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+# Embeddings
+
+[TOC]
+
+## Introduction
+
+An embedding is a mapping from discrete objects, such as words, to vectors of
+real numbers. For example, a 300-dimensional embedding for English words could
+include:
+
+```
+blue: (0.01359, 0.00075997, 0.24608, ..., -0.2524, 1.0048, 0.06259)
+blues: (0.01396, 0.11887, -0.48963, ..., 0.033483, -0.10007, 0.1158)
+orange: (-0.24776, -0.12359, 0.20986, ..., 0.079717, 0.23865, -0.014213)
+oranges: (-0.35609, 0.21854, 0.080944, ..., -0.35413, 0.38511, -0.070976)
+```
+
+Embeddings let you apply machine learning to discrete inputs. Classifiers, and
+neural networks more generally, are designed to work with dense continuous
+vectors, where all values contribute to define what an object is. If discrete
+objects are naively encoded as discrete atoms, e.g., unique id numbers, they
+hinder learning and generalization. One way to think of embeddings is as a way
+to transform non-vector objects into useful inputs for machine learning.
+
+Embeddings are also useful as outputs of machine learning. Because embeddings
+map objects to vectors, applications can use similarity in vector space (e.g.,
+Euclidean distance or the angle between vectors) as a robust and flexible
+measure of object similarity. One common use is to find nearest neighbors.
+Using the same word embeddings above, for instance, here are the three nearest
+neighbors for each word and the corresponding angles (in degrees):
+
+```
+blue: (red, 47.6°), (yellow, 51.9°), (purple, 52.4°)
+blues: (jazz, 53.3°), (folk, 59.1°), (bluegrass, 60.6°)
+orange: (yellow, 53.5°), (colored, 58.0°), (bright, 59.9°)
+oranges: (apples, 45.3°), (lemons, 48.3°), (mangoes, 50.4°)
+```
+
+This would tell an application that apples and oranges are in some way more
+similar (45.3° apart) than lemons and oranges (48.3° apart).
+
+## Training an Embedding
+
+To train word embeddings in TensorFlow, we first need to split the text into
+words and assign an integer to every word in the vocabulary. Let us assume that
+this has already been done, and that `word_ids` is a vector of these integers.
+For example, the sentence “I have a cat.” could be split into
+`[“I”, “have”, “a”, “cat”, “.”]` and then the corresponding `word_ids` tensor
+would have shape `[5]` and consist of 5 integers. To get these word ids
+embedded, we need to create the embedding variable and use the `tf.gather`
+function as follows:
+
+```
+word_embeddings = tf.get_variable(“word_embeddings”,
+ [vocabulary_size, embedding_size])
+embedded_word_ids = tf.gather(word_embeddings, word_ids)
+```
+
+After this, the tensor `embedded_word_ids` will have shape `[5, embedding_size]`
+in our example and contain the embeddings (dense vectors) for each of the 5
+words. The variable `word_embeddings` will be learned and at the end of the
+training it will contain the embeddings for all words in the vocabulary.
+The embeddings can be trained in many ways, depending on the data available.
+For example, one could use a recurrent neural network to predict the next word
+from the previous one given a large corpus of sentences, or one could train
+two networks to do multi-lingual translation. These methods are described in
+[Vector Representations of Words](../tutorials/word2vec.md) tutorial, but in
+all cases there is an embedding variable like above and words are embedded
+using `tf.gather`, as shown.
+
+## Visualizing Embeddings
+
+TensorBoard has a built-in visualizer, called the Embedding Projector,
+for interactive visualization of embeddings. The embedding projector will read
+the embeddings from your checkpoint file and project them into 3 dimensions using
+[principal component analysis](https://en.wikipedia.org/wiki/Principal_component_analysis).
+For a visual explanation of PCA, see
+[this article](http://setosa.io/ev/principal-component-analysis/). Another
+very useful projection you can use is
+[t-SNE](https://en.wikipedia.org/wiki/T-distributed_stochastic_neighbor_embedding).
+
+If you are working with an embedding, you'll probably want to attach
+labels/images to the data points. You can do this by generating a
+[metadata file](#metadata) containing the labels for each point and configuring
+the projector either by using our Python API, or manually constructing and
+saving a
+[projector_config.pbtxt](https://github.com/tensorflow/tensorflow/blob/master/tensorflow/tensorboard/plugins/projector/projector_config.proto)
+in the same directory as your checkpoint file.
+
+### Setup
+
+For in depth information on how to run TensorBoard and make sure you are
+logging all the necessary information, see
+[TensorBoard: Visualizing Learning](../get_started/summaries_and_tensorboard.md).
+
+To visualize your embeddings, there are 3 things you need to do:
+
+1) Setup a 2D tensor that holds your embedding(s).
+
+```python
+embedding_var = tf.get_variable(....)
+```
+
+2) Periodically save your model variables in a checkpoint in
+LOG_DIR
.
+
+```python
+saver = tf.train.Saver()
+saver.save(session, os.path.join(LOG_DIR, "model.ckpt"), step)
+```
+
+3) (Optional) Associate metadata with your embedding.
+
+If you have any metadata (labels, images) associated with your embedding, you
+can tell TensorBoard about it either by directly storing a
+[projector_config.pbtxt](https://github.com/tensorflow/tensorflow/blob/master/tensorflow/tensorboard/plugins/projector/projector_config.proto)
+in the LOG_DIR
, or use our python API.
+
+For instance, the following projector_config.ptxt
associates the
+word_embedding
tensor with metadata stored in $LOG_DIR/metadata.tsv
:
+
+```
+embeddings {
+ tensor_name: 'word_embedding'
+ metadata_path: '$LOG_DIR/metadata.tsv'
+}
+```
+
+The same config can be produced programmatically using the following code snippet:
+
+```python
+from tensorflow.contrib.tensorboard.plugins import projector
+
+# Create randomly initialized embedding weights which will be trained.
+vocabulary_size = 10000
+embedding_size = 200
+embedding_var = tf.get_variable('word_embedding', [vocabulary_size, embedding_size])
+
+# Format: tensorflow/tensorboard/plugins/projector/projector_config.proto
+config = projector.ProjectorConfig()
+
+# You can add multiple embeddings. Here we add only one.
+embedding = config.embeddings.add()
+embedding.tensor_name = embedding_var.name
+# Link this tensor to its metadata file (e.g. labels).
+embedding.metadata_path = os.path.join(LOG_DIR, 'metadata.tsv')
+
+# Use the same LOG_DIR where you stored your checkpoint.
+summary_writer = tf.summary.FileWriter(LOG_DIR)
+
+# The next line writes a projector_config.pbtxt in the LOG_DIR. TensorBoard will
+# read this file during startup.
+projector.visualize_embeddings(summary_writer, config)
+```
+
+After running your model and training your embeddings, run TensorBoard and point
+it to the LOG_DIR
of the job.
+
+```python
+tensorboard --logdir=LOG_DIR
+```
+
+Then click on the *Embeddings* tab on the top pane
+and select the appropriate run (if there are more than one run).
+
+
+### Metadata
+Usually embeddings have metadata associated with it (e.g. labels, images). The
+metadata should be stored in a separate file outside of the model checkpoint
+since the metadata is not a trainable parameter of the model. The format should
+be a [TSV file](https://en.wikipedia.org/wiki/Tab-separated_values)
+(tab characters shown in red) with the first line containing column headers
+(shown in bold) and subsequent lines contain the metadata values:
+
+
+Word\tFrequency
+ Airplane\t345
+ Car\t241
+ ...
+
+
+There is no explicit key shared with the main data file; instead, the order in
+the metadata file is assumed to match the order in the embedding tensor. In
+other words, the first line is the header information and the (i+1)-th line in
+the metadata file corresponds to the i-th row of the embedding tensor stored in
+the checkpoint.
+
+Note: If the TSV metadata file has only a single column, then we don’t expect a
+header row, and assume each row is the label of the embedding. We include this
+exception because it matches the commonly-used "vocab file" format.
+
+### Images
+If you have images associated with your embeddings, you will need to
+produce a single image consisting of small thumbnails of each data point.
+This is known as the
+[sprite image](https://www.google.com/webhp#q=what+is+a+sprite+image).
+The sprite should have the same number of rows and columns with thumbnails
+stored in row-first order: the first data point placed in the top left and the
+last data point in the bottom right:
+
+
+
+ 0 |
+ 1 |
+ 2 |
+
+
+ 3 |
+ 4 |
+ 5 |
+
+
+ 6 |
+ 7 |
+ |
+
+
+
+Note in the example above that the last row doesn't have to be filled. For a
+concrete example of a sprite, see
+[this sprite image](https://www.tensorflow.org/images/mnist_10k_sprite.png) of 10,000 MNIST digits
+(100x100).
+
+Note: We currently support sprites up to 8192px X 8192px.
+
+After constructing the sprite, you need to tell the Embedding Projector where
+to find it:
+
+
+```python
+embedding.sprite.image_path = PATH_TO_SPRITE_IMAGE
+# Specify the width and height of a single thumbnail.
+embedding.sprite.single_image_dim.extend([w, h])
+```
+
+### Interaction
+
+The Embedding Projector has three panels:
+
+1. *Data panel* on the top left, where you can choose the run, the embedding
+ tensor and data columns to color and label points by.
+2. *Projections panel* on the bottom left, where you choose the type of
+ projection (e.g. PCA, t-SNE).
+3. *Inspector panel* on the right side, where you can search for particular
+ points and see a list of nearest neighbors.
+
+### Projections
+The Embedding Projector has three methods of reducing the dimensionality of a
+data set: two linear and one nonlinear. Each method can be used to create either
+a two- or three-dimensional view.
+
+**Principal Component Analysis** A straightforward technique for reducing
+dimensions is Principal Component Analysis (PCA). The Embedding Projector
+computes the top 10 principal components. The menu lets you project those
+components onto any combination of two or three. PCA is a linear projection,
+often effective at examining global geometry.
+
+**t-SNE** A popular non-linear dimensionality reduction technique is t-SNE.
+The Embedding Projector offers both two- and three-dimensional t-SNE views.
+Layout is performed client-side animating every step of the algorithm. Because
+t-SNE often preserves some local structure, it is useful for exploring local
+neighborhoods and finding clusters. Although extremely useful for visualizing
+high-dimensional data, t-SNE plots can sometimes be mysterious or misleading.
+See this [great article](http://distill.pub/2016/misread-tsne/) for how to use
+t-SNE effectively.
+
+**Custom** You can also construct specialized linear projections based on text
+searches for finding meaningful directions in space. To define a projection
+axis, enter two search strings or regular expressions. The program computes the
+centroids of the sets of points whose labels match these searches, and uses the
+difference vector between centroids as a projection axis.
+
+### Navigation
+
+To explore a data set, you can navigate the views in either a 2D or a 3D mode,
+zooming, rotating, and panning using natural click-and-drag gestures.
+Clicking on a point causes the right pane to show an explicit textual list of
+nearest neighbors, along with distances to the current point. The
+nearest-neighbor points themselves are highlighted on the projection.
+
+Zooming into the cluster gives some information, but it is sometimes more
+helpful to restrict the view to a subset of points and perform projections only
+on those points. To do so, you can select points in multiple ways:
+
+1. After clicking on a point, its nearest neighbors are also selected.
+2. After a search, the points matching the query are selected.
+3. Enabling selection, clicking on a point and dragging defines a selection
+ sphere.
+
+After selecting a set of points, you can isolate those points for
+further analysis on their own with the "Isolate Points" button in the Inspector
+pane on the right hand side.
+
+
+
+*Selection of the nearest neighbors of “important” in a word embedding dataset.*
+
+The combination of filtering with custom projection can be powerful. Below, we filtered
+the 100 nearest neighbors of “politics” and projected them onto the
+“best” - “worst” vector as an x axis. The y axis is random.
+
+You can see that on the right side we have “ideas”, “science”, “perspective”,
+“journalism” while on the left we have “crisis”, “violence” and “conflict”.
+
+
+
+
+
+ |
+
+
+ |
+
+
+
+ Custom projection controls.
+ |
+
+ Custom projection of neighbors of "politics" onto "best" - "worst" vector.
+ |
+
+
+
+### Collaborative Features
+
+To share your findings, you can use the bookmark panel in the bottom right
+corner and save the current state (including computed coordinates of any
+projection) as a small file. The Projector can then be pointed to a set of one
+or more of these files, producing the panel below. Other users can then walk
+through a sequence of bookmarks.
+
+
+
+
+## Mini-FAQ
+
+**Is "embedding" an action or a thing?**
+Both. People talk about embedding words in a vector space (action) and about
+producing word embeddings (things). Common to both is the notion of embedding
+as a mapping from discrete objects to vectors. Creating or applying that
+mapping is an action, but the mapping itself is a thing.
+
+**Are embeddings high-dimensional or low-dimensional?**
+It depends. A 300-dimensional vector space of words and phrases, for instance,
+is often called low-dimensional (and dense) when compared to the millions of
+words and phrases it can contain. But mathematically it is high-dimensional,
+displaying many properties that are dramatically different from what our human
+intuition has learned about 2- and 3-dimensional spaces.
+
+**Is an embedding the same as an embedding layer?**
+No; an embedding layer is a part of neural network, but an embedding is a more
+general concept.