title: Don't understand the output of Principal Component Analysis (PCA) in Python
body: <p>I did a PCA in Python on audio spectrograms and face the following problem: I have a matrix, where each row consists of flattened song features. After applying PCA it's clear to me, that the dimensions are reduced. BUT I can't find those dimensional data in the regular dataset. </p>
  
  <pre><code>import sys
  import glob
  
  from scipy.io.wavfile import read
  from scipy import signal
  from scipy.fftpack import fft
  import numpy as np
  import matplotlib.pyplot as plt
  import pylab
  
  # Read file to get samplerate and numpy array containing the signal 
  
  files = glob.glob('../some/*.wav')
  
  song_list = []
  
  for wav in files:
  
      (fs, x) = read(wav)
  
      channels = [
          np.array(x[:, 0]),
          np.array(x[:, 1])
      ]
  
      # Combine channels to make a mono signal out of stereo
      channel =  np.mean(channels, axis=0)
      channel = channel[0:1024,]
      # Generate spectrogram 
      ## Freqs is the same with different songs, t differs slightly
      Pxx, freqs, t, plot = pylab.specgram(
          channel,
          NFFT=128, 
          Fs=44100, 
          detrend=pylab.detrend_none,
          window=pylab.window_hanning,
          noverlap=int(128 * 0.5))
      # Magnitude Spectrum to use
      Pxx = Pxx[0:2]
      X_flat = Pxx.flatten()
      song_list.append(X_flat)
  
  song_matrix = np.vstack(song_list)
  </code></pre>
  
  <p>If I now apply PCA to the song_matrix...</p>
  
  <pre><code>import matplotlib
  from matplotlib.mlab import PCA
  from sklearn import decomposition
  
  
  #test = matplotlib.mlab.PCA(song_matrix.T)
  
  pca = decomposition.PCA(n_components=2)
  song_matrix_pca = pca.fit_transform(song_matrix.T)
  
  
  pca.components_ #These components should be most helpful to discriminate between the songs due to their high variance
  pca.components_
  </code></pre>
  
  <p>...the final 2 components are the following:
  <a href="http://i.stack.imgur.com/uXNQ6.png" rel="nofollow">Final components - two dimensions from 15 wav-files</a>
  <strong>The problem is, that I can't find those two vectors in the original dataset with all dimensions</strong> What am I doing wrong or am I misinterpreting the whole thing?</p>