{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tranlation Matrix Tutorial" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What is it ?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose we are given a set of word pairs and their associated vector representaion $\\{x_{i},z_{i}\\}_{i=1}^{n}$, where $x_{i} \\in R^{d_{1}}$ is the distibuted representation of word $i$ in the source language, and ${z_{i} \\in R^{d_{2}}}$ is the vector representation of its translation. Our goal is to find a transformation matrix $W$ such that $Wx_{i}$ approximates $z_{i}$. In practice, $W$ can be learned by the following optimization prolem:\n", "\n", "