數據統計

目錄

• Outline
• Vector norm
  • Eukl. Norm
  • L1 Norm
• reduce_min/max/mean
• argmax/argmin
• tf.equal
• Accuracy
• tf.unique

Outline

• tf.norm

• tf.reduce_min/max/mean

• tf.argmax/argmin
• tf.equal

• tf.unique

Vector norm

• Eukl. Norm
  \[ ||x||_2=|\sum_{k}x_k^2|^{\frac{1}{2}} \]
• Max.norm
  \[ ||x||_{\infty}=max_k|x_k| \]

• L1-Norm
  \[ ||x||_1=\sum_{k}|x_k| \]

• Here talks about Vector Norm

Eukl. Norm

import tensorflow as tf

a = tf.ones([2, 2])
a

<tf.Tensor: id=11, shape=(2, 2), dtype=float32, numpy=
array([[1., 1.],
       [1., 1.]], dtype=float32)>

tf.norm(a)

<tf.Tensor: id=7, shape=(), dtype=float32, numpy=2.0>

tf.sqrt(tf.reduce_sum(tf.square(a)))

<tf.Tensor: id=16, shape=(), dtype=float32, numpy=2.0>

a = tf.ones([4, 28, 28, 3])
a.shape

TensorShape([4, 28, 28, 3])

tf.norm(a)

<tf.Tensor: id=25, shape=(), dtype=float32, numpy=96.99484>

tf.sqrt(tf.reduce_sum(tf.square(a)))

<tf.Tensor: id=30, shape=(), dtype=float32, numpy=96.99484>

L1 Norm

b = tf.ones([2, 2])

tf.norm(b)

<tf.Tensor: id=45, shape=(), dtype=float32, numpy=2.0>

tf.norm(b, ord=2, axis=1)

<tf.Tensor: id=51, shape=(2,), dtype=float32, numpy=array([1.4142135, 1.4142135], dtype=float32)>

tf.norm(b, ord=1)

<tf.Tensor: id=56, shape=(), dtype=float32, numpy=4.0>

# 列爲總體
tf.norm(b, ord=1, axis=0)

<tf.Tensor: id=66, shape=(2,), dtype=float32, numpy=array([2., 2.], dtype=float32)>

# 行爲總體
tf.norm(b, ord=1, axis=1)

<tf.Tensor: id=71, shape=(2,), dtype=float32, numpy=array([2., 2.], dtype=float32)>

reduce_min/max/mean

• reduce，操做可能會有減維的功能，如[2,2]，對行求max，會變成[2]

a = tf.random.normal([4, 10])

tf.reduce_min(a), tf.reduce_max(a), tf.reduce_mean(a)

(<tf.Tensor: id=80, shape=(), dtype=float32, numpy=-2.215113>,
 <tf.Tensor: id=82, shape=(), dtype=float32, numpy=1.9458845>,
 <tf.Tensor: id=84, shape=(), dtype=float32, numpy=-0.045550883>)

# 對某一行求max
tf.reduce_min(a, axis=1), tf.reduce_max(a, axis=1), tf.reduce_mean(a, axis=1)

(<tf.Tensor: id=98, shape=(4,), dtype=float32, numpy=array([-2.215113 , -1.5824796, -1.4861531, -1.3477703], dtype=float32)>,
 <tf.Tensor: id=100, shape=(4,), dtype=float32, numpy=array([0.9380455, 1.1625607, 1.9458845, 1.492183 ], dtype=float32)>,
 <tf.Tensor: id=102, shape=(4,), dtype=float32, numpy=array([-0.48791748,  0.25639585,  0.07420422, -0.02488617], dtype=float32)>)

argmax/argmin

a.shape

TensorShape([4, 10])

tf.argmax(a).shape

TensorShape([10])

# 返回index
tf.argmax(a)

<tf.Tensor: id=112, shape=(10,), dtype=int64, numpy=array([1, 1, 2, 3, 2, 1, 3, 1, 2, 1])>

# 對第1維做用
tf.argmin(a).shape

TensorShape([10])

# 對第2維做用
tf.argmin(a, axis=1).shape

TensorShape([4])

tf.equal

a = tf.constant([1, 2, 3, 2, 5])

b = tf.range(5)

tf.equal(a, b)

<tf.Tensor: id=186, shape=(5,), dtype=bool, numpy=array([False, False, False, False, False])>

res = tf.equal(a, b)

# 對True和False轉換爲1和0
tf.reduce_sum(tf.cast(res, dtype=tf.int32))

<tf.Tensor: id=191, shape=(), dtype=int32, numpy=0>

Accuracy

a = tf.random.normal([2, 3])
a

<tf.Tensor: id=198, shape=(2, 3), dtype=float32, numpy=
array([[ 0.25201225, -1.3897187 ,  0.29240564],
       [-1.0671712 ,  2.1487093 ,  0.690736  ]], dtype=float32)>

pred = tf.cast(tf.argmax(a, axis=1), dtype=tf.int32)
pred.shape

TensorShape([2])

y = tf.constant([2, 1])
y

<tf.Tensor: id=163, shape=(2,), dtype=int32, numpy=array([2, 1], dtype=int32)>

tf.equal(y, pred)

<tf.Tensor: id=165, shape=(2,), dtype=bool, numpy=array([ True,  True])>

correct = tf.reduce_sum(tf.cast(tf.equal(y, pred), dtype=tf.int32))

correct

<tf.Tensor: id=170, shape=(), dtype=int32, numpy=2>

correct / 2

<tf.Tensor: id=175, shape=(), dtype=float64, numpy=1.0>

tf.unique

• 用於去重

a = tf.range(5)
a

<tf.Tensor: id=235, shape=(5,), dtype=int32, numpy=array([0, 1, 2, 3, 4], dtype=int32)>

# 返回索引
tf.unique(a)

Unique(y=<tf.Tensor: id=237, shape=(5,), dtype=int32, numpy=array([0, 1, 2, 3, 4], dtype=int32)>, idx=<tf.Tensor: id=238, shape=(5,), dtype=int32, numpy=array([0, 1, 2, 3, 4], dtype=int32)>)

a = tf.constant([4, 2, 2, 4, 3])
a

<tf.Tensor: id=226, shape=(5,), dtype=int32, numpy=array([4, 2, 2, 4, 3], dtype=int32)>

res = tf.unique(a)

Unique(y=<tf.Tensor: id=228, shape=(3,), dtype=int32, numpy=array([4, 2, 3], dtype=int32)>, idx=<tf.Tensor: id=229, shape=(5,), dtype=int32, numpy=array([0, 1, 1, 0, 2], dtype=int32)>)