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racheltho committed Jul 26, 2017
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},
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"source": [
"#### Matrix-Matrix Products"
]
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"<img src=\"images/shop.png\" alt=\"floating point\" style=\"width: 100%\"/>(Source: [Several Simple Real-world Applications of Linear Algebra Tools](https://www.mff.cuni.cz/veda/konference/wds/proc/pdf06/WDS06_106_m8_Ulrychova.pdf))"
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"source": [
"#### Answer"
]
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},
{
"cell_type": "markdown",
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"source": [
"#### Image Data"
]
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"source": [
"Images can be represented by matrices.\n",
"\n",
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},
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"source": [
"#### Convolution"
]
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"*Convolutions* are the heart of convolutional neural networks (CNNs), a type of deep learning, responsible for the huge advances in image recognitionin the last few years. They are now increasingly being used for speech as well, such as [Facebook AI's results](https://code.facebook.com/posts/1978007565818999/a-novel-approach-to-neural-machine-translation/) for speech translation which are 9x faster than RNNs (the current most popular approach for speech translation).\n",
"\n",
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},
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"source": [
"### Matrix Decompositions"
]
},
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"source": [
"We will be talking about Matrix Decompositions every day of this course, and will cover the below examples in future lessons:"
]
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"- **Topic Modeling** (NMF and SVD. SVD uses QR) A group of documents can be represented by a term-document matrix\n",
"<img src=\"images/document_term.png\" alt=\"term-document matrix\" style=\"width: 70%\"/>\n",
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},
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"- **Background removal** (robust PCA, which uses truncated SVD)\n",
"![background removal](images/surveillance3.png)"
]
},
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"- **Google's PageRank Algorithm** (eigen decomposition)\n",
"\n",
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"- List of other decompositions and some applications [matrix factorization jungle](https://sites.google.com/site/igorcarron2/matrixfactorizations)"
]
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"metadata": {},
"source": [
"Timeline History of Floating Point Arithmetic:\n",
"- ~8000 BC: Babylonian radix-60 system was earliest floating-point system (Donald Knuth). Represented the significand of a radix-60 floating-point representation (if ratio of two numbers is a power of 60, represented the same)\n",
"- ~1600 BC: Babylonian radix-60 system was earliest floating-point system (Donald Knuth). Represented the significand of a radix-60 floating-point representation (if ratio of two numbers is a power of 60, represented the same)\n",
"- 1630 Slide rule. Manipulate only significands (radix-10)\n",
"- 1914 Leonardo Torres y Quevedo described an electromechanical implementation of Babbage's Analytical Engine with Floating Point Arithmetic.\n",
"- 1941 First real, modern implementation. Konrad Zuse's Z3 computer. Used radix-2, with 14 bit significand, 7 bit exponents, and 1 sign bit.\n",
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