cirquit
PhD student with a focus on machine learning, distributed systems and functional programming.
Machine Learning Introduction
Introduction
1
Introduction
2
- Fundamentals
-
Introduction Supervised Learning
- Neural Nets with AND
- MNIST
-
Introduction Unsupervised Learning
- K-Means Clustering
-
Introduction Reinforcement Learning
- Q-Learning
- Summary
Structure
Fundamentals
3
Fundamentals
- What is ML?
- Why do we need it?
- What are the use cases?
- Do I need a Ph.D to understand all of this?
Supervised Learning
4
Supervised Learning
Mammal
Not a mammal
Mammal?
Supervised Learning
5
Logical AND - Problem
x1
x2
0
1
0
1
| x1 | x2 | ∧ |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
∧ = 0
∧ = 1
0
0
0
1
Supervised Learning
6
Logical AND - Problem
x1
x2
0
1
0
1
h < 0
h >= 0
h = 0 => x_2 = \frac{a + b \cdot x_1}{-c}
h=0=>x2=−ca+b⋅x1
h = a + b \cdot x_1 + c \cdot x_2
h=a+b⋅x1+c⋅x2
h
h
How to learn such a function?
Supervised Learning
7
Perceptron
\sum
∑
x_1
x1
x_2
x2
\cdot w_1
⋅w1
\cdot w_2
⋅w2
\sigma
σ
\sigma(\sum_{i=0} x_i \cdot w_i)
σ(∑i=0xi⋅wi)
x = input
x=input
w = weights
w=weights
\sigma = activation\; function
σ=activationfunction
x_n
xn
\cdot w_n
⋅wn
1
1
\cdot w_0
⋅w0
Supervised Learning
8
Perceptron for AND
\sum
∑
x_1
x1
x_2
x2
\cdot\; w_1
⋅w1
\cdot \; w_2
⋅w2
w_0 + x_1\cdot w_1 + x_2 \cdot w_2
w0+x1⋅w1+x2⋅w2
1
1
\cdot \; w_0
⋅w0
< 0: 0 (false)
>= 0: 1 (true)
h = a + x_1\cdot b + x_2 \cdot c
h=a+x1⋅b+x2⋅c
\sigma
σ
Supervised Learning
9
Perceptron for AND
-0.3 + 0 \cdot 0.3 + 1 \cdot 0.5 = 0.2
−0.3+0⋅0.3+1⋅0.5=0.2
0 = false
1 = true
Input:
x_1 = 0, \; x_2 = 1
x1=0,x2=1
Randomly choosen weights:
w_0 = -0.3, \; w_1 = 0.3, \; x_2 = 0.5
w0=−0.3,w1=0.3,x2=0.5
x1
x2
0
1
0
1
\sigma(0.2) = 1
σ(0.2)=1
Supervised Learning
10
Cost Function
| x_1 | x_2 | y | ^y | C |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | -1 |
| 1 | 0 | 0 | 1 | -1 |
| 1 | 1 | 1 | 1 | 0 |
\hat{y} = our\;result
y^=ourresult
y = desired\;result
y=desiredresult
cost = - \sum_{i\in\mathcal{M}} | y_i - \hat{y_i}|
cost=−∑i∈M∣yi−yi^∣
x1
x2
0
1
0
1
-1
-1
\mathcal{M} := misclassified\; patterns
M:=misclassifiedpatterns
= -2
=−2
Supervised Learning
11
Backpropagation
\hat{y} = \sigma (\sum_{i = 0} x_i \cdot w_i)
y^=σ(∑i=0xi⋅wi)
cost = -\sum_{i\in\mathcal{M}} | y_i - \hat{y_i}|
cost=−∑i∈M∣yi−yi^∣
\frac{\partial cost}{\partial w_i} \approx -\sum_{i \in \mathcal{M}} - x_i
∂wi∂cost≈−∑i∈M−xi
-1
0
0
1
- \sum |y_i - \hat{y_i} |
−∑∣yi−yi^∣
| \mathcal{M} |
∣M∣
w_i \leftarrow w_i + \eta \cdot (\sum_{i\in\mathcal{M}} -x_i)
wi←wi+η⋅(∑i∈M−xi)
Update rule:
Supervised Learning
12
Backpropagation
x_0 = 1, x_1 = 0, x_2 = 1
x0=1,x1=0,x2=1
w_i \leftarrow w_i + \eta \cdot (\sum_{i\in\mathcal{M}} -x_i)
wi←wi+η⋅(∑i∈M−xi)
Misclassified:
Update rule:
\eta = 0.1
η=0.1
Learning rate:
Weights:
w_0 = -0.3, w_1 = 0.3, w_2 = 0.5
w0=−0.3,w1=0.3,w2=0.5
w_0 = -0.3 + 0.1 \cdot (-1 - 1) = -0.5
w0=−0.3+0.1⋅(−1−1)=−0.5
w_1 = \;\;\;0.3 + 0.1 \cdot (0 - 1)\;\;\: = \;\;0.2
w1=0.3+0.1⋅(0−1)=0.2
w_2 = \;\;\;0.5 + 0.1 \cdot (-1 - 0) = \;\;0.4
w2=0.5+0.1⋅(−1−0)=0.4
Supervised Learning
13
Test
x1
x2
0
1
0
1
\sigma(-0.5 + 0.2 \cdot 0 + 0.4 \cdot 0) = \sigma(-0.5) = 0 \;
σ(−0.5+0.2⋅0+0.4⋅0)=σ(−0.5)=0
\sigma(-0.5 + 0.2 \cdot 0 + 0.4 \cdot 1) = \sigma(-0.1) = 0 \;
σ(−0.5+0.2⋅0+0.4⋅1)=σ(−0.1)=0
\sigma(-0.5 + 0.2 \cdot 1 + 0.4 \cdot 0) = \sigma(-0.3) = 0 \;
σ(−0.5+0.2⋅1+0.4⋅0)=σ(−0.3)=0
\sigma(-0.5 + 0.2 \cdot 1 + 0.4 \cdot 1) = \sigma(0.1) = 1 \;
σ(−0.5+0.2⋅1+0.4⋅1)=σ(0.1)=1
x_1 = 0, x_2 = 1:
x1=0,x2=1:
x_1 = 0, x_2 = 0:
x1=0,x2=0:
x_1 = 1, x_2 = 0:
x1=1,x2=0:
x_1 = 1, x_2 = 1:
x1=1,x2=1:
Supervised Learning
14
Summary
x1
x2
0
1
0
- Get labeled data (AND - Table)
- Run the data and calculate the error
- Use partial deriviative of cost function to create a learning rule
- For every mislabled sample, apply learning rule
- Hope that it's linear separable
XOR
1
Supervised Learning
15
Example - MNIST
?
13% #0
0% #1
5% #2
1% #3
67% #4
2% #5
2% #6
3% #7
3% #8
4% #9
Supervised Learning
16
Example - MNIST
?
13% #0
0% #1
5% #2
1% #3
67% #4
2% #5
2% #6
3% #7
3% #8
4% #9
Supervised Learning
17
Multiple Perceptrons
x_1
x1
x_2
x2
x =
x=
x_n
xn
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
b/w pixel data
softmax
softmax
\sigma(\textbf{z})_j = \frac{e^{\textbf{z}_j}}{\sum^{K}_{k = 1} e^{\textbf{z}_k}}
σ(z)j=∑k=1Kezkezj
13% #0
0% #1
5% #2
1% #3
67% #4
2% #5
2% #6
3% #7
3% #8
4% #9
\textbf{z}
z
Supervised Learning
18
Linear Separable
:= 0,1,0
:=0,1,0
:= 1,1,1
:=1,1,1
:= 1,1,0
:=1,1,0
:= 0,1,0
:=0,1,0
:= 1,1,1
:=1,1,1
:= 1,1,0
:=1,1,0
:= 0,1,1
:=0,1,1
:= 1,1,0
:=1,1,0
0
0
1
1
Index
b/w
= 6
=6
= 4
=4
= 5
=5
Supervised Learning
19
Multiple Layers of Perceptrons
x_1
x1
x_2
x2
x =
x=
x_n
xn
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
b/w pixel data
softmax
softmax
\sigma(\textbf{z})_j = \frac{e^{\textbf{z}_j}}{\sum^{K}_{k = 1} e^{\textbf{z}_k}}
σ(z)j=∑k=1Kezkezj
13% #0
0% #1
5% #2
1% #3
67% #4
2% #5
2% #6
3% #7
3% #8
4% #9
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
\sum
∑
Supervised Learning
20
Additional Information
- Convolutional Networks
- Recurrent Networks
- LSTM Neurons
Supervised Learning
21
Neural Style Transfer
https://handong1587.github.io/deep_learning/2015/10/09/fun-with-deep-learning.html
Supervised Learning
22
Neural Photorealistic Style Transfer
https://github.com/luanfujun/deep-photo-styletransfer
Supervised Learning
23
Text to Speech
Normal text
Randomly generated text
Music
https://deepmind.com/blog/wavenet-generative-model-raw-audio/
Unsupervised Learning
24
Unsupervised Learning
Feature 1
Feature 2
Feature 1
Feature 2
Unknown structure
Known structure
Unsupervised Learning
25
K - Means Clustering
Feature 1
Feature 2
0
0
1
1
2
2
3
3
1
1
2
2
3
3
X = \{ (1,2), (1,1), (2,3), (3,3) \}
X={(1,2),(1,1),(2,3),(3,3)}
C_1 = \{ (1,1) \}
C1={(1,1)}
C_2 = \{ (3,3) \}
C2={(3,3)}
euclid(\textbf{x}, \textbf{y}) = \sqrt{(\sum_{i = 0}^n (x_i - y_i)^2)}
euclid(x,y)=(∑i=0n(xi−yi)2)
euclid(x_1, C_1) = \sqrt{(1-2)^2 + (2-1)^2} = 1.41
euclid(x1,C1)=(1−2)2+(2−1)2=1.41
euclid(x_1, C_2) = \sqrt{(1-3)^2 + (2-3)^2} = 2.23
euclid(x1,C2)=(1−3)2+(2−3)2=2.23
Unsupervised Learning
26
K - Means Clustering
Feature 1
Feature 2
0
0
1
1
2
2
3
3
1
1
2
2
3
3
X = \{ (1,2), (1,1), (2,3), (3,3) \}
X={(1,2),(1,1),(2,3),(3,3)}
C_1 = \{ (1,1) \}
C1={(1,1)}
C_2 = \{ (3,3) \}
C2={(3,3)}
euclid(\textbf{x}, \textbf{y}) = \sqrt{(\sum_{i = 0}^n (x_i - y_i)^2)}
euclid(x,y)=(∑i=0n(xi−yi)2)
euclid(x_1, C_1) = \sqrt{(1-2)^2 + (2-1)^2} = 1.41
euclid(x1,C1)=(1−2)2+(2−1)2=1.41
euclid(x_1, C_2) = \sqrt{(1-3)^2 + (2-3)^2} = 2.23
euclid(x1,C2)=(1−3)2+(2−3)2=2.23
C_1 = \{ (\frac{1 + 1}{2} \cdot , \frac{1 + 2}{2}) \} = \{(1, 1.5)\}
C1={(21+1⋅,21+2)}={(1,1.5)}
Unsupervised Learning
27
K - Means Clustering
Feature 1
Feature 2
0
0
1
1
2
2
3
3
1
1
2
2
3
3
X = \{ (1,2), (1,1), (2,3), (3,3) \}
X={(1,2),(1,1),(2,3),(3,3)}
C_1 = \{ (1,1.5) \}
C1={(1,1.5)}
C_2 = \{ (3,3) \}
C2={(3,3)}
euclid(\textbf{x}, \textbf{y}) = \sqrt{(\sum_{i = 0}^n (x_i - y_i)^2)}
euclid(x,y)=(∑i=0n(xi−yi)2)
euclid(x_3, C_1) = \sqrt{(2-1)^2 + (3-1)^2} = 2.23
euclid(x3,C1)=(2−1)2+(3−1)2=2.23
euclid(x_3, C_2) = \sqrt{(2-3)^2 + (3-3)^2} = 1
euclid(x3,C2)=(2−3)2+(3−3)2=1
C_2 = \{ (\frac{2 + 3}{2}, \frac{3 + 3}{2}) \} = \{(2.5, 3)\}
C2={(22+3,23+3)}={(2.5,3)}
Unsupervised Learning
28
K - Means Clustering
Feature 1
Feature 2
0
0
1
1
2
2
3
3
1
1
2
2
3
3
X = \{ (1,2), (1,1), (2,3), (3,3) \}
X={(1,2),(1,1),(2,3),(3,3)}
C_1 = \{ (1,1.5) \}
C1={(1,1.5)}
C_2 = \{ (2.5,3) \}
C2={(2.5,3)}
euclid(\textbf{x}, \textbf{y}) = \sqrt{(\sum_{i = 0}^n (x_i - y_i)^2)}
euclid(x,y)=(∑i=0n(xi−yi)2)
\forall x \in X: euclid(x, C_1) < euclid(x,C_2): x \in C_1
∀x∈X:euclid(x,C1)<euclid(x,C2):x∈C1
\forall x \in X: euclid(x, C_1) > euclid(x,C_2): x \in C_2
∀x∈X:euclid(x,C1)>euclid(x,C2):x∈C2
\text{if updated, recompute centroid of } C_{1,2}
if updated, recompute centroid of C1,2
Unsupervised Learning
29
K - Means Clustering - Caveats
Feature 1
Feature 2
0
0
1
1
2
2
3
3
1
1
2
2
3
3
- Amount of clusters
Unsupervised Learning
30
K - Means Clustering - Caveats
Feature 1
Feature 2
0
0
1
1
2
2
3
3
1
1
2
2
3
3
- Amount of clusters
- Similarity measure
Unsupervised Learning
31
K - Means Clustering - Caveats
Feature 1
Feature 2
0
0
1
1
2
2
3
3
1
1
2
2
3
3
- Amount of clusters
- Similarity measure
- No convergence
Unsupervised Learning
32
Additional Information
- Principal Component Analysis
- Support Vector Machines
- Autoencoder
Unsupervised Learning
33
K-Means Clustering of 40K samples of homework
http://practicalquant.blogspot.de/2013/10/semi-automatic-method-for-grading-a-million-homework-assignments.html
Reinforcement Learning
34
Reinforcement Learning
Environment
Agent
Action
State
Reward
Reinforcement Learning
35
Formalizing RL
Environment
Agent
Action
s_t = \text{current state}
st=current state
r_t = \text{reward}
rt=reward
a_t = \text{action}
at=action
State
Reward
s_0
s0
r_1
r1
a_0
a0
\rightarrow
→
s_1
s1
,
,
,
,
t \;\;= \text{timestep}
t=timestep
Reinforcement Learning
36
Formalizing RL
Environment
Agent
Action
s_t = \text{current state}
st=current state
r_t = \text{reward}
rt=reward
a_t = \text{action}
at=action
State
Reward
s_0
s0
r_1
r1
a_0
a0
\rightarrow
→
s_1
s1
,
,
,
,
r_2
r2
a_1
a1
\rightarrow
→
s_2
s2
,
,
,
,
t \;\;= \text{timestep}
t=timestep
s_{n-1}
sn−1
r_n
rn
a_{n-1}
an−1
\rightarrow
→
s_n
sn
,
,
,
,
Reinforcement Learning
37
Reward
Environment
Agent
Action
s_t = \text{current state}
st=current state
r_t = \text{reward}
rt=reward
a_t = \text{action}
at=action
State
Reward
R = r_1 + r_2 + \ldots + r_n
R=r1+r2+…+rn
t \;\;= \text{timestep}
t=timestep
Reinforcement Learning
38
Timed Reward
Environment
Agent
Action
s_t = \text{current state}
st=current state
r_t = \text{reward}
rt=reward
a_t = \text{action}
at=action
State
Reward
R_t = r_t + r_{t+1} + \ldots + r_n
Rt=rt+rt+1+…+rn
t \;\;= \text{timestep}
t=timestep
Reinforcement Learning
39
Discount Rate
Environment
Agent
Action
s_t = \text{current state}
st=current state
r_t = \text{reward}
rt=reward
a_t = \text{action}
at=action
State
Reward
t \;\;= \text{timestep}
t=timestep
R_t = r_t +
Rt=rt+
\gamma \;= \text{discount rate} \; [0,1]
γ=discount rate[0,1]
(r_{t+1} + \ldots + r_n)
(rt+1+…+rn)
\gamma \cdot
γ⋅
Reinforcement Learning
40
Discount Rate
Environment
Agent
Action
s_t = \text{current state}
st=current state
r_t = \text{reward}
rt=reward
a_t = \text{action}
at=action
State
Reward
t \;\;= \text{timestep}
t=timestep
R_t = r_t +
Rt=rt+
\gamma \;= \text{discount rate} \; [0,1]
γ=discount rate[0,1]
r_{t+1} +
rt+1+
\gamma \cdot
γ⋅
r_{t+2} + \ldots +
rt+2+…+
r_n
rn
\gamma^2 \cdot
γ2⋅
\gamma^{n-t} \cdot
γn−t⋅
Reinforcement Learning
41
Short-Sighted Reward
Environment
Agent
Action
s_t = \text{current state}
st=current state
r_t = \text{reward}
rt=reward
a_t = \text{action}
at=action
State
Reward
t \;\;= \text{timestep}
t=timestep
R_t = r_t +
Rt=rt+
\gamma \;= 0
γ=0
r_{t+1} +
rt+1+
0 \cdot
0⋅
r_{t+2} + \ldots +
rt+2+…+
r_n
rn
0 \cdot
0⋅
0 \;\cdot
0⋅
\rightarrow R_t = r_t
→Rt=rt
Reinforcement Learning
42
Balanced Rewards
Environment
Agent
Action
s_t = \text{current state}
st=current state
r_t = \text{reward}
rt=reward
a_t = \text{action}
at=action
State
Reward
t \;\;= \text{timestep}
t=timestep
R_t = r_t +
Rt=rt+
\gamma \;= 0.9
γ=0.9
r_{t+1} +
rt+1+
0.9 \cdot
0.9⋅
r_{t+2} + \ldots +
rt+2+…+
r_n
rn
0.81 \cdot
0.81⋅
(\gamma^{n-t} \ll 0.9) \cdot
(γn−t≪0.9)⋅
Reinforcement Learning
43
Q(uality) - Learning
Environment
Agent
Action
s_t = \text{current state}
st=current state
r_t = \text{reward}
rt=reward
a_t = \text{action}
at=action
State
Reward
t \;\;= \text{timestep}
t=timestep
R_{t+1}
Rt+1
\gamma \;= \text{discount rate}
γ=discount rate
Q(
Q(
s_t
st
,
,
a_t
at
) = max (
)=max(
Represents the quality of an action in the current state, while continuing to play optimally from that point on
)
)
Reinforcement Learning
44
Q(uality) - Learning
s_t = \text{current state}
st=current state
r_t = \text{reward}
rt=reward
a_t = \text{action}
at=action
t \;\;= \text{timestep}
t=timestep
R_{t+1}
Rt+1
\gamma \;= \text{discount rate}
γ=discount rate
Q(
Q(
s_t
st
,
,
a_t
at
) = max (
)=max(
)
)
\pi \;= \text{policy}
π=policy
\pi
π
(
(
s_t
st
) = argmax_a[Q(
)=argmaxa[Q(
s_t
st
,
,
a
a
)]
)]
Problem: How to construct such a Q function?
Reinforcement Learning
45
Bellmann Equation
s_t = \text{current state}
st=current state
r_t = \text{reward}
rt=reward
a_t = \text{action}
at=action
t \;\;= \text{timestep}
t=timestep
\gamma \;= \text{discount rate}
γ=discount rate
Q
Q
(
(
s_t
st
) =
)=
s_{t+1}
st+1
,
,
a_{t+1}
at+1
)]
)]
,
,
a_t
at
r_{t+1}
rt+1
+ \; \gamma \cdot max_{a_{t+1}}[Q(
+γ⋅maxat+1[Q(
Maximal reward is defined as immediate reward + maximum future reward for next state
Reinforcement Learning
46
Learning Q-Function
s_t = \text{current state}
st=current state
r_t = \text{reward}
rt=reward
a_t = \text{action}
at=action
t \;\;= \text{timestep}
t=timestep
\gamma \;= \text{discount rate}
γ=discount rate
s_0
s0
a_0
a0
a_1
a1
\ldots
…
a_n
an
s_1
s1
s_n
sn
\vdots
⋮
0
0
0
0
\ldots
…
0
0
0
0
0
0
\ldots
…
0
0
\vdots
⋮
\vdots
⋮
\vdots
⋮
\ddots
⋱
0
0
0
0
\ldots
…
0
0
s_0
s0
\rightarrow
→
Reinforcement Learning
47
Learning Q-Function
s_0
s0
a_0
a0
a_1
a1
\ldots
…
a_n
an
s_1
s1
s_n
sn
\vdots
⋮
0.1
0.1
0
0
\ldots
…
0
0
0
0
0
0
\ldots
…
0
0
\vdots
⋮
\vdots
⋮
\vdots
⋮
\ddots
⋱
0
0
0
0
\ldots
…
0
0
s_0
s0
\rightarrow
→
\pi
π
(
(
s_0
s0
) = argmax_a[Q(
)=argmaxa[Q(
s_0
s0
,
,
a
a
)]
)]
s_1
s1
,
,
r_1 = 0.1
r1=0.1
\leftarrow \text{execute}
←execute
a_0
a0
Q[
Q[
s_0
s0
] =
]=
,
,
a_0
a0
0.1
0.1
Q[
Q[
s_0
s0
]
]
,
,
a_0
a0
+ \; \alpha \cdot(
+α⋅(
+ \; \gamma \cdot max_{a}[Q(
+γ⋅maxa[Q(
s_1
s1
,
,
a
a
)]
)]
-\;Q(
−Q(
s_0
s0
,
,
a_0
a0
)])
)])
\text{restart with}
restart with
s_1
s1
0
0
=
=
a_0
a0
Reinforcement Learning
48
Learning Q-Function with NNs
s_0
s0
\vdots
⋮
s_0
s0
\rightarrow
→
\pi
π
(
(
s_0
s0
) = \text{feedforward}
)=feedforward
s_0
s0
s_1
s1
,
,
r_1 = 0.1
r1=0.1
\leftarrow \text{execute}
←execute
a_0
a0
0.1
0.1
+ \; \gamma \cdot max_{a}[Q(
+γ⋅maxa[Q(
s_1
s1
,
,
a
a
)]
)]
\text{restart with}
restart with
s_1
s1
Q(
Q(
\rightarrow
→
NN
\rightarrow
→
s_0
s0
,
,
a_0
a0
)
)
Q(
Q(
\rightarrow
→
s_0
s0
,
,
a_1
a1
)
)
Q(
Q(
\rightarrow
→
s_0
s0
,
,
a_n
an
)
)
\text{feedforward}
feedforward
s_1
s1
\rightarrow
→
max_{a}[Q(
maxa[Q(
s_1
s1
,
,
a
a
)]
)]
\text{backprop for }
backprop for
s_0
s0
\text{with}
with
a_0
a0
,
,
Reinforcement Learning
49
Additional Information
Experience Replay
Exploration - Exploitation
\epsilon - \text{greedy}
ϵ−greedy
Slides adapted from excellent tutorial
https://www.nervanasys.com/demystifying-deep-reinforcement-learning/
Reinforcement Learning
50
TORCS
https://yanpanlau.github.io/2016/10/11/Torcs-Keras.html
Reinforcement Learning
51
Buzzwords we learned today
Perceptron
Backpropagation
Neural Nets
Supervised Learning
MNIST Dataset
Linear Separable
Unsupervised Learning
Clustering
K-Means
Distance Measures
Convergence
RL Learning
Policy
Q-Learning
Discount Rate
TORCS
Reinforcement Learning
52
Imagesources
- Cetacea - http://www.toggo.de/media/slider-wal-3-14295-10110.jpg
- Orca - http://elelur.com/mammals/orca.html
- Pinniped - http://www.interestingfunfacts.com/amazing-facts-about-pinniped.html
- Deep Sea Frill Shark - http://images.nationalgeographic.com/wpf/media-live/photos/000/181/cache/deep-sea01-frill-shark_18161_600x450.jpg
- Shark - http://www.livescience.com/55001-shark-attacks-increasing.html
- Dolphin - http://weknownyourdreamz.com/dolphin.html
Machine Learning Introduction Introduction 1
Machine Learning Introduction
By cirquit
Machine Learning Introduction
- 171
