python spark: narrowing down most relevant features using PCA

Question

I am using spark 2.2 with python. I am using PCA from ml.feature module. I am using VectorAssembler to feed my features to PCA. To clarify, let's say I have a table with three columns col1, col2 and col3 then I am doing:

from pyspark.ml.feature import VectorAssembler
assembler = VectorAssembler(inputCols=table.columns, outputCol="features")
df = assembler.transform(table).select("features")
from pyspark.ml.feature import PCA
pca = PCA(k=2, inputCol="features", outputCol="pcaFeatures")
model = pca.fit(df)

At this time I have run PCA with 2 components and I can look at its values as:

m = model.pc.values.reshape(3, 2)

which corresponds to 3 (= number of columns in my original table) rows and 2 (= number of components in my PCA) columns. My question is are the three rows here in the same order in which I had specified my input columns to the vector assembler above? To clarify it further does the above matrix correspond to:

          | PC1 | PC2 |
 ---------|-----|-----|
    col1  |     |     |
 ---------|-----|-----|
    col2  |     |     |
 ---------|-----|-----|
    col3  |     |     |
 ---------+-----+-----+

Note that the example here is only for clarity. In my real problem I am dealing with ~1600 columns and bunch of selections. I could not find any definitive answer to this in spark documentation. I want to do this to pick best columns / features from my original table to train my model based on the top principal components. Or is there anything else / better in spark ML PCA that I should be looking at to deduce such result?

Or I cannot use PCA for this and have to use other techniques like spearman ranking etc.?

Answer 1

are the (...) rows here in the same order in which I had specified my input columns

Yes, they are. Let's trace what is going on:

from pyspark.ml.feature import PCA, VectorAssembler

data = [
    (0.0, 1.0, 0.0, 7.0, 0.0), (2.0, 0.0, 3.0, 4.0, 5.0), 
    (4.0, 0.0, 0.0, 6.0, 7.0)
]

df = spark.createDataFrame(data, ["u", "v", "x", "y", "z"])

VectorAseembler follows the order of columns:

assembler = VectorAssembler(inputCols=df.columns, outputCol="features")
vectors = assembler.transform(df).select("features")

vectors.schema[0].metadata
# {'ml_attr': {'attrs': {'numeric': [{'idx': 0, 'name': 'u'},
#     {'idx': 1, 'name': 'v'},
#     {'idx': 2, 'name': 'x'},
#     {'idx': 3, 'name': 'y'},
#     {'idx': 4, 'name': 'z'}]},
#   'num_attrs': 5}}

So are principal components

model = PCA(inputCol="features", outputCol="pc_features", k=3).fit(vectors)

?model.pc
# Type:        property
# String form: <property object at 0x7feb5bdc1d68>
# Docstring:  
# Returns a principal components Matrix.
# Each column is one principal component.
# 
# .. versionadded:: 2.0.0

Finally sanity check:

import numpy as np

x = np.array(data)
y = model.pc.values.reshape(3, 5).transpose()
z = np.array(model.transform(vectors).rdd.map(lambda x: x.pc_features).collect())

np.linalg.norm(x.dot(y) - z)
# 8.881784197001252e-16