Human activity sensor data contains observations derived from sensor measurements taken from smartphones worn by people while doing different activities (walking, lying, sitting etc).
Rare events prediction in complex technical systems has been very interesting and critical issue for many industrial and commercial fields due to huge increase of sensors and rapid growth
Construct a map of 10 US cities based on the distances between those cities, using cmdscale.
Demonstration of dot product, orthogonality also includes some vector addition. Information from this tutorial is used in qr decomposition and multiple regression regression approach
Linstats package provides a uniform mechanism for building any supported linear model. Once built the same model can be analyzed in many ways including least-squares regression, fit and
This demo showcases visualization and analysis for forecasting energy demand based on historical data. We have access to hour-by-hour utility usage for the year 2006, including
Consider the hypercube and an inscribed hypersphere with radius . Then the fraction of the volume of the cube contained in the hypersphere is given by:
Examples A and B make it clear that if we are trying to view uniform data over the hypercube most (spherical) neighborhoods will be empty! Let us examine what happens if the data follow the
The dynamic response of a 100 m high clamped-free steel beam is studied. Simulated time series are used, where the first three eigen-modes have been taken into account. More precisely, the
This case study analyzes the amount of vibration a passenger experiences for a vehicle traveling over a road disturbance (bump). We want to determine the amount of reduction in displacement
The time series from a SDOF is computed using the central difference method, and a white noise is used as an input force.
Hypothesis testing based on a model that is invalid can lead to faulty conclusions. this tutorial goes over a few basic diagnostic procedures that can be used to test whether a model is valid.
This tutorial will go over some of the functions available for making inferences and testing hypothesis. I assume that you know how to construct a model using encode. If not see the
This is an enhanced version of the regstats function (statistics toolbox). Here are implemented several ways to estimate robust standard errors (se) for the coefficients\n. Also, it
This file describes the development of a failure boundary identication algorithm shown in "Using Statistics and Optimization to Support Design Activities" Webinar, July 21, 2009.
This tutorial describes multivariate guassians as it walks through the major functioniality of the mmvn toolkit
In this script, I reproduce the results presented by John D. Holmes in the first part of the chapter 2 of his book: Wind loading of structures . The notations he uses are slightly different in
Among many statistical anomaly detection techniques, Hotelling’s T-square method, a multivariate statistical analysis technique, has been one of the most typical method. This method
From: "Using Statistics and Optimization to Support Design Activities" Webinar, July 21, 2009.
In order to illustrate some of the numerical calculations required for testing hypothesis on canonical variance components based on the LRT statistic (37), as presented in Example 3, let us
Though Hotelling’s T-square method is applicable for many multi-dimensional data sets, this method has a fundamental assumption that the data follow a unimodal distribution. So, when the
The previous methods, Hotelling’s T-square method and Gaussian mixture model, use Gaussian distribution-based parametric model. However, in practical situation, sometimes data
Implement soft clustering on simulated data from a mixture of Gaussian distributions.
Q = 1*Q_1 + 2*Q_1 + 3*Q_5 For chi2 distribution use the NEGATIVE (!) sign for degrees of freedom
Cluster simulated data from a mixture of Gaussian distributions, and how to work with gmdistribution objects.
Determine the best Gaussian mixture model (GMM) fit by adjusting the number of components and the component covariance matrix structure.
To support the port passing problem I'll need to derive some recurrence equations that allow us to talk about the expected number of steps given that we win Gambler's Ruin (rather than lose).
Consider 2 spheres centered on the origin, one with radius and the other with slightly smaller radius . The volume of a -dimensional hypershere with radius is given by:
| AdaBoost : Implemented in 2-dimensional projection space. (i.e.Number of Pricipal Components = 2) |
Pi day is coming and you have been invited to dine with an eccentric but mathematically minded host. She has provided many interesting delicacies and you have now finally arrived at the cheese
We are trying to extend the case where a Markov Chain representing Gambler's Ruin contains one boundary that does not adsorb the chain, but instead reflects it. This can be represented with
For a table size of 3 it is fairly simple to enumerate all possible paths and their probabilities. So to deduce the expected path length all we need to do is sum over all the paths. Looking first at