REFERENCE TO PROJECT: prince
THE MAIN DIFFERENCES AS SHOWN BELOW:
- LIGHTER: REMOVE REPETITIVE CALCULATION,ACCELERATING MAIN CALCULATION.
- MORE STANDARD: EACH ALGORITHM IMPLEMENTS fit,transform,fit_transform METHODS FOLLOWING THE MAIN STRUCTURE of scikit-learn API
Light_FAMD is a library for prcessing factor analysis of mixed data. This includes a variety of methods including principal component analysis (PCA) and multiply correspondence analysis (MCA). The goal is to provide an efficient and light implementation for each algorithm along with a scikit-learn API.
Light_FAMD doesn't have any extra dependencies apart from the usual suspects (sklearn, pandas, numpy) which are included with Anaconda.
import numpy as np; np.random.set_state(42) # This is for doctests reproducibilityEach base estimator(CA,PCA) provided by Light_FAMD extends scikit-learn's (TransformerMixin,BaseEstimator).which means we could use directly fit_transform,and (set_params,get_params) methods.
Under the hood Light_FAMD uses a randomised version of SVD. This algorithm finds a (usually very good) approximate truncated singular value decomposition using randomization to speed up the computations. It is particularly fast on large matrices on which you wish to extract only a small number of components. In order to obtain further speed up, n_iter can be set <=2 (at the cost of loss of precision). However if you want reproducible results then you should set the random_state parameter.
In this package,inheritance relationship as shown below(A->B:A is superclass of B):
- PCA -> MFA -> FAMD
- CA ->MCA
You are supposed to use each method depending on your situation:
- All your variables are numeric: use principal component analysis (
PCA) - You have a contingency table: use correspondence analysis (
CA) - You have more than 2 variables and they are all categorical: use multiple correspondence analysis (
MCA) - You have groups of categorical or numerical variables: use multiple factor analysis (
MFA) - You have both categorical and numerical variables: use factor analysis of mixed data (
FAMD)
Notice that Light_FAMD does't support the sparse input,see Truncated_FAMD for an alternative of sparse and big data.
PCA(rescale_with_mean=True, rescale_with_std=True, n_components=2, n_iter=3, copy=True, check_input=True, random_state=None, engine='auto'):
Args:
rescale_with_mean(bool): Whether to substract each column's mean or not.rescale_with_std(bool): Whether to divide each column by it's standard deviation or not.n_components(int): The number of principal components to compute.n_iter(int): The number of iterations used for computing the SVD.copy(bool): Whether to perform the computations inplace or not.check_input(bool): Whether to check the consistency of the inputs or not.engine(string):"auto":randomized_svd,"fbpca":Facebook's randomized SVD implementationrandom_state(int, RandomState instance or None, optional (default=None):The seed of the -pseudo random number generator to use when shuffling the data. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. Return ndarray (M,k),M:Number of samples,K:Number of components.
Fitted Estimator Attributes:
components_(array), shape (n_components, n_features) Principal axes in feature space, representing the directions of maximum variance in the data. The components are sorted by explained_variance_.explained_variance_(array), shape (n_components,):The amount of variance explained by each of the selected components.explained_variance_ratio_(array), shape (n_components,):Percentage of variance explained by each of the selected components.singular_values_(array),shape (n_components,):The singular values corresponding to each of the selected components. The singular values are equal to the 2-norms of the n_components variables in the lower-dimensional space.
Examples:
>>>import numpy as np
>>>from Light_Famd import PCA
>>>X = pd.DataFrame(np.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]]),columns=list('ABC'))
>>>pca = PCA(n_components=2)
>>>pca.fit(X)
PCA(check_input=True, copy=True, engine='auto', n_components=2, n_iter=3,
random_state=None, rescale_with_mean=True, rescale_with_std=True)
>>>print(pca.explained_variance_)
[11.89188304 0.10811696]
>>>print(pca.explained_variance_ratio_)
[0.9909902530309821, 0.00900974696901714]
>>>print(pca.column_correlation(X)) #You could call this method once estimator is >fitted.correlation_ratio is pearson correlation between 2 columns values,
where p-value >=0.05 this similarity is `Nan`.
0 1
A -0.995485 NaN
B -0.995485 NaN
>>>print(pca.transform(X))
[[ 0.82732684 -0.17267316]
[ 1.15465367 0.15465367]
[ 1.98198051 -0.01801949]
[-0.82732684 0.17267316]
[-1.15465367 -0.15465367]
[-1.98198051 0.01801949]]
>>>print(pca.fit_transform(X))
>[[ 0.82732684 -0.17267316]
[ 1.15465367 0.15465367]
[ 1.98198051 -0.01801949]
[-0.82732684 0.17267316]
[-1.15465367 -0.15465367]
[-1.98198051 0.01801949]]
CA(n_components=2, n_iter=10, copy=True, check_input=True, random_state=None, engine='auto'):
Args:
n_components(int): The number of principal components to compute.copy(bool): Whether to perform the computations inplace or not.check_input(bool): Whether to check the consistency of the inputs or not.engine(string):"auto":randomized_svd,"fbpca":Facebook's randomized SVD implementationrandom_state(int, RandomState instance or None, optional (default=None):The seed of the -pseudo random number generator to use when shuffling the data. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
Return ndarray (M,k),M:Number of samples,K:Number of components.
Examples:
>>>import numpy as np
>>>from Light_Famd import CA
>>>X = pd.DataFrame(data=np.random.randint(0,100,size=(10,4)),columns=list('ABCD'))
>>>ca=CA(n_components=2,n_iter=2)
>>>ca.fit(X)
CA(check_input=True, copy=True, engine='auto', n_components=2, n_iter=2,
random_state=None)
>>> print(ca.explained_variance_)
[0.09359686 0.04793262]
>>>print(ca.explained_variance_ratio_)
[0.5859714238674507, 0.3000864001658787]
>>>print(ca.transform(X))
[[-0.18713811 0.09830335]
[ 0.34735892 0.34924107]
[ 0.33511949 -0.29842395]
[-0.26200927 -0.14201485]
[-0.21803569 0.0977655 ]
[-0.25482535 -0.16019826]
[ 0.09899818 -0.15015664]
[-0.24835074 0.54054788]
[-0.21056433 -0.29941039]
[ 0.33904416 0.04835469]]
MCA class inherits from CA class.
>>>import pandas as pd
>>>X=pd.DataFrame(np.random.choice(list('abcde'),size=(10,4),replace=True),columns =list('ABCD'))
>>>print(X)
A B C D
0 e a a b
1 b e c a
2 e b a c
3 e e b c
4 b c d d
5 c d a c
6 a c e a
7 d b d b
8 e a e e
9 c a e b
>>>mca=MCA(n_components=2)
>>>mca.fit(X)
MCA(check_input=True, copy=True, engine='auto', n_components=2, n_iter=10,
random_state=None)
>>>print(mca.explained_variance_)
[0.8286237 0.67218257]
>>>print(mca.explained_variance_ratio_)
[0.2071559239010482, 0.16804564240579373]
>>>print(mca.transform(X))
[[-0.75608657 0.17650888]
[ 1.39846026 -1.17201511]
[-0.77421024 -0.04847214]
[-0.32829309 -1.19959921]
[ 1.49371661 0.90485916]
[-1.00518879 -0.41815679]
[ 1.11265365 -0.14764943]
[-0.07786514 1.66121318]
[-0.51081888 -0.06676941]
[-0.55236782 0.31008086]]
MFA class inherits from PCA class.
Since FAMD class inherits from MFA and the only thing to do for FAMD is to determine groups parameter compare to its superclass MFA.therefore we skip this chapiter and go directly to FAMD.
The FAMD inherits from the MFA class, which entails that you have access to all it's methods and properties of MFA class.
>>>import pandas as pd
>>>X_n = pd.DataFrame(data=np.random.randint(0,100,size=(10,2)),columns=list('AB'))
>>>X_c =pd.DataFrame(np.random.choice(list('abcde'),size=(10,4),replace=True),columns =list('CDEF'))
>>>X=pd.concat([X_n,X_c],axis=1)
>>>print(X)
A B C D E F
0 11 67 a a d e
1 43 67 d d d a
2 40 3 d b c b
3 81 66 e b c c
4 36 50 e a c e
5 95 69 b d e a
6 57 71 d c d c
7 29 58 e e d d
8 67 27 b e d e
9 78 20 e d a a
>>>famd = Light_FAMD.FAMD(n_components=2)
>>>famd.fit(X)
FAMD(check_input=True, copy=True, engine='auto', n_components=2, n_iter=3,
random_state=None)
>>>print(famd.explained_variance_)
[15.41428212 9.53118994]
>>>print(famd.explained_variance_ratio_)
[0.27600556629884937, 0.17066389830189396]
>>> print(famd.column_correlation(X))
0 1
A NaN NaN
B NaN NaN
C_a NaN NaN
C_b NaN NaN
C_d NaN NaN
C_e NaN NaN
D_a NaN NaN
D_b NaN NaN
D_c NaN NaN
D_d NaN 0.947742
D_e NaN NaN
E_a NaN NaN
E_c NaN NaN
E_d 0.759576 NaN
E_e NaN NaN
F_a NaN 0.947742
F_b NaN NaN
F_c NaN NaN
F_d NaN NaN
F_e NaN NaN
>>>print(famd.transform(X))
[[ 4.15746579 -2.87023941]
[ 4.95755717 3.74813131]
[ 2.6358626 -1.87761681]
[ 3.4203849 -2.2485009 ]
[ 4.10436826 -3.57317268]
[ 2.88436338 5.65046057]
[ 3.92172253 -0.41161253]
[ 4.48442501 -1.30359035]
[ 4.42018651 -0.77402381]
[ 3.66615694 4.15701604]]
print(famd.fit_transform(X))
[[ 4.15746579 -2.87023941]
[ 4.95755717 3.74813131]
[ 2.6358626 -1.87761681]
[ 3.4203849 -2.2485009 ]
[ 4.10436826 -3.57317268]
[ 2.88436338 5.65046057]
[ 3.92172253 -0.41161253]
[ 4.48442501 -1.30359035]
[ 4.42018651 -0.77402381]
[ 3.66615694 4.15701604]]