# Math

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## Performing Efficient Broad Crawls with the AOPIC Algorithm

This article explains how the Adaptive On-Line Page Importance Computation (AOPIC) algorithm works. AOPIC is useful for performing efficient broad crawls of large slices of the internet. The key idea behind the algorithm is that pages are crawled based on a continuously improving estimate of page importance. This effectively allows the user of the algorithm to allocate the bulk of their limited bandwidth on the most important pages that their crawler encounters.

## How Are Principal Component Analysis and Singular Value Decomposition Related?

Introduction Principal Component Analysis, or PCA, is a well-known and widely used technique applicable to a wide variety of applications such as dimensionality reduction, data compression, feature extraction, and visualization. The basic idea is to project a dataset from many correlated coordinates onto fewer uncorrelated coordinates called principal components while still retaining most of the variability present in the data. Singular Value Decomposition, or SVD, is a computational method often employed to calculate principal components for a dataset.

## Markov's and Chebyshev's Inequalities Explained

Confidence Values If you’ve ever learned any basic statistics or probability then you’ve probably encountered the 68-95-99.7 rule at some point. This rule is simply the statement that, for a normally distributed variable, roughly 68% of values will fall within one standard deviation of the mean, 95% of values within two standard deviations, and 99.7% within three standard deviations. These confidence values are quite useful to memorize because values that are computed from data are often approximately normally distributed due to the central limit theorem.

## Understanding Neural Network Weight Initialization

Choosing Weights: Small Changes, Big Differences There are a number of important, and sometimes subtle, choices that need to be made when building and training a neural network. You have to decide which loss function to use, how many layers to have, what stride and kernel size to use for each convolution layer, which optimization algorithm is best suited for the network, etc. With so many things that need to be decided, the choice of initial weights may, at first glance, seem like just another relatively minor pre-training detail, but weight initialization can actually have a profound impact on both the convergence rate and final quality of a network.