Recipe Objective

While working on a large dataset with many feature and after creating a Sparse Matrix and training a model it takes a high computational cost. Managing and vizualizing the matrix is also very difficult. So we need to reduce the dimension of the matrix.

So this recipe is a short example of how can reduce dimentionality on Sparse Matrix in Python.

Step 1 - Import the library - GridSearchCv

Here we have imported various modules like StandardardScaler, datasets, TruncatedSVD and csr_matrix from differnt libraries. We will understand the use of these later while using it in the in the code snipet.
For now just have a look on these imports.

Step 2 - Setup the Data

Here we have used datasets to load the inbuilt digits dataset. We have used standardscaler to scale the data such that the mean becomes 0 and standard deviation to 1. We have also made a sparse matrix of the data by the function csr_matrix. digits = datasets.load_digits() X = StandardScaler().fit_transform(digits.data) print(X) X_sparse = csr_matrix(X) print(X_sparse)

Step 3 - Using GridSearchCV

We can truncate the marix that is we can reduce the dimension of the matrix by using the function TruncatedSVD with a parameter n_components which shows the final number of fetures we want. So we have fit and transform the matrix in the function to get the truncated matrix. tsvd = TruncatedSVD(n_components=10) X_sparse_tsvd = tsvd.fit(X_sparse).transform(X_sparse) print(); print(X_sparse_tsvd)

Step 6 - Printing Results

Now we are using print statements to print the results. print("Original number of features:", X_sparse.shape[1]) print("Reduced number of features:", X_sparse_tsvd.shape[1]) print(); print(tsvd.explained_variance_ratio_[0:6].sum()) As an output we get:

[[ 0.         -0.33501649 -0.04308102 ... -1.14664746 -0.5056698
  -0.19600752]
 [ 0.         -0.33501649 -1.09493684 ...  0.54856067 -0.5056698
  -0.19600752]
 [ 0.         -0.33501649 -1.09493684 ...  1.56568555  1.6951369
  -0.19600752]
 ...
 [ 0.         -0.33501649 -0.88456568 ... -0.12952258 -0.5056698
  -0.19600752]
 [ 0.         -0.33501649 -0.67419451 ...  0.8876023  -0.5056698
  -0.19600752]
 [ 0.         -0.33501649  1.00877481 ...  0.8876023  -0.26113572
  -0.19600752]]

  (0, 1)	-0.3350164872543856
  (0, 2)	-0.04308101770538793
  (0, 3)	0.2740715207154218
  (0, 4)	-0.6644775126361527
  (0, 5)	-0.8441293865949171
  (0, 6)	-0.40972392088346243
  (0, 7)	-0.1250229232970408
  (0, 8)	-0.05907755711884675
  (0, 9)	-0.6240092623290964
  (0, 10)	0.4829744992519545
  (0, 11)	0.7596224512649244
  (0, 12)	-0.05842586308220443
  (0, 13)	1.1277211297338117
  (0, 14)	0.8795830595483867
  (0, 15)	-0.13043338063115095
  (0, 16)	-0.04462507326885248
  (0, 17)	0.11144272449970435
  (0, 18)	0.8958804382797294
  (0, 19)	-0.8606663175537699
  (0, 20)	-1.1496484601880896
  (0, 21)	0.5154718747277965
  (0, 22)	1.905963466976408
  (0, 23)	-0.11422184388584329
  (0, 24)	-0.03337972630405602
  (0, 25)	0.48648927722411006
  :	:
  (1796, 38)	-0.8226945146290309
  (1796, 40)	-0.061343668908253476
  (1796, 41)	0.8105536026095989
  (1796, 42)	1.3950951873625397
  (1796, 43)	-0.19072005925701047
  (1796, 44)	-0.5868275383619802
  (1796, 45)	1.3634658076459107
  (1796, 46)	0.5874903313016945
  (1796, 47)	-0.08874161717060432
  (1796, 48)	-0.035433262605025426
  (1796, 49)	4.179200682513991
  (1796, 50)	1.505078217025183
  (1796, 51)	0.0881769306516768
  (1796, 52)	-0.26718796251356636
  (1796, 53)	1.2010187221077009
  (1796, 54)	0.8692294429227895
  (1796, 55)	-0.2097851269640334
  (1796, 56)	-0.023596458909150665
  (1796, 57)	0.7715345500122912
  (1796, 58)	0.47875261517372414
  (1796, 59)	-0.020358468129093202
  (1796, 60)	0.4441643511677691
  (1796, 61)	0.8876022965425754
  (1796, 62)	-0.26113572420685327
  (1796, 63)	-0.1960075186604789

[[ 1.91421562 -0.95449937 -3.94604425 ...  1.4963196   0.1160377
  -0.80839011]
 [ 0.58898173  0.9246434   3.92476559 ...  0.55743317  1.08360629
   0.07914133]
 [ 1.30203646 -0.31719139  3.02334129 ...  1.15547162  0.78332798
  -1.12203121]
 ...
 [ 1.02259528 -0.14791152  2.46997819 ...  0.52912028  2.04799351
  -2.0550423 ]
 [ 1.07605482 -0.38090797 -2.45549106 ...  0.76221796  1.07481616
  -0.33991093]
 [-1.25770756 -2.22760395  0.28362814 ... -1.20258084  0.80783614
  -1.84480729]]

Original number of features: 64
Reduced number of features: 10

0.4561203224142434