MATLAB Examples

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

Human activity sensor data contains observations derived from sensor measurements taken from smartphones worn by people while doing different activities (walking, lying, sitting etc).

Demonstration of dot product, orthogonality also includes some vector addition. Information from this tutorial is used in qr decomposition and multiple regression regression approach

This example was authored by the MathWorks community.

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 eigenmodes 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

Construct a map of 10 US cities based on the distances between those cities, using cmdscale.

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

The time series from a SDOF is computed using the central difference method, and a white noise is used as an input force.

This HighChart object enables easy use of the javascript technology provided by http://www.highcharts.com/ to generate interactive and dynamic charts in MATLAB web browser.

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

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

This tutorial describes multivariate guassians as it walks through the major functioniality of the mmvn toolkit

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.

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 [1]. The notations he uses are slightly different in

The previous methods, Hotelling’s T-square method and Gaussian mixture model, use Gaussian distribution-based parametric model. However, in practical situation, sometimes data

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

From WinningGamblersRuin.mlx we know that

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).

Q = 1*Q_1 + 2*Q_1 + 3*Q_5 For chi2 distribution use the NEGATIVE (!) sign for degrees of freedom

多変数の時系列データを複数使用します。それぞれの時系列データはそれぞれ同じ型ですが、別々のエンジンで計測しされたものです。 通常エンジンにはユーザーにはわからない様々なレベルの摩耗、製造変動が初期段階から存在しますが、故障しているわけではありません。

The Cox-Ingersoll-Ross process

After Cross-Validation, Optimal 'c' value- Yeilding Best Performance (F-measure)

Implement soft clustering on simulated data from a mixture of Gaussian distributions.

Choosen Weak classifiers:

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.

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) |

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故障が発生した場合の損失が甚大である場合、保守的なスケジュールで（より短い期間で）メンテナンスを行うことで、故障の発生を避けるアプローチはよく取られます。 ただこのアプローチでは結果として必要以上にメンテナンスを実施することに繋がることが多く、余計なコストとなります。

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

Perform ridge regression.

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