Data does not always come in a way our machine learning algorithms expects it. We saw that concept a handful of times already: we extracted extra features (e.g. polynomial features), we did dimensionality reduction, we used manifold techniques. Yet, all these things may still fail against certain data.
And we look at yet another dataset. We import the usual stuff and the wine dataset, which is an example of data that would fail a simple dimensionality reduction.
The set is made of chemical measurement over three different vineyards in Italy. One can take it as a classification problem of attempting to identify the vineyard from the chemical composition. We will use is for dimensionality reduction.
import numpy as np import pandas as pd import matplotlib.pyplot as plt %matplotlib inline plt.style.use('seaborn-talk') from sklearn.datasets import load_wine wine = load_wine() print(wine['DESCR'])
.. _wine_dataset: Wine recognition dataset ------------------------ **Data Set Characteristics:** :Number of Instances: 178 (50 in each of three classes) :Number of Attributes: 13 numeric, predictive attributes and the class :Attribute Information: - Alcohol - Malic acid - Ash - Alcalinity of ash - Magnesium - Total phenols - Flavanoids - Nonflavanoid phenols - Proanthocyanins - Color intensity - Hue - OD280/OD315 of diluted wines - Proline - class: - class_0 - class_1 - class_2 :Summary Statistics: ============================= ==== ===== ======= ===== Min Max Mean SD ============================= ==== ===== ======= ===== Alcohol: 11.0 14.8 13.0 0.8 Malic Acid: 0.74 5.80 2.34 1.12 Ash: 1.36 3.23 2.36 0.27 Alcalinity of Ash: 10.6 30.0 19.5 3.3 Magnesium: 70.0 162.0 99.7 14.3 Total Phenols: 0.98 3.88 2.29 0.63 Flavanoids: 0.34 5.08 2.03 1.00 Nonflavanoid Phenols: 0.13 0.66 0.36 0.12 Proanthocyanins: 0.41 3.58 1.59 0.57 Colour Intensity: 1.3 13.0 5.1 2.3 Hue: 0.48 1.71 0.96 0.23 OD280/OD315 of diluted wines: 1.27 4.00 2.61 0.71 Proline: 278 1680 746 315 ============================= ==== ===== ======= ===== :Missing Attribute Values: None :Class Distribution: class_0 (59), class_1 (71), class_2 (48) :Creator: R.A. Fisher :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov) :Date: July, 1988 This is a copy of UCI ML Wine recognition datasets. https://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data The data is the results of a chemical analysis of wines grown in the same region in Italy by three different cultivators. There are thirteen different measurements taken for different constituents found in the three types of wine. Original Owners: Forina, M. et al, PARVUS - An Extendible Package for Data Exploration, Classification and Correlation. Institute of Pharmaceutical and Food Analysis and Technologies, Via Brigata Salerno, 16147 Genoa, Italy. Citation: Lichman, M. (2013). UCI Machine Learning Repository [https://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science. .. topic:: References (1) S. Aeberhard, D. Coomans and O. de Vel, Comparison of Classifiers in High Dimensional Settings, Tech. Rep. no. 92-02, (1992), Dept. of Computer Science and Dept. of Mathematics and Statistics, James Cook University of North Queensland. (Also submitted to Technometrics). The data was used with many others for comparing various classifiers. The classes are separable, though only RDA has achieved 100% correct classification. (RDA : 100%, QDA 99.4%, LDA 98.9%, 1NN 96.1% (z-transformed data)) (All results using the leave-one-out technique) (2) S. Aeberhard, D. Coomans and O. de Vel, "THE CLASSIFICATION PERFORMANCE OF RDA" Tech. Rep. no. 92-01, (1992), Dept. of Computer Science and Dept. of Mathematics and Statistics, James Cook University of North Queensland. (Also submitted to Journal of Chemometrics).
One should explore the data first. We will simply plot as many dimensions as we can at once.
fig, ax = plt.subplots(figsize=(14, 6)) ax.scatter(wine.data[:, 0], wine.data[:, 1], s=30*wine.data[:, 2], c=wine.target, cmap='plasma');
The classes seem to be difficult to separate. Yet, we have just a few dimensions and a handful of samples, therefore we can perform a full PCA and see whether we can project this data into a different space.
from sklearn.decomposition import PCA pca = PCA() pca.fit(wine.data) fig, ax = plt.subplots(figsize=(14, 10)) ax.plot(np.cumsum(pca.explained_variance_ratio_)) ax.set(xlabel='components', ylabel='explained variance');
Oh wow, two dimensional space seem to explain the data variance well enough. And, since we can visualize a two dimensional space easily, we should do it.
pca = PCA(n_components=2) wine_pca = pca.fit_transform(wine.data) fig, ax = plt.subplots(figsize=(14, 6)) ax.scatter(wine_pca[:, 0], wine_pca[:, 1], s=60, c=wine.target, cmap='plasma');
Despite the fact that we did dimensionality reduction the data does not look separable.
Let's try something different, let's describe this data using
df = pd.DataFrame(wine.data, columns=[wine.feature_names]) df.describe()
The values of magnesium and proline have completely different magnitudes from all other features. These features have much bigger values than all the others, and since PCA will evaluate variance based on the values alone, it will take these two features as the main variance explanation. In other words, instead of finding the main variance in the data PCA is simply finding these two features.
Until now we worked with PCA on images, in which each dimension follows the same scale: the possible values of the pixel which are from $0$ to $255$. Such a well behaved set of dimensions is uncommon in most datasets, notably if the data are not images.
Let's scale those things down and then apply PCA.
StandardScaler centers the mean of every feature to zero,
and ensures that the variance of each feature is exactly one.
from sklearn.preprocessing import StandardScaler from sklearn.pipeline import make_pipeline preprocess = make_pipeline(StandardScaler(), PCA(n_components=2)) wine_pca = preprocess.fit_transform(wine.data) fig, ax = plt.subplots(figsize=(14, 6)) ax.scatter(wine_pca[:, 0], wine_pca[:, 1], s=60, c=wine.target, cmap='plasma');
Now this is rather easy to separate. And moreover, we probably do not need a complex classifier for it.
We have two take away messages here. The first is that if we had believed that the PCA examples we have done earlier are good representations for all data sets we would be in trouble when faced with a dataset of non-images. Not scaling the data before PCA is one of the most common mistakes one makes when working with data preprocessing.
Another thing that we did not see before is the use of a pipeline
with two preprocessors.
We could now add a third
sklearn object, perhaps a classifier,
to the pipeline and build a three piece pipeline.
A pipeline is not limited to two
sklearn objects glued together,
often one may need a longer one.
The dataset after scaling is quite easy to classify,
we will leave the concatenation of a model to the pipeline
and classification to you.