2nd pass for some paragraphs in ch5. (#263)

05.understand_sentiment/README.en.md

@@ -4,7 +4,7 @@ The source codes of this section can be located at [book/understand_sentiment](h
 
 ## Background
 
-In natural language processing, sentiment analysis refers to describing emotion status in texts. The texts may refer to a sentence, a paragraph or a document. Emotion status can be a binary classification problem (positive/negative or happy/sad), or a three-class problem (positive/neutral/negative). Sentiment analysis can be applied widely in various situations, such as online shopping (Amazon, Taobao), travel and movie websites. It can be used to grasp from the reviews how the customers feel about the product. Table 1 is an example of sentiment analysis in movie reviews:
+In natural language processing, sentiment analysis refers to determining the emotion expressed in a piece of text. The text can be a sentence, a paragraph, or a document. Emotion categorization can be binary -- positive/negative or happy/sad -- or in three classes -- positive/neutral/negative. Sentiment analysis is applicable in a wide range of services, such as e-commerce sites like Amazon and Taobao, hospitality services like Airbnb and hotels.com, and movie rating sites like Rotten Tomatoes and IMDB. It can be used to gauge from the reviews how the customers feel about the product. Table 1 illustrates an example of sentiment analysis in movie reviews:
 
 | Movie Review       | Category  |
 | --------     | -----  |
@@ -15,23 +15,22 @@ In natural language processing, sentiment analysis refers to describing emotion
 
 <p align="center">Table 1 Sentiment Analysis in Movie Reviews</p>
 
-In natural language processing, sentiment analysis can be categorized as a **Text Classification problem**, i.e., to categorize a piece of text to a specific class. It involves two related tasks: text representation and classification. Before deep learning becomes heated, the main-stream methods for the former include BOW (bag of words) and topic modeling, while the latter contain SVM(support vector machine), LR(logistic regression).
+In natural language processing, sentiment analysis can be categorized as a **Text Classification problem**, i.e., to categorize a piece of text to a specific class. It involves two related tasks: text representation and classification. Before the emergence of deep learning techniques, the mainstream methods for text representation include BOW (*bag of words*) and topic modeling, while the latter contain SVM (*support vector machine*) and LR (*logistic regression*).
 
-For a piece of text, BOW model ignores its word order, grammar and syntax, and regard it as a set of words, so BOW does not capture all the information in the text. For example, “this movie is extremely bad“ and “boring, dull and empty work” describe very similar semantic with low similarity in sense of BOW. Also, “the movie is bad“ and “the movie is not bad“ have high similarity with BOW feature, but they express completely opposite semantics.
+The BOW model does not capture all the information in a piece of text, as it ignores syntax and grammar and just treats the text as a set of words. For example, “this movie is extremely bad“ and “boring, dull, and empty work” describe very similar semantic meaning, yet their BOW representations have with little similarity. Furthermore, “the movie is bad“ and “the movie is not bad“ have high similarity with BOW features, but they express completely opposite semantics.
 
-
-In this chapter, we introduce our deep learning model which handles these issues in BOW. Our model embeds texts into a low-dimensional space and takes word order into consideration. It is an end-to-end framework, and has large performance improvement over traditional methods \[[1](#Reference)\].
+This chapter introduces a deep learning model that handles these issues in BOW. Our model embeds texts into a low-dimensional space and takes word order into consideration. It is an end-to-end framework and it has large performance improvement over traditional methods \[[1](#Reference)\].
 
 ## Model Overview
 
-The model we used in this chapter is the CNN (Convolutional Neural Networks) and RNN (Recurrent Neural Networks) with some specific extension.
+The model we used in this chapter uses **Convolutional Neural Networks** (**CNNs**) and **Recurrent Neural Networks** (**RNNs**) with some specific extensions.
 
 
 ### Convolutional Neural Networks for Texts (CNN)
 
-Convolutional Neural Networks are always applied in data with grid-like topology, such as 2-d images and 1-d texts. CNN can combine extracted multiple local features to produce higher-level abstract semantics. Experimentally, CNN is very efficient for image and text modeling.
+**Convolutional Neural Networks** are frequently applied to data with grid-like topology such as two-dimensional images and one-dimensional texts. A CNN can extract multiple local features, combine them, and produce high-level abstractions, which correspond to semantic understanding. Empirically, CNN is shown to be efficient for image and text modeling.
 
-CNN mainly contains convolution and pooling operation, with various extensions. We briefly describe CNN here with an example \[[1](#Refernce)\]. As shown in Figure 1：
+CNN mainly contains convolution and pooling operation, with versatile combinations in various applications. Here, we briefly describe a CNN used to classify texts\[[1](#Refernce)\], as shown in Figure 1.
 
 
 <p align="center">
@@ -39,47 +38,46 @@ CNN mainly contains convolution and pooling operation, with various extensions.
 Figure 1. CNN for text modeling.
 </p>
 
-Assuming the length of the sentence is $n$, where the $i$-th word has embedding as $x_i\in\mathbb{R}^k$，where $k$ is the embedding dimensionality.
+Let $n$ be the length of the sentence to process, and the $i$-th word has embedding as $x_i\in\mathbb{R}^k$，where $k$ is the embedding dimensionality.
 
-First, we concatenate the words together: we piece every $h$ words as a window of length $h$: $x_{i:i+h-1}$. It refers to $x_{i},x_{i+1},\ldots,x_{i+h-1}$, where $i$ is the first word in the window, ranging from $1$ to $n-h+1$: $x_{i:i+h-1}\in\mathbb{R}^{hk}$.
+First, we concatenate the words by piecing together every $h$ words, each as a window of length $h$. This window is denoted as $x_{i:i+h-1}$, consisting of $x_{i},x_{i+1},\ldots,x_{i+h-1}$, where $x_i$ is the first word in the window and $i$ takes value ranging from $1$ to $n-h+1$: $x_{i:i+h-1}\in\mathbb{R}^{hk}$.
 
-Next, we apply the convolution operation: we apply the kernel $w\in\mathbb{R}^{hk}$ in each window, extracting features $c_i=f(w\cdot x_{i:i+h-1}+b)$，
-where $b\in\mathbb{R}$ is the bias and $f$ is a non-linear activation function such as $sigmoid$. Applying CNN on every window ${x_{1:h},x_{2:h+1},\ldots,x_{n-h+1:n}}$ produces a feature map as:
+Next, we apply the convolution operation: we apply the kernel $w\in\mathbb{R}^{hk}$ in each window, extracting features $c_i=f(w\cdot x_{i:i+h-1}+b)$, where $b\in\mathbb{R}$ is the bias and $f$ is a non-linear activation function such as $sigmoid$. Convolving by the kernel at every window ${x_{1:h},x_{2:h+1},\ldots,x_{n-h+1:n}}$ produces a feature map in the following form:
 
 $$c=[c_1,c_2,\ldots,c_{n-h+1}], c \in \mathbb{R}^{n-h+1}$$
 
-Next, we apply max pooling over time to represent the whole sentence $\hat c$, which is the maximum element across the feature map:
+Next, we apply *max pooling* over time to represent the whole sentence $\hat c$, which is the maximum element across the feature map:
 
 $$\hat c=max(c)$$
 
 In real applications, we will apply multiple CNN kernels on the sentences. It can be implemented efficiently by concatenating the kernels together as a matrix. Also, we can use CNN kernels with different kernel size (as shown in Figure 1 in different colors).
 
-Finally, the CNN features are concatenated together to produce a fixed-length representation, which can be combined with a softmax for sentiment analysis problem.
+Finally, concatenating the resulting features produces a fixed-length representation, which can be combined with a softmax to form the model for the sentiment analysis problem.
 
-For short texts, above CNN model can achieve high accuracy \[[1](#Reference)\]. If we want to extract more abstract representation, we may apply a deeper CNN model \[[2](#Reference),[3](#Reference)\].
+For short texts, the aforementioned CNN model can achieve very high accuracy \[[1](#Reference)\]. If we want to extract more abstract representations, we may apply a deeper CNN model \[[2](#Reference),[3](#Reference)\].
 
 ### Recurrent Neural Network (RNN)
 
-RNN is an effective model for sequential data. Theoretical, the  computational ability of RNN is Turing-complete \[[4](#Reference)\]. NLP is a classical sequential data, and RNN (especially its variant LSTM\[[5](#Reference)\]) achieves State-of-the-Art performance on various tasks in NLP, such as language modeling, syntax parsing, POS-tagging, image captioning, dialog, machine translation and so forth.
+RNN is an effective model for sequential data. In terms of computability, the RNN is Turing-complete \[[4](#Reference)\]. Since NLP is a classical problem on sequential data, the RNN, especially its variant LSTM\[[5](#Reference)\]), achieves state-of-the-art performance on various NLP tasks, such as language modeling, syntax parsing, POS-tagging, image captioning, dialog, machine translation, and so forth.
 
 <p align="center">
 <img src="image/rnn.png" width = "60%" align="center"/><br/>
-Figure 2. An illustration of an unrolled RNN across “time”.
+Figure 2. An illustration of an unfolded RNN in time.
 </p>
 
-As shown in Figure 2, we unroll an RNN: at $t$-th time step, the network takes the $t$-th input vector and the latent state from last time-step $h_{t-1}$ as inputs and compute the latent state of current step. The whole process is repeated until all inputs are consumed. If we regard the RNN as a function $f$, it can be formulated as:
+As shown in Figure 2, we unfold an RNN: at the $t$-th time step, the network takes two inputs: the $t$-th input vector $\vec{x_t}$ and the latent state from the last time-step $\vec{h_{t-1}}$. From those, it computes the latent state of the current step $\vec{h_t}$. This process is repeated until all inputs are consumed. Denoting the RNN as function $f$, it can be formulated as follows:
 
-$$h_t=f(x_t,h_{t-1})=\sigma(W_{xh}x_t+W_{hh}h_{h-1}+b_h)$$
+$$\vec{h_t}=f(\vec{x_t},\vec{h_{t-1}})=\sigma(W_{xh}\vec{x_t}+W_{hh}\vec{h_{h-1}}+\vec{b_h})$$
 
-where $W_{xh}$ is the weight matrix from input to latent; $W_{hh}$ is the latent-to-latent matrix; $b_h$ is the latent bias and $\sigma$ refers to the $sigmoid$function.
+where $W_{xh}$ is the weight matrix to feed into the latent layer; $W_{hh}$ is the latent-to-latent matrix; $b_h$ is the latent bias and $\sigma$ refers to the $sigmoid$ function.
 
-In NLP, words are first represented as a one-hot vector and then mapped to an embedding. The embedded feature goes through an RNN as input $x_t$ at every time step. Moreover, we can add other layers on top of RNN. e.g., a deep or stacked RNN. Also, the last latent state can be used as a feature for sentence classification.
+In NLP, words are often represented as a one-hot vectors and then mapped to an embedding. The embedded feature goes through an RNN as input $x_t$ at every time step. Moreover, we can add other layers on top of RNN, such as a deep or stacked RNN. Finally, the last latent state may be used as a feature for sentence classification.
 
 ### Long-Short Term Memory (LSTM)
 
-For data of long sequence, training RNN sometimes has gradient vanishing and explosion problem \[[6](#)\]. To solve this problem Hochreiter S, Schmidhuber J. (1997) proposed the LSTM(long short term memory\[[5](#Reference)\]).  
+Training an RNN on long sequential data sometimes leads to the gradient vanishing or exploding\[[6](#)\]. To solve this problem Hochreiter S, Schmidhuber J. (1997) proposed **Long Short Term Memory** (LSTM)\[[5](#Reference)\]).
 
-Compared with simple RNN, the structrue of LSTM has included memory cell $c$, input gate $i$, forget gate $f$ and output gate $o$. These gates and memory cells largely improves the ability of handling long sequences. We can formulate LSTM-RNN as a function $F$ as：
+Compared to the structure of a simple RNN, an LSTM includes memory cell $c$, input gate $i$, forget gate $f$ and output gate $o$. These gates and memory cells dramatically improve the ability for the network to handle long sequences. We can formulate the **LSTM-RNN**, denoted as a function $F$, as follows：
 
 $$ h_t=F(x_t,h_{t-1})$$
 
@@ -87,12 +85,12 @@ $F$ contains following formulations\[[7](#Reference)\]：
 \begin{align}
 i_t & = \sigma(W_{xi}x_t+W_{hi}h_{h-1}+W_{ci}c_{t-1}+b_i)\\\\
 f_t & = \sigma(W_{xf}x_t+W_{hf}h_{h-1}+W_{cf}c_{t-1}+b_f)\\\\
-c_t & = f_t\odot c_{t-1}+i_t\odot tanh(W_{xc}x_t+W_{hc}h_{h-1}+b_c)\\\\
+c_t & = f_t\odot c_{t-1}+i_t\odot \tanh(W_{xc}x_t+W_{hc}h_{h-1}+b_c)\\\\
 o_t & = \sigma(W_{xo}x_t+W_{ho}h_{h-1}+W_{co}c_{t}+b_o)\\\\
-h_t & = o_t\odot tanh(c_t)\\\\
+h_t & = o_t\odot \tanh(c_t)\\\\
 \end{align}
 
-In the equation，$i_t, f_t, c_t, o_t$ stand for input gate, forget gate, memory cell and output gate separately; $W$ and $b$ are model parameters. The $tanh$ is a hyperbolic tangent， and $\odot$ denotes an element-wise product operation. Input gate controls the magnitude of new input into the memory cell $c$; forget gate controls memory propagated from the last time step; output gate controls output magnitude. The three gates are computed similarly with different parameters, and they influence memory cell $c$ separately, as shown in Figure 3:
+In the equation，$i_t, f_t, c_t, o_t$ stand for input gate, forget gate, memory cell and output gate, respectively. $W$ and $b$ are model parameters, $\tanh$ is a hyperbolic tangent, and $\odot$ denotes an element-wise product operation. The input gate controls the magnitude of the new input into the memory cell $c$; the forget gate controls the memory propagated from the last time step; the output gate controls the magnitutde of the output. The three gates are computed similarly with different parameters, and they influence memory cell $c$ separately, as shown in Figure 3:
 
 <p align="center">
 <img src="image/lstm_en.png" width = "65%" align="center"/><br/>

05.understand_sentiment/index.en.html

@@ -46,7 +46,7 @@ The source codes of this section can be located at [book/understand_sentiment](h
 
 ## Background
 
-In natural language processing, sentiment analysis refers to describing emotion status in texts. The texts may refer to a sentence, a paragraph or a document. Emotion status can be a binary classification problem (positive/negative or happy/sad), or a three-class problem (positive/neutral/negative). Sentiment analysis can be applied widely in various situations, such as online shopping (Amazon, Taobao), travel and movie websites. It can be used to grasp from the reviews how the customers feel about the product. Table 1 is an example of sentiment analysis in movie reviews:
+In natural language processing, sentiment analysis refers to determining the emotion expressed in a piece of text. The text can be a sentence, a paragraph, or a document. Emotion categorization can be binary -- positive/negative or happy/sad -- or in three classes -- positive/neutral/negative. Sentiment analysis is applicable in a wide range of services, such as e-commerce sites like Amazon and Taobao, hospitality services like Airbnb and hotels.com, and movie rating sites like Rotten Tomatoes and IMDB. It can be used to gauge from the reviews how the customers feel about the product. Table 1 illustrates an example of sentiment analysis in movie reviews:
 
 | Movie Review       | Category  |
 | --------     | -----  |
@@ -57,23 +57,22 @@ In natural language processing, sentiment analysis refers to describing emotion
 
 <p align="center">Table 1 Sentiment Analysis in Movie Reviews</p>
 
-In natural language processing, sentiment analysis can be categorized as a **Text Classification problem**, i.e., to categorize a piece of text to a specific class. It involves two related tasks: text representation and classification. Before deep learning becomes heated, the main-stream methods for the former include BOW (bag of words) and topic modeling, while the latter contain SVM(support vector machine), LR(logistic regression).
+In natural language processing, sentiment analysis can be categorized as a **Text Classification problem**, i.e., to categorize a piece of text to a specific class. It involves two related tasks: text representation and classification. Before the emergence of deep learning techniques, the mainstream methods for text representation include BOW (*bag of words*) and topic modeling, while the latter contain SVM (*support vector machine*) and LR (*logistic regression*).
 
-For a piece of text, BOW model ignores its word order, grammar and syntax, and regard it as a set of words, so BOW does not capture all the information in the text. For example, “this movie is extremely bad“ and “boring, dull and empty work” describe very similar semantic with low similarity in sense of BOW. Also, “the movie is bad“ and “the movie is not bad“ have high similarity with BOW feature, but they express completely opposite semantics.
+The BOW model does not capture all the information in a piece of text, as it ignores syntax and grammar and just treats the text as a set of words. For example, “this movie is extremely bad“ and “boring, dull, and empty work” describe very similar semantic meaning, yet their BOW representations have with little similarity. Furthermore, “the movie is bad“ and “the movie is not bad“ have high similarity with BOW features, but they express completely opposite semantics.
 
-
-In this chapter, we introduce our deep learning model which handles these issues in BOW. Our model embeds texts into a low-dimensional space and takes word order into consideration. It is an end-to-end framework, and has large performance improvement over traditional methods \[[1](#Reference)\].
+This chapter introduces a deep learning model that handles these issues in BOW. Our model embeds texts into a low-dimensional space and takes word order into consideration. It is an end-to-end framework and it has large performance improvement over traditional methods \[[1](#Reference)\].
 
 ## Model Overview
 
-The model we used in this chapter is the CNN (Convolutional Neural Networks) and RNN (Recurrent Neural Networks) with some specific extension.
+The model we used in this chapter uses **Convolutional Neural Networks** (**CNNs**) and **Recurrent Neural Networks** (**RNNs**) with some specific extensions.
 
 
 ### Convolutional Neural Networks for Texts (CNN)
 
-Convolutional Neural Networks are always applied in data with grid-like topology, such as 2-d images and 1-d texts. CNN can combine extracted multiple local features to produce higher-level abstract semantics. Experimentally, CNN is very efficient for image and text modeling.
+**Convolutional Neural Networks** are frequently applied to data with grid-like topology such as two-dimensional images and one-dimensional texts. A CNN can extract multiple local features, combine them, and produce high-level abstractions, which correspond to semantic understanding. Empirically, CNN is shown to be efficient for image and text modeling.
 
-CNN mainly contains convolution and pooling operation, with various extensions. We briefly describe CNN here with an example \[[1](#Refernce)\]. As shown in Figure 1：
+CNN mainly contains convolution and pooling operation, with versatile combinations in various applications. Here, we briefly describe a CNN used to classify texts\[[1](#Refernce)\], as shown in Figure 1.
 
 
 <p align="center">
@@ -81,47 +80,46 @@ CNN mainly contains convolution and pooling operation, with various extensions.
 Figure 1. CNN for text modeling.
 </p>
 
-Assuming the length of the sentence is $n$, where the $i$-th word has embedding as $x_i\in\mathbb{R}^k$，where $k$ is the embedding dimensionality.
+Let $n$ be the length of the sentence to process, and the $i$-th word has embedding as $x_i\in\mathbb{R}^k$，where $k$ is the embedding dimensionality.
 
-First, we concatenate the words together: we piece every $h$ words as a window of length $h$: $x_{i:i+h-1}$. It refers to $x_{i},x_{i+1},\ldots,x_{i+h-1}$, where $i$ is the first word in the window, ranging from $1$ to $n-h+1$: $x_{i:i+h-1}\in\mathbb{R}^{hk}$.
+First, we concatenate the words by piecing together every $h$ words, each as a window of length $h$. This window is denoted as $x_{i:i+h-1}$, consisting of $x_{i},x_{i+1},\ldots,x_{i+h-1}$, where $x_i$ is the first word in the window and $i$ takes value ranging from $1$ to $n-h+1$: $x_{i:i+h-1}\in\mathbb{R}^{hk}$.
 
-Next, we apply the convolution operation: we apply the kernel $w\in\mathbb{R}^{hk}$ in each window, extracting features $c_i=f(w\cdot x_{i:i+h-1}+b)$，
-where $b\in\mathbb{R}$ is the bias and $f$ is a non-linear activation function such as $sigmoid$. Applying CNN on every window ${x_{1:h},x_{2:h+1},\ldots,x_{n-h+1:n}}$ produces a feature map as:
+Next, we apply the convolution operation: we apply the kernel $w\in\mathbb{R}^{hk}$ in each window, extracting features $c_i=f(w\cdot x_{i:i+h-1}+b)$, where $b\in\mathbb{R}$ is the bias and $f$ is a non-linear activation function such as $sigmoid$. Convolving by the kernel at every window ${x_{1:h},x_{2:h+1},\ldots,x_{n-h+1:n}}$ produces a feature map in the following form:
 
 $$c=[c_1,c_2,\ldots,c_{n-h+1}], c \in \mathbb{R}^{n-h+1}$$
 
-Next, we apply max pooling over time to represent the whole sentence $\hat c$, which is the maximum element across the feature map:
+Next, we apply *max pooling* over time to represent the whole sentence $\hat c$, which is the maximum element across the feature map:
 
 $$\hat c=max(c)$$
 
 In real applications, we will apply multiple CNN kernels on the sentences. It can be implemented efficiently by concatenating the kernels together as a matrix. Also, we can use CNN kernels with different kernel size (as shown in Figure 1 in different colors).
 
-Finally, the CNN features are concatenated together to produce a fixed-length representation, which can be combined with a softmax for sentiment analysis problem.
+Finally, concatenating the resulting features produces a fixed-length representation, which can be combined with a softmax to form the model for the sentiment analysis problem.
 
-For short texts, above CNN model can achieve high accuracy \[[1](#Reference)\]. If we want to extract more abstract representation, we may apply a deeper CNN model \[[2](#Reference),[3](#Reference)\].
+For short texts, the aforementioned CNN model can achieve very high accuracy \[[1](#Reference)\]. If we want to extract more abstract representations, we may apply a deeper CNN model \[[2](#Reference),[3](#Reference)\].
 
 ### Recurrent Neural Network (RNN)
 
-RNN is an effective model for sequential data. Theoretical, the  computational ability of RNN is Turing-complete \[[4](#Reference)\]. NLP is a classical sequential data, and RNN (especially its variant LSTM\[[5](#Reference)\]) achieves State-of-the-Art performance on various tasks in NLP, such as language modeling, syntax parsing, POS-tagging, image captioning, dialog, machine translation and so forth.
+RNN is an effective model for sequential data. In terms of computability, the RNN is Turing-complete \[[4](#Reference)\]. Since NLP is a classical problem on sequential data, the RNN, especially its variant LSTM\[[5](#Reference)\]), achieves state-of-the-art performance on various NLP tasks, such as language modeling, syntax parsing, POS-tagging, image captioning, dialog, machine translation, and so forth.
 
 <p align="center">
 <img src="image/rnn.png" width = "60%" align="center"/><br/>
-Figure 2. An illustration of an unrolled RNN across “time”.
+Figure 2. An illustration of an unfolded RNN in time.
 </p>
 
-As shown in Figure 2, we unroll an RNN: at $t$-th time step, the network takes the $t$-th input vector and the latent state from last time-step $h_{t-1}$ as inputs and compute the latent state of current step. The whole process is repeated until all inputs are consumed. If we regard the RNN as a function $f$, it can be formulated as:
+As shown in Figure 2, we unfold an RNN: at the $t$-th time step, the network takes two inputs: the $t$-th input vector $\vec{x_t}$ and the latent state from the last time-step $\vec{h_{t-1}}$. From those, it computes the latent state of the current step $\vec{h_t}$. This process is repeated until all inputs are consumed. Denoting the RNN as function $f$, it can be formulated as follows:
 
-$$h_t=f(x_t,h_{t-1})=\sigma(W_{xh}x_t+W_{hh}h_{h-1}+b_h)$$
+$$\vec{h_t}=f(\vec{x_t},\vec{h_{t-1}})=\sigma(W_{xh}\vec{x_t}+W_{hh}\vec{h_{h-1}}+\vec{b_h})$$
 
-where $W_{xh}$ is the weight matrix from input to latent; $W_{hh}$ is the latent-to-latent matrix; $b_h$ is the latent bias and $\sigma$ refers to the $sigmoid$function.
+where $W_{xh}$ is the weight matrix to feed into the latent layer; $W_{hh}$ is the latent-to-latent matrix; $b_h$ is the latent bias and $\sigma$ refers to the $sigmoid$ function.
 
-In NLP, words are first represented as a one-hot vector and then mapped to an embedding. The embedded feature goes through an RNN as input $x_t$ at every time step. Moreover, we can add other layers on top of RNN. e.g., a deep or stacked RNN. Also, the last latent state can be used as a feature for sentence classification.
+In NLP, words are often represented as a one-hot vectors and then mapped to an embedding. The embedded feature goes through an RNN as input $x_t$ at every time step. Moreover, we can add other layers on top of RNN, such as a deep or stacked RNN. Finally, the last latent state may be used as a feature for sentence classification.
 
 ### Long-Short Term Memory (LSTM)
 
-For data of long sequence, training RNN sometimes has gradient vanishing and explosion problem \[[6](#)\]. To solve this problem Hochreiter S, Schmidhuber J. (1997) proposed the LSTM(long short term memory\[[5](#Reference)\]).  
+Training an RNN on long sequential data sometimes leads to the gradient vanishing or exploding\[[6](#)\]. To solve this problem Hochreiter S, Schmidhuber J. (1997) proposed **Long Short Term Memory** (LSTM)\[[5](#Reference)\]).
 
-Compared with simple RNN, the structrue of LSTM has included memory cell $c$, input gate $i$, forget gate $f$ and output gate $o$. These gates and memory cells largely improves the ability of handling long sequences. We can formulate LSTM-RNN as a function $F$ as：
+Compared to the structure of a simple RNN, an LSTM includes memory cell $c$, input gate $i$, forget gate $f$ and output gate $o$. These gates and memory cells dramatically improve the ability for the network to handle long sequences. We can formulate the **LSTM-RNN**, denoted as a function $F$, as follows：
 
 $$ h_t=F(x_t,h_{t-1})$$
 
@@ -129,12 +127,12 @@ $F$ contains following formulations\[[7](#Reference)\]：
 \begin{align}
 i_t & = \sigma(W_{xi}x_t+W_{hi}h_{h-1}+W_{ci}c_{t-1}+b_i)\\\\
 f_t & = \sigma(W_{xf}x_t+W_{hf}h_{h-1}+W_{cf}c_{t-1}+b_f)\\\\
-c_t & = f_t\odot c_{t-1}+i_t\odot tanh(W_{xc}x_t+W_{hc}h_{h-1}+b_c)\\\\
+c_t & = f_t\odot c_{t-1}+i_t\odot \tanh(W_{xc}x_t+W_{hc}h_{h-1}+b_c)\\\\
 o_t & = \sigma(W_{xo}x_t+W_{ho}h_{h-1}+W_{co}c_{t}+b_o)\\\\
-h_t & = o_t\odot tanh(c_t)\\\\
+h_t & = o_t\odot \tanh(c_t)\\\\
 \end{align}
 
-In the equation，$i_t, f_t, c_t, o_t$ stand for input gate, forget gate, memory cell and output gate separately; $W$ and $b$ are model parameters. The $tanh$ is a hyperbolic tangent， and $\odot$ denotes an element-wise product operation. Input gate controls the magnitude of new input into the memory cell $c$; forget gate controls memory propagated from the last time step; output gate controls output magnitude. The three gates are computed similarly with different parameters, and they influence memory cell $c$ separately, as shown in Figure 3:
+In the equation，$i_t, f_t, c_t, o_t$ stand for input gate, forget gate, memory cell and output gate, respectively. $W$ and $b$ are model parameters, $\tanh$ is a hyperbolic tangent, and $\odot$ denotes an element-wise product operation. The input gate controls the magnitude of the new input into the memory cell $c$; the forget gate controls the memory propagated from the last time step; the output gate controls the magnitutde of the output. The three gates are computed similarly with different parameters, and they influence memory cell $c$ separately, as shown in Figure 3:
 
 <p align="center">
 <img src="image/lstm_en.png" width = "65%" align="center"/><br/>