[C語言]--APCS (106/10/28)

106年10月28日 APCS程式設計實作題 from 艾鍗科技

APCS 程式設計實作題 物品堆疊 from 艾鍗科技

 

Gnuplot-3D

splot "data.txt" using 1:2:3 with lines

#data.txt 每一條線隔2行空白, 線可分開繪製, 若是只隔一行空白則會連起來




#data.txt
# X   Y    Z
16    16   0
16   32   1
16   64   15
16    128  4
16    256  9


32    16   10
32   32   21
32    64   31
32    128  34
32    256  49


64    16   0
64   32   12
64   64   19
64    128  41
64    256  93


128   16   30
128   32   31
128   64   15
128   128  14
128   256  93


256   16   30
256   32   31
256   64   80
256   128  14
256   256  5

GPU vs CPU

如果你要跑CNN或是RNN , 由於Training Accuracy 要降, 沒有執行一定次數的參數update是無法做到的, 所以資料量大又要不斷運算, 藉由GPU來執行,會快上超多!

經實測結果以下面兩種平台法測試, 速度真得差了很多...

平台1: 沒有GPU的平台
CPU: model name   : Intel(R) Xeon(R) CPU E5-2620 v3 @ 2.40GHz
# of Thread    : 12
RAM: 10G
OS: Ubuntu 16.04

平台2 : 具有GPU的平台

CPU model name    : Intel Core i7-7700K CPU @ 4.5GHz

# of Thread     : 6

GPU: GeForce GTX 1080

RAM:  32G

OS: Ubuntu 16.04

DeviceQuery Example

.py 和 ipython notebook (.ipynb) 互轉?

1) 如何將 xxx .py 轉成 xxx.ipynb ?

在jupyter  notebook , 在一個cell 上執行

%load relu.py

就可以將relu.py 程式碼讀入, 然後再存檔, 就會自動存成了 relu.ipynb 了!

2) 如何將 xxx .ipynb 轉成 xxx.py ?

若有很多.ipynb 要轉換成.py , 可以執行下列命令
(在juypter notebook 下, 開啓一個程式cell來執行, 將hw3,ipynb --> hw3.py )

!jupyter nbconvert --to script hw3.ipynb

CNN using keras

傳統 DNN, Layer 是一個平面的

在CNN中, 每一個Layer是一個Cube

A ConvNet arranges its neurons in three dimensions (width, height, depth), as visualized in one of the layers. Every layer of a ConvNet transforms the 3D input volume to a 3D output volume of neuron activations. In this example, the red input layer holds the image, so its width and height would be the dimensions of the image, and the depth would be 3 (Red, Green, Blue channels).



An example input volume in red (e.g. a 32x32x3 CIFAR-10 image), and an example volume of neurons in the first Convolutional layer. Each neuron in the convolutional layer is connected only to a local region in the input volume spatially, but to the full depth (i.e. all color channels). Note, there are multiple neurons (5 in this example) along the depth, all looking at the same region in the input - see discussion of depth columns in text below


he neurons from the Neural Network chapter remain unchanged: They still compute a dot product of their weights with the input followed by a non-linearity, but their connectivity is now restricted to be local spatially.


 

Pooling layer downsamples the volume spatially, independently in each depth slice of the input volume. Left: In this example, the input volume of size [224x224x64] is pooled with filter size 2, stride 2 into output volume of size [112x112x64]. Notice that the volume depth is preserved. Right: The most common downsampling operation is max, giving rise to max pooling, here shown with a stride of 2. That is, each max is taken over 4 numbers (little 2x2 square).

如何計算參數量

# The data, shuffled and split between train and test sets:
(x_train, y_train), (x_test, y_test) = cifar10.load_data()
print('x_train shape:', x_train.shape)
print('y_train shape:', y_train.shape)
print(x_train.shape[0], 'train samples')
print(x_test.shape[0], 'test samples')

# Convert class vectors to binary class matrices.
y_train = keras.utils.to_categorical(y_train, num_classes)
y_test = keras.utils.to_categorical(y_test, num_classes)

model = Sequential()
model.add(Conv2D(2, (5, 5), padding='same', input_shape=x_train.shape[1:]))
print('input_shape:',x_train.shape[1:])
model.add(Activation('relu'))
model.add(Conv2D(32, (3, 3)))
model.add(Activation('relu'))
model.add(MaxPooling2D(pool_size=(2, 2)))
model.add(Dropout(0.25))

model.add(Conv2D(64, (3, 3), padding='same'))
model.add(Activation('relu'))
model.add(Conv2D(64, (3, 3)))
model.add(Activation('relu'))
model.add(MaxPooling2D(pool_size=(2, 2)))
model.add(Dropout(0.25))

model.add(Flatten())
model.add(Dense(512))
model.add(Activation('relu'))
model.add(Dropout(0.5))
model.add(Dense(num_classes))
model.add(Activation('softmax'))

# initiate RMSprop optimizer
opt = keras.optimizers.rmsprop(lr=0.0001, decay=1e-6)

# Let's train the model using RMSprop
model.compile(loss='categorical_crossentropy',
              optimizer=opt,
              metrics=['accuracy'])
model.summary()

x_train = x_train.astype('float32')
x_test = x_test.astype('float32')
x_train /= 255
x_test /= 255

_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
conv2d_46 (Conv2D)           (None, 32, 32, 2)         152  ((5*5*3)+1)*2=152
                                  其他位置也都是共用這152參數,所以不是圖愈大參數愈多
                                  +1: bias 項, WX+b

______________________________________________________________

activation_67 (Activation)   (None, 32, 32, 2)         0         
_________________________________________________________________
conv2d_47 (Conv2D)           (None, 30, 30, 32)        608  ((3*3*2)+1)*32=608      

_________________________________________________________________
activation_68 (Activation)   (None, 30, 30, 32)        0         
_________________________________________________________________
max_pooling2d_23 (MaxPooling (None, 15, 15, 32)        0         
_________________________________________________________________
dropout_34 (Dropout)         (None, 15, 15, 32)        0         
_________________________________________________________________
conv2d_48 (Conv2D)           (None, 15, 15, 64)        18496     
_________________________________________________________________
activation_69 (Activation)   (None, 15, 15, 64)        0         
_________________________________________________________________
conv2d_49 (Conv2D)           (None, 13, 13, 64)        36928     
_________________________________________________________________
activation_70 (Activation)   (None, 13, 13, 64)        0         
_________________________________________________________________
max_pooling2d_24 (MaxPooling (None, 6, 6, 64)          0         
_________________________________________________________________
dropout_35 (Dropout)         (None, 6, 6, 64)          0         
_________________________________________________________________
flatten_12 (Flatten)         (None, 2304)              0         
_________________________________________________________________
dense_23 (Dense)             (None, 512)               1180160   
_________________________________________________________________
activation_71 (Activation)   (None, 512)               0         
_________________________________________________________________
dropout_36 (Dropout)         (None, 512)               0         
_________________________________________________________________
dense_24 (Dense)             (None, 10)                5130      
_________________________________________________________________
activation_72 (Activation)   (None, 10)                0         
=================================================================
Total params: 1,241,474
Trainable params: 1,241,474
Non-trainable params: 0
_________________________________________________________________

PCA

In PCA, we are interested to find the directions (components) that maximize the variance in our dataset. In DataSet, 某些Feature對於每一筆X有比較大的差異, 對Y分類影響會比較明顯。若Feature 對於所有X都差不多, 則此Feature並不是作為分群(Partition)的最好選擇。

PCA(n_components=2), 會自動找出前2個主要Feature。下圖為2維, 畫出其分類(0,1,2)的狀態

==============

Residual variance ?

Then you fit a regression model. You use the regression equation to calculate a predicted score for each person.

Then you find the difference between the predicted scores and the actual scores. You calculate the variance of the set of scores. It's the residual variance. The residual variance will be less than the total variance (or if your predictors are completely useless, they will be equal).

How much variance did you explain?
Explained variance = (total variance - residual variance)

The proportion of variance explained is therefore:

explained variance / total variance

If your predicted scores exactly match the outcome scores, you've perfectly predicted the scores, and you've explained all of the variance. The residuals are all zero.  

(Note: The calculations are done with sums of squares, variances will give a very slightly different answer as they are usually calculated as SS/(N-1). But if the sample is large, this difference is trivial).

Multi-layer Perceptron classifier

sklearn.linear_model.LogisticRegression
This model optimizes the log-loss function using LBFGS or stochastic gradient descent.

solver : 要使用那一種演算法去解最佳化的問題, 如 weight optimization.

solver : {‘newton-cg’, ‘lbfgs’, ‘liblinear’, ‘sag’, ‘saga’},
   default: ‘liblinear’ Algorithm to use in the optimization problem.

batch_size : int, optional, default ‘auto’

Size of minibatches for stochastic optimizers. If the solver is ‘lbfgs’, the classifier will not use minibatch. When set to “auto”, batch_size=min(200, n_samples)

max_iter : int, optional, default 200

Maximum number of iterations. The solver iterates until convergence (determined by ‘tol’) or this number of iterations. For stochastic solvers (‘sgd’, ‘adam’), note that this determines the number of epochs (how many times each data point will be used), not the number of gradient steps.

that is , total parameter update= (# of batch_size) * (# of epochs)

tol : float, optional, default 1e-4

Tolerance for the optimization. When the loss or score is not improving by at least tol for two consecutive iterations, unless learning_rate is set to ‘adaptive’, convergence is considered to be reached and training stops.

momentum : float, default 0.9

Momentum for gradient descent update. Should be between 0 and 1. Only used when solver=’sgd’.

early_stopping : bool, default False

Whether to use early stopping to terminate training when validation score is not improving. If set to true, it will automatically set aside 10% of training data as validation and terminate training when validation score is not improving by at least tol for two consecutive epochs. Only effective when solver=’sgd’ or ‘adam’

validation_fraction : float, optional, default 0.1

The proportion of training data to set aside as validation set for early stopping. Must be between 0 and 1. Only used if early_stopping is True

fit(X, y)	Fit the model to data matrix X and target(s) y.
get_params([deep])	Get parameters for this estimator.
predict(X)	Predict using the multi-layer perceptron classifier
predict_log_proba(X)	Return the log of probability estimates.
predict_proba(X)	Probability estimates.
score(X, y[, sample_weight])	Returns the mean accuracy on the given test data and labels.
set_params(**params)	Set the parameters of this estimator.

predict_proba(X) Probability estimates. The returned estimates for all classes are ordered by the label of classes.

Y=predict_proba(X) is a method of a (soft) classifier outputting the probability of the instance being in each of the classes.
Y 是一個list, 列出X 會落在Y分類中的機率值
若是二元分類, 則Y為落在0 或落在1的機率
若是多元分類, 則Y為落在各類別的機率值 (加起來的機率總合為1)