What do the 'normalize' parameters mean in sklearns confusion_matrix? - machine-learning

I am using sklearns confusion_matrix package to plot the results coupled with the accuracy, recall and precision score etc and the graph renders as it should. However I am slightly confused by what the different values for what the normalize parameter mean. Why do we do it and what are the differences between the 3 options? As quoting from their documentation:
normalize{‘true’, ‘pred’, ‘all’}, default=None
Normalizes confusion matrix over the true (rows), predicted (columns) conditions or all the population.
If None, confusion matrix will not be normalized.
Does it normalize the points to a percentage format to make it easily visually if datasets are too large? Or am I missing the point all together here. I have searched but the questions all appear to be stating how to do it, rather than the meaning behind them.

A normalized version makes it easier to visually interpret how the labels are being predicted and also to perform comparisons. You can also pass values_format= '.0%' to display the values as percentages. The normalize parameter specifies what the denominator should be
'true': sum of rows (True label)
'pred': sum of columns (Predicted label)
'all': sum of all
Example:
import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LogisticRegression
from sklearn.datasets import make_moons
from sklearn.metrics import plot_confusion_matrix
from sklearn.model_selection import train_test_split
# Generate some example data
X, y = make_moons(noise=0.3, random_state=0)
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.1, random_state=10)
# Train the classifier
clf = LogisticRegression()
clf.fit(X, y)
plot_confusion_matrix(clf, X_test, y_test); plt.title("Not normalized");
plot_confusion_matrix(clf, X_test, y_test, values_format= '.0%', normalize='true'); plt.title("normalize='true'");
plot_confusion_matrix(clf, X_test, y_test, values_format= '.0%', normalize='pred'); plt.title("normalize='pred'");
plot_confusion_matrix(clf, X_test, y_test, values_format= '.0%', normalize='all'); plt.title("normalize='all'");

Yes, you can think of it as a percentage. The default is to just show the absolute count value in each cell of the confusion matrix, i.e. how often each combination of true and predicted category levels occurrs.
But if you choose e.g. normalize='all', every count value will be divided by the sum of all count values, so that you have relative frequencies whose sum over the whole matrix is 1. Similarly, if you pick normalize='true', you will have relative frequencies per row.

If you repeat an experiment with different sample sizes, you may want to compare confusion matrices across experiments. To do so, you wouldn't want to see the total counts for each matrix. Instead, you would want to see the counts normalized but you need to decide if you want terms normalized by total number of samples ("all"), predicted class counts ("pred"), or true class counts ("true"). For example:
In [30]: yt
Out[30]: array([1, 0, 0, 0, 0, 1, 1, 0, 0, 0])
In [31]: yp
Out[31]: array([0, 0, 1, 0, 1, 0, 0, 1, 0, 0])
In [32]: confusion_matrix(yt, yp)
Out[32]:
array([[4, 3],
[3, 0]])
In [33]: confusion_matrix(yt, yp, normalize='pred')
Out[33]:
array([[0.57142857, 1. ],
[0.42857143, 0. ]])
In [34]: confusion_matrix(yt, yp, normalize='true')
Out[34]:
array([[0.57142857, 0.42857143],
[1. , 0. ]])
In [35]: confusion_matrix(yt, yp, normalize='all')
Out[35]:
array([[0.4, 0.3],
[0.3, 0. ]])

Related

How to overfit data with Keras?

I'm trying to build a simple regression model using keras and tensorflow. In my problem I have data in the form (x, y), where x and y are simply numbers. I'd like to build a keras model in order to predict y using x as an input.
Since I think images better explains thing, these are my data:
We may discuss if they are good or not, but in my problem I cannot really cheat them.
My keras model is the following (data are splitted 30% test (X_test, y_test) and 70% training (X_train, y_train)):
model = tf.keras.Sequential()
model.add(tf.keras.layers.Dense(32, input_shape=() activation="relu", name="first_layer"))
model.add(tf.keras.layers.Dense(16, activation="relu", name="second_layer"))
model.add(tf.keras.layers.Dense(1, name="output_layer"))
model.compile(loss = "mean_squared_error", optimizer = "adam", metrics=["mse"] )
history = model.fit(X_train, y_train, epochs=500, batch_size=1, verbose=0, shuffle=False)
eval_result = model.evaluate(X_test, y_test)
print("\n\nTest loss:", eval_result, "\n")
predict_Y = model.predict(X)
note: X contains both X_test and X_train.
Plotting the prediction I get (blue squares are the prediction predict_Y)
I'm playing a lot with layers, activation funztions and other parameters. My goal is to find the best parameters to train the model, but the actual question, here, is slightly different: in fact I have hard times to force the model to overfit the data (as you can see from the above results).
Does anyone have some sort of idea about how to reproduce overfitting?
This is the outcome I would like to get:
(red dots are under blue squares!)
EDIT:
Here I provide you the data used in the example above: you can copy paste directly to a python interpreter:
X_train = [0.704619794270697, 0.6779457393024553, 0.8207082120250023, 0.8588819357831449, 0.8692320257603844, 0.6878750931810429, 0.9556331888763945, 0.77677964510883, 0.7211381534179618, 0.6438319113259414, 0.6478339581502052, 0.9710222750072649, 0.8952188423349681, 0.6303124926673513, 0.9640316662124185, 0.869691568491902, 0.8320164648420931, 0.8236399177660375, 0.8877334038470911, 0.8084042532069621, 0.8045680821762038]
y_train = [0.7766424210611557, 0.8210846773655833, 0.9996114311913593, 0.8041331063189883, 0.9980525368790883, 0.8164056182686034, 0.8925487603333683, 0.7758207470960685, 0.37345286573743475, 0.9325789202459493, 0.6060269037514895, 0.9319771743389491, 0.9990691225991941, 0.9320002808310418, 0.9992560731072977, 0.9980241561997089, 0.8882905258641204, 0.4678339275898943, 0.9312152374846061, 0.9542371205095945, 0.8885893668675711]
X_test = [0.9749191829308574, 0.8735366740730178, 0.8882783211709133, 0.8022891400991644, 0.8650601322313454, 0.8697902997857514, 1.0, 0.8165876695985228, 0.8923841531760973]
y_test = [0.975653685270635, 0.9096752789481569, 0.6653736469114154, 0.46367666660348744, 0.9991817903431941, 1.0, 0.9111205717076893, 0.5264993912088891, 0.9989199241685126]
X = [0.704619794270697, 0.77677964510883, 0.7211381534179618, 0.6478339581502052, 0.6779457393024553, 0.8588819357831449, 0.8045680821762038, 0.8320164648420931, 0.8650601322313454, 0.8697902997857514, 0.8236399177660375, 0.6878750931810429, 0.8923841531760973, 0.8692320257603844, 0.8877334038470911, 0.8735366740730178, 0.8207082120250023, 0.8022891400991644, 0.6303124926673513, 0.8084042532069621, 0.869691568491902, 0.9710222750072649, 0.9556331888763945, 0.8882783211709133, 0.8165876695985228, 0.6438319113259414, 0.8952188423349681, 0.9749191829308574, 1.0, 0.9640316662124185]
Y = [0.7766424210611557, 0.7758207470960685, 0.37345286573743475, 0.6060269037514895, 0.8210846773655833, 0.8041331063189883, 0.8885893668675711, 0.8882905258641204, 0.9991817903431941, 1.0, 0.4678339275898943, 0.8164056182686034, 0.9989199241685126, 0.9980525368790883, 0.9312152374846061, 0.9096752789481569, 0.9996114311913593, 0.46367666660348744, 0.9320002808310418, 0.9542371205095945, 0.9980241561997089, 0.9319771743389491, 0.8925487603333683, 0.6653736469114154, 0.5264993912088891, 0.9325789202459493, 0.9990691225991941, 0.975653685270635, 0.9111205717076893, 0.9992560731072977]
Where X contains the list of the x values and Y the corresponding y value. (X_test, y_test) and (X_train, y_train) are two (non overlapping) subset of (X, Y).
To predict and show the model results I simply use matplotlib (imported as plt):
predict_Y = model.predict(X)
plt.plot(X, Y, "ro", X, predict_Y, "bs")
plt.show()
Overfitted models are rarely useful in real life. It appears to me that OP is well aware of that but wants to see if NNs are indeed capable of fitting (bounded) arbitrary functions or not. On one hand, the input-output data in the example seems to obey no discernible pattern. On the other hand, both input and output are scalars in [0, 1] and there are only 21 data points in the training set.
Based on my experiments and results, we can indeed overfit as requested. See the image below.
Numerical results:
x y_true y_pred error
0 0.704620 0.776642 0.773753 -0.002889
1 0.677946 0.821085 0.819597 -0.001488
2 0.820708 0.999611 0.999813 0.000202
3 0.858882 0.804133 0.805160 0.001026
4 0.869232 0.998053 0.997862 -0.000190
5 0.687875 0.816406 0.814692 -0.001714
6 0.955633 0.892549 0.893117 0.000569
7 0.776780 0.775821 0.779289 0.003469
8 0.721138 0.373453 0.374007 0.000554
9 0.643832 0.932579 0.912565 -0.020014
10 0.647834 0.606027 0.607253 0.001226
11 0.971022 0.931977 0.931549 -0.000428
12 0.895219 0.999069 0.999051 -0.000018
13 0.630312 0.932000 0.930252 -0.001748
14 0.964032 0.999256 0.999204 -0.000052
15 0.869692 0.998024 0.997859 -0.000165
16 0.832016 0.888291 0.887883 -0.000407
17 0.823640 0.467834 0.460728 -0.007106
18 0.887733 0.931215 0.932790 0.001575
19 0.808404 0.954237 0.960282 0.006045
20 0.804568 0.888589 0.906829 0.018240
{'me': -0.00015776709314323828,
'mae': 0.00329163070145315,
'mse': 4.0713782563067185e-05,
'rmse': 0.006380735268216915}
OP's code seems good to me. My changes were minor:
Use deeper networks. It may not actually be necessary to use a depth of 30 layers but since we just want to overfit, I didn't experiment too much with what's the minimum depth needed.
Each Dense layer has 50 units. Again, this may be overkill.
Added batch normalization layer every 5th dense layer.
Decreased learning rate by half.
Ran optimization for longer using the all 21 training examples in a batch.
Used MAE as objective function. MSE is good but since we want to overfit, I want to penalize small errors the same way as large errors.
Random numbers are more important here because data appears to be arbitrary. Though, you should get similar results if you change random number seed and let the optimizer run long enough. In some cases, optimization does get stuck in a local minima and it would not produce overfitting (as requested by OP).
The code is below.
import numpy as np
import pandas as pd
import tensorflow as tf
from tensorflow.keras.layers import Input, Dense, BatchNormalization
from tensorflow.keras.models import Model
from tensorflow.keras.optimizers import Adam
import matplotlib.pyplot as plt
# Set seed just to have reproducible results
np.random.seed(84)
tf.random.set_seed(84)
# Load data from the post
# https://stackoverflow.com/questions/61252785/how-to-overfit-data-with-keras
X_train = np.array([0.704619794270697, 0.6779457393024553, 0.8207082120250023,
0.8588819357831449, 0.8692320257603844, 0.6878750931810429,
0.9556331888763945, 0.77677964510883, 0.7211381534179618,
0.6438319113259414, 0.6478339581502052, 0.9710222750072649,
0.8952188423349681, 0.6303124926673513, 0.9640316662124185,
0.869691568491902, 0.8320164648420931, 0.8236399177660375,
0.8877334038470911, 0.8084042532069621,
0.8045680821762038])
Y_train = np.array([0.7766424210611557, 0.8210846773655833, 0.9996114311913593,
0.8041331063189883, 0.9980525368790883, 0.8164056182686034,
0.8925487603333683, 0.7758207470960685,
0.37345286573743475, 0.9325789202459493,
0.6060269037514895, 0.9319771743389491, 0.9990691225991941,
0.9320002808310418, 0.9992560731072977, 0.9980241561997089,
0.8882905258641204, 0.4678339275898943, 0.9312152374846061,
0.9542371205095945, 0.8885893668675711])
X_test = np.array([0.9749191829308574, 0.8735366740730178, 0.8882783211709133,
0.8022891400991644, 0.8650601322313454, 0.8697902997857514,
1.0, 0.8165876695985228, 0.8923841531760973])
Y_test = np.array([0.975653685270635, 0.9096752789481569, 0.6653736469114154,
0.46367666660348744, 0.9991817903431941, 1.0,
0.9111205717076893, 0.5264993912088891, 0.9989199241685126])
X = np.array([0.704619794270697, 0.77677964510883, 0.7211381534179618,
0.6478339581502052, 0.6779457393024553, 0.8588819357831449,
0.8045680821762038, 0.8320164648420931, 0.8650601322313454,
0.8697902997857514, 0.8236399177660375, 0.6878750931810429,
0.8923841531760973, 0.8692320257603844, 0.8877334038470911,
0.8735366740730178, 0.8207082120250023, 0.8022891400991644,
0.6303124926673513, 0.8084042532069621, 0.869691568491902,
0.9710222750072649, 0.9556331888763945, 0.8882783211709133,
0.8165876695985228, 0.6438319113259414, 0.8952188423349681,
0.9749191829308574, 1.0, 0.9640316662124185])
Y = np.array([0.7766424210611557, 0.7758207470960685, 0.37345286573743475,
0.6060269037514895, 0.8210846773655833, 0.8041331063189883,
0.8885893668675711, 0.8882905258641204, 0.9991817903431941, 1.0,
0.4678339275898943, 0.8164056182686034, 0.9989199241685126,
0.9980525368790883, 0.9312152374846061, 0.9096752789481569,
0.9996114311913593, 0.46367666660348744, 0.9320002808310418,
0.9542371205095945, 0.9980241561997089, 0.9319771743389491,
0.8925487603333683, 0.6653736469114154, 0.5264993912088891,
0.9325789202459493, 0.9990691225991941, 0.975653685270635,
0.9111205717076893, 0.9992560731072977])
# Reshape all data to be of the shape (batch_size, 1)
X_train = X_train.reshape((-1, 1))
Y_train = Y_train.reshape((-1, 1))
X_test = X_test.reshape((-1, 1))
Y_test = Y_test.reshape((-1, 1))
X = X.reshape((-1, 1))
Y = Y.reshape((-1, 1))
# Is data scaled? NNs do well with bounded data.
assert np.all(X_train >= 0) and np.all(X_train <= 1)
assert np.all(Y_train >= 0) and np.all(Y_train <= 1)
assert np.all(X_test >= 0) and np.all(X_test <= 1)
assert np.all(Y_test >= 0) and np.all(Y_test <= 1)
assert np.all(X >= 0) and np.all(X <= 1)
assert np.all(Y >= 0) and np.all(Y <= 1)
# Build a model with variable number of hidden layers.
# We will use Keras functional API.
# https://www.perfectlyrandom.org/2019/06/24/a-guide-to-keras-functional-api/
n_dense_layers = 30 # increase this to get more complicated models
# Define the layers first.
input_tensor = Input(shape=(1,), name='input')
layers = []
for i in range(n_dense_layers):
layers += [Dense(units=50, activation='relu', name=f'dense_layer_{i}')]
if (i > 0) & (i % 5 == 0):
# avg over batches not features
layers += [BatchNormalization(axis=1)]
sigmoid_layer = Dense(units=1, activation='sigmoid', name='sigmoid_layer')
# Connect the layers using Keras Functional API
mid_layer = input_tensor
for dense_layer in layers:
mid_layer = dense_layer(mid_layer)
output_tensor = sigmoid_layer(mid_layer)
model = Model(inputs=[input_tensor], outputs=[output_tensor])
optimizer = Adam(learning_rate=0.0005)
model.compile(optimizer=optimizer, loss='mae', metrics=['mae'])
model.fit(x=[X_train], y=[Y_train], epochs=40000, batch_size=21)
# Predict on various datasets
Y_train_pred = model.predict(X_train)
# Create a dataframe to inspect results manually
train_df = pd.DataFrame({
'x': X_train.reshape((-1)),
'y_true': Y_train.reshape((-1)),
'y_pred': Y_train_pred.reshape((-1))
})
train_df['error'] = train_df['y_pred'] - train_df['y_true']
print(train_df)
# A dictionary to store all the errors in one place.
train_errors = {
'me': np.mean(train_df['error']),
'mae': np.mean(np.abs(train_df['error'])),
'mse': np.mean(np.square(train_df['error'])),
'rmse': np.sqrt(np.mean(np.square(train_df['error']))),
}
print(train_errors)
# Make a plot to visualize true vs predicted
plt.figure(1)
plt.clf()
plt.plot(train_df['x'], train_df['y_true'], 'r.', label='y_true')
plt.plot(train_df['x'], train_df['y_pred'], 'bo', alpha=0.25, label='y_pred')
plt.grid(True)
plt.xlabel('x')
plt.ylabel('y')
plt.title(f'Train data. MSE={np.round(train_errors["mse"], 5)}.')
plt.legend()
plt.show(block=False)
plt.savefig('true_vs_pred.png')
A problem you may encountering is that you don't have enough training data for the model to be able to fit well. In your example, you only have 21 training instances, each with only 1 feature. Broadly speaking with neural network models, you need on the order of 10K or more training instances to produce a decent model.
Consider the following code that generates a noisy sine wave and tries to train a densely-connected feed-forward neural network to fit the data. My model has two linear layers, each with 50 hidden units and a ReLU activation function. The experiments are parameterized with the variable num_points which I will increase.
import tensorflow as tf
from tensorflow import keras
from tensorflow.keras import layers
import numpy as np
import matplotlib.pyplot as plt
np.random.seed(7)
def generate_data(num_points=100):
X = np.linspace(0.0 , 2.0 * np.pi, num_points).reshape(-1, 1)
noise = np.random.normal(0, 1, num_points).reshape(-1, 1)
y = 3 * np.sin(X) + noise
return X, y
def run_experiment(X_train, y_train, X_test, batch_size=64):
num_points = X_train.shape[0]
model = keras.Sequential()
model.add(layers.Dense(50, input_shape=(1, ), activation='relu'))
model.add(layers.Dense(50, activation='relu'))
model.add(layers.Dense(1, activation='linear'))
model.compile(loss = "mse", optimizer = "adam", metrics=["mse"] )
history = model.fit(X_train, y_train, epochs=10,
batch_size=batch_size, verbose=0)
yhat = model.predict(X_test, batch_size=batch_size)
plt.figure(figsize=(5, 5))
plt.plot(X_train, y_train, "ro", markersize=2, label='True')
plt.plot(X_train, yhat, "bo", markersize=1, label='Predicted')
plt.ylim(-5, 5)
plt.title('N=%d points' % (num_points))
plt.legend()
plt.grid()
plt.show()
Here is how I invoke the code:
num_points = 100
X, y = generate_data(num_points)
run_experiment(X, y, X)
Now, if I run the experiment with num_points = 100, the model predictions (in blue) do a terrible job at fitting the true noisy sine wave (in red).
Now, here is num_points = 1000:
Here is num_points = 10000:
And here is num_points = 100000:
As you can see, for my chosen NN architecture, adding more training instances allows the neural network to better (over)fit the data.
If you do have a lot of training instances, then if you want to purposefully overfit your data, you can either increase the neural network capacity or reduce regularization. Specifically, you can control the following knobs:
increase the number of layers
increase the number of hidden units
increase the number of features per data instance
reduce regularization (e.g. by removing dropout layers)
use a more complex neural network architecture (e.g. transformer blocks instead of RNN)
You may be wondering if neural networks can fit arbitrary data rather than just a noisy sine wave as in my example. Previous research says that, yes, a big enough neural network can fit any data. See:
Universal approximation theorem. https://en.wikipedia.org/wiki/Universal_approximation_theorem
Zhang 2016, "Understanding deep learning requires rethinking generalization". https://arxiv.org/abs/1611.03530
As discussed in the comments, you should make a Python array (with NumPy) like this:-
Myarray = [[0.65, 1], [0.85, 0.5], ....]
Then you would just call those specific parts of the array whom you need to predict. Here the first value is the x-axis value. So you would call it to obtain the corresponding pair stored in Myarray
There are many resources to learn these types of things. some of them are ===>
https://www.geeksforgeeks.org/python-using-2d-arrays-lists-the-right-way/
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=video&cd=2&cad=rja&uact=8&ved=0ahUKEwjGs-Oxne3oAhVlwTgGHfHnDp4QtwIILTAB&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DQgfUT7i4yrc&usg=AOvVaw3LympYRszIYi6_OijMXH72

Found input variables with inconsistent numbers of samples: [2, 144]

I am having a training data set consisting of 144 feedback with 72 positive and 72 negative respectively. there are two target labels positive and negative respectively. Consider the following code segment :
import pandas as pd
feedback_data = pd.read_csv('output.csv')
print(feedback_data)
data target
0 facilitates good student teacher communication. positive
1 lectures are very lengthy. negative
2 the teacher is very good at interaction. positive
3 good at clearing the concepts. positive
4 good at clearing the concepts. positive
5 good at teaching. positive
6 does not shows test copies. negative
7 good subjective knowledge. positive
from sklearn.feature_extraction.text import CountVectorizer
cv = CountVectorizer(binary = True)
cv.fit(feedback_data)
X = cv.transform(feedback_data)
X_test = cv.transform(feedback_data_test)
from sklearn import svm
from sklearn.metrics import accuracy_score
from sklearn.model_selection import train_test_split
target = [1 if i<72 else 0 for i in range(144)]
# the below line gives error
X_train, X_val, y_train, y_val = train_test_split(X, target, train_size = 0.50)
I do not understand what the problem is. Please help.
You are not using the count vectorizer right. This what you have now:
from sklearn.feature_extraction.text import CountVectorizer
cv = CountVectorizer(binary = True)
cv.fit(df)
X = cv.transform(df)
X
<2x2 sparse matrix of type '<class 'numpy.int64'>'
with 2 stored elements in Compressed Sparse Row format>
So you see that you don't achieve what you want. you do not transform each line correctly. You don't even train the count vectorizer right because you use the entire DataFrame and not just the corpus of comments.
To solve the issue we need to make sure that the Count is well done:
if you do this (Use the right corpus):
cv = CountVectorizer(binary = True)
cv.fit(df['data'].values)
X = cv.transform(df)
X
<2x23 sparse matrix of type '<class 'numpy.int64'>'
with 0 stored elements in Compressed Sparse Row format>
you see that we are coming close to what we want. We just have to transform it right (transform each line):
cv = CountVectorizer(binary = True)
cv.fit(df['data'].values)
X = df['data'].apply(lambda x: cv.transform([x])).values
X
array([<1x23 sparse matrix of type '<class 'numpy.int64'>'
with 5 stored elements in Compressed Sparse Row format>,
...
<1x23 sparse matrix of type '<class 'numpy.int64'>'
with 3 stored elements in Compressed Sparse Row format>], dtype=object)
We have a more suitable X! Now we just need to check if we can split:
target = [1 if i<72 else 0 for i in range(8)] # The dataset is here of size 8
# the below line gives error
X_train, X_val, y_train, y_val = train_test_split(X, target, train_size = 0.50)
And it works!
You need to be sure you understand what CountVectorizer do to use it the right way

CountVectorizer Error: ValueError: setting an array element with a sequence

I am having a data set of 144 student feedback with 72 positive and 72 negative feedback respectively. The data set has two attributes namely data and target which contain the sentence and the sentiment(positive or negative) respectively.
Consider the following code:
import pandas as pd
feedback_data = pd.read_csv('output.csv')
print(feedback_data)
data target
0 facilitates good student teacher communication. positive
1 lectures are very lengthy. negative
2 the teacher is very good at interaction. positive
3 good at clearing the concepts. positive
4 good at clearing the concepts. positive
5 good at teaching. positive
6 does not shows test copies. negative
7 good subjective knowledge. positive
8 good communication skills. positive
9 good teaching methods. positive
10 posseses very good and thorough knowledge of t... positive
11 posseses superb ability to provide a lots of i... positive
12 good conceptual skills and knowledge for subject. positive
13 no commuication outside class. negative
14 rude behaviour. negative
15 very negetive attitude towards students. negative
16 good communication skills, lacks time punctual... positive
17 explains in a better way by giving practical e... positive
18 hardly comes on time. negative
19 good communication skills. positive
20 to make students comfortable with the subject,... negative
21 associated to original world. positive
22 lacks time punctuality. negative
from sklearn.feature_extraction.text import CountVectorizer
cv = CountVectorizer(binary = True)
cv.fit(feedback_data['data'].values)
X = feedback_data['data'].apply(lambda X : cv.transform([X])).values
X_test = cv.transform(feedback_data_test)
from sklearn import svm
from sklearn.metrics import accuracy_score
from sklearn.model_selection import train_test_split
target = [1 if i<72 else 0 for i in range(144)]
print(target)
X_train, X_val, y_train, y_val = train_test_split(X, target, train_size = 0.50)
clf = svm.SVC(kernel = 'linear', gamma = 0.001, C = 0.05)
#The below line gives the error
clf.fit(X , target)
I do not know what is wrong. Please help
The error comes from the way X as been done. You cannot use directly X in the Fit method. You need first to transform it a little bit more (i could not have told you that for the other problem as i did not have the info)
right now you have the following:
array([<1x23 sparse matrix of type '<class 'numpy.int64'>'
with 5 stored elements in Compressed Sparse Row format>,
...
<1x23 sparse matrix of type '<class 'numpy.int64'>'
with 3 stored elements in Compressed Sparse Row format>], dtype=object)
Which is enough to do a split.
We are just going to transform it you can understand and so will the fit method:
X = list([list(x.toarray()[0]) for x in X])
What we do is convert the sparse matrix to a numpy array, take the first element (it has only one element) and then convert it to a list to make sure it has the right dimension.
Now why are we doing this:
X is something like that
>>>X[0]
<1x23 sparse matrix of type '<class 'numpy.int64'>'
with 5 stored elements in Compressed Sparse Row format>
so we transform it to see what it realy is:
>>>X[0].toarray()
array([[0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0,
0]], dtype=int64)
and then as you see there is a slight issue with the dimension so we take the first element.
going back to a list does nothing, it's just for you to understand well what you see. (you can dump it for speed)
your code is now this:
cv = CountVectorizer(binary = True)
cv.fit(df['data'].values)
X = df['data'].apply(lambda X : cv.transform([X])).values
X = list([list(x.toarray()[0]) for x in X])
clf = svm.SVC(kernel = 'linear', gamma = 0.001, C = 0.05)
clf.fit(X, target)

Under what parameters are SVC and LinearSVC in scikit-learn equivalent?

I read this thread about the difference between SVC() and LinearSVC() in scikit-learn.
Now I have a data set of binary classification problem(For such a problem, the one-to-one/one-to-rest strategy difference between both functions could be ignore.)
I want to try under what parameters would these 2 functions give me the same result. First of all, of course, we should set kernel='linear' for SVC()
However, I just could not get the same result from both functions. I could not find the answer from the documents, could anybody help me to find the equivalent parameter set I am looking for?
Updated:
I modified the following code from an example of the scikit-learn website, and apparently they are not the same:
import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm, datasets
# import some data to play with
iris = datasets.load_iris()
X = iris.data[:, :2] # we only take the first two features. We could
# avoid this ugly slicing by using a two-dim dataset
y = iris.target
for i in range(len(y)):
if (y[i]==2):
y[i] = 1
h = .02 # step size in the mesh
# we create an instance of SVM and fit out data. We do not scale our
# data since we want to plot the support vectors
C = 1.0 # SVM regularization parameter
svc = svm.SVC(kernel='linear', C=C).fit(X, y)
lin_svc = svm.LinearSVC(C=C, dual = True, loss = 'hinge').fit(X, y)
# create a mesh to plot in
x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
# title for the plots
titles = ['SVC with linear kernel',
'LinearSVC (linear kernel)']
for i, clf in enumerate((svc, lin_svc)):
# Plot the decision boundary. For that, we will assign a color to each
# point in the mesh [x_min, m_max]x[y_min, y_max].
plt.subplot(1, 2, i + 1)
plt.subplots_adjust(wspace=0.4, hspace=0.4)
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
# Put the result into a color plot
Z = Z.reshape(xx.shape)
plt.contourf(xx, yy, Z, cmap=plt.cm.Paired, alpha=0.8)
# Plot also the training points
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Paired)
plt.xlabel('Sepal length')
plt.ylabel('Sepal width')
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())
plt.xticks(())
plt.yticks(())
plt.title(titles[i])
plt.show()
Result:
Output Figure from previous code
In mathematical sense you need to set:
SVC(kernel='linear', **kwargs) # by default it uses RBF kernel
and
LinearSVC(loss='hinge', **kwargs) # by default it uses squared hinge loss
Another element, which cannot be easily fixed is increasing intercept_scaling in LinearSVC, as in this implementation bias is regularized (which is not true in SVC nor should be true in SVM - thus this is not SVM) - consequently they will never be exactly equal (unless bias=0 for your problem), as they assume two different models
SVC : 1/2||w||^2 + C SUM xi_i
LinearSVC: 1/2||[w b]||^2 + C SUM xi_i
Personally I consider LinearSVC one of the mistakes of sklearn developers - this class is simply not a linear SVM.
After increasing intercept scaling (to 10.0)
However, if you scale it up too much - it will also fail, as now tolerance and number of iterations are crucial.
To sum up: LinearSVC is not linear SVM, do not use it if do not have to.

Machine Learning- Dividing data into test and train sets

How to divide a given dataset into train and test sets along with their correct labels.
There is an implementation for same through sklearn library :
from sklearn.cross_validation import train_test_split
train, test = train_test_split(df, test_size = 0.2)
where df is the original dataset....for eg : a list of strings
The problem is that it doesnt take the target/labels along with the data sets. So we cannot track which label belongs to what data point...
Is there any way to bind data points and their labels and then split the data sets into train and test?
sklearn.cross_validation.train_test_split essentially takes a variable number of arrays which it will split
*arrays : sequence of arrays or scipy.sparse matrices with same shape[0]
Returns:
splitting : list of arrays, length=2 * len(arrays)
List containing train-test split of input array.
so you can just add along the labels list:
from sklearn import cross_validation
df = ['the', 'quick', 'brown', 'fox']
labels = [0, 1, 0, 0]
>> cross_validation.train_test_split(df, labels, test_size=0.2)
[['quick', 'fox', 'the'], ['brown'], [1, 0, 0], [0]]

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