster the vectors |Vi|, using K-Means
- For each cluster, find the corresponding vector Vi which is closest to the mean of the cluster.
Since so many of readers have mentioned the covariance calculation: in the paper, it states that both cov and corr are okay. and calculation of cov is embeded in PCA. That’s why you might be confused by the first step
from sklearn.decomposition import PCA from sklearn.cluster import KMeans from collections import defaultdict from sklearn.metrics.pairwise import euclidean_distances from sklearn.preprocessing import StandardScaler class PFA(object): def __init__(self, n_features, q=None): self.q = q self.n_features = n_features def fit(self, X): if not self.q: self.q = X.shape sc = StandardScaler() X = sc.fit_transform(X) pca = PCA(n_components=self.q).fit(X) # calculation Cov matrix is embeded in PCA A_q = pca.components_.T kmeans = KMeans(n_clusters=self.n_features).fit(A_q) clusters = kmeans.predict(A_q) cluster_centers = kmeans.cluster_centers_ dists = defaultdict(list) for i, c in enumerate(clusters): dist = euclidean_distances([A_q[i, :]], [cluster_centers[c, :]]) dists[c].append((i, dist)) self.indices_ = [sorted(f, key=lambda x: x) for f in dists.values()] self.features_ = X[:, self.indices_]
pfa = PFA(n_features=10) pfa.fit(dataset) # To get the transformed matrix x = pfa.features_ # To get the column indices of the kept features column_indices = pfa.indices_
Next time we’ll take a closer look at supervised method.