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Questions tagged [functional-data-analysis]

Functional Data Analysis defines a framework where the fundamental units of analysis are functions.

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Bilinear Process

how to generate a functional bilinear process such as: $ X_{n+1}= \int\psi(t,s)X_{n}(s)ds + \iint\phi(t,s,u)X_{n}(s)\varepsilon_{n}(u)dsdu + \varepsilon_{n+1}(t) $ ? About the first integral there ...
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1answer
20 views

Analyse variation between distribution curves according to factors

I have a set of continuous distributions representing the leaf area density found at different heights through a forest canopy. e.g. like that found in Whitehurst et al. (2013): For each of these ...
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1answer
43 views

Covariance kernel of a Gaussian process

I just started studying the theory of Gaussian processes. I'm mainly interested in studying functional data and I haven't found the answer to my doubt. Let's say I have some curves that I consider as ...
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9 views

Calculating gradient/rate of use

I have some data regarding my pellet usage. I monitor the level of pellets in the hopper, with a certain degree of inaccuracy because of the tesselation of the pellets. I would like to calculate the ...
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35 views

Which method for anomaly detection on curves of sensor data

I have data of measurements of a sensor. The sensor measures a numeric value at 20 fixed positions every few seconds. You can think of a camera traversing over a plate and measuring the amount of ...
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17 views

Kernel specification in FAR(1) model

0 down vote favorite I'm trying to simulate from a functional AR(1) model. I read in 'Introduction to Functional Data Analysis' (by Kokoszka and Reimherr) an example of R code to do this, but I dind'...
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1answer
171 views

Functional Data Analysis and Splines Regression

I'm new to Functional Data Analysis so my question will'be very simple for an expert in this topic. Operatively, when I fit a model like this, in R : model<- lm( y ~ bs( x, df = k, degree = l ) )...
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28 views

Reduce range of function for functional PCA in R - Functional Data Analysis

I have discrete measurements of river flow spanning 22 years. As river flow is naturally continuous, I have attempted to fit a function to the data using the FDA package in R: library(FDA) set.seed(1)...
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29 views

Numeric Functional Regression coefficients

I'm working on some data where I have thousands of curves in the defined as: $P(t)$ that basically represent eluition profiles of some proteins. My aim is to represent each of this $P(t)$ curves ...
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0answers
126 views

How to calculate RKHS norm of a function under given kernel transformation

This was a question asked before in mathoverflow but not yet got answered. I have the same problem when reading Srinivas et al (2010) [appendix B]'s paper. Here are my problems: Definitions: ...
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0answers
112 views

Illustration of functional gradient descent

I'm trying to understand boosting as gradient descent (GD) in functional space. I've followed the argument in the classic paper on the subject, but would characterize my understanding as tenuous at ...
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0answers
54 views

Specifying interaction formulae in a signal regression (with mgcv)

Signal regression, or scalar-on-function regression is considered a sub-class of functional regression approaches where the response variable is a scalar and the predictors can be one or more linear ...
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100 views

Which Time Series Algorithm to Choose?

I have a curious problem related to time series analysis. We have lots of data with timestamps (event data). We want to use it for two purposes: Find Historical Trends in data Make accurate ...
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1answer
66 views

What statistics can be used for correlating gene expression on a specific organ with its function

My hypothesis is that a gene whose function is related to an organ will have higher gene expression in that organ compared to other organs. An example of my hypothesis: From a published literature, ...
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2answers
216 views

Is this feature extraction?

I have a data set consisting of a large number of univariate time series. I have empirical reasons to expect that each time series can be well described by a function with a small number of ...
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0answers
53 views

Is it possible to calculate AIC or BIC for functional regression models?

I am doing a functional regression using the fRegress() function of the "fda" package in R. For comparing some of these models I wanted to calculate AIC or BIC over the model I have which has class "...
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1answer
20 views

Generate funciton with specified bases

I am trying to simulate functional data using specified bases and a set of random coefficients. For example, I can generate a function on $[0,1]$ with Fourier basis like $$f(x) = \sum_{i=0}^k a_i sin(...
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3answers
202 views

Positive smoothing with the fda-package (Functional data analysis)

In the book Functional Data Analysis with R (Ramsay&Silverman) there is described the possibility to do the "positive smoothing" if it’s needed instead of the "normal smoothing". In the books ...
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92 views

clustering discrete functional data

I have a set of data, where each data is of the form $(X, Y)$, $X := (x_1, x_2 \dots x_m) $ and $Y := (f^1_1(X), f^1_2(X) \dots f^1_m(X))$ or $Y := (f^2_1(X), f^2_2(X) \dots f^2_m(X))$. In a data if ...
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1answer
261 views

Functional Principal Component Analysis (FPCA): Mean Function

How does one calculate a mean function in Functional Principal Component Analysis (FPCA) given a data set with an unknown distribution? (A theoretical approach if possible) I am wanting to implement ...
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0answers
109 views

Clustering of temperature and precipitation courses. Searching for approach

I would like to cluster not only single observations, but I would like to cluster all observations for temperature together as a temperature course. So the goal is to cluster the temperature courses. ...
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85 views

How to do linear regression on categorical independent variable in excel?

I am newbie in data analytics world and I am trying to do linear regression on super-store sales database. The database contain fields like OrderID, OrderDate, ShipDate, ShipMode, CustomerID, ...
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42 views

mgcv GAM - is it possible to include the 'simple' product of two 1-d smooths?

I am trying to test out various mgcv::gam models in a scalar-on-function regression analysis. The following is the 'hierarchy' of models I would like to test: $$ ...
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0answers
24 views

Usefulness of integral operator as generalization of a matrix? (Intuition)

In this paper by Neumaier, page 5, he says [This problem] can be posed as the problem of solving the linear system $Ax=b$ where $A$ is the integral operator defined by \begin{equation} Ax(t) := ...
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0answers
93 views

Effect of image resolution on visual word features

I have trained and tested an image classifier using visual words (bagoffeature MATLAB) for a simple disease/no disease classification. However, my disease set is from a different camera (50dpi) from ...
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59 views

What is the basic difference between Sieves, Series and Splines estimators?

As far as I know, Sieve Estimators consists in a broader class of estimators for a function g(x) lying in a space of functions G. The estimation basically consists in choosing the function that best ...
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25 views

Scalar-on-function regression with random initial time

I was trying to answer this question Estimating the effect of different histories of exposure, on a scalar response measured at the end of a study Executive summary if you don't want to read the ...
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2answers
356 views

Principal Component analysis (vector space or inner product space?)

(WARNING: This question might seem dumb) I see that the optimization problem in PCA involves the notion of inner product. For example, to solve for the loadings in second principal component, the ...
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1answer
508 views

How to build a machine learning system (smart system) that updates automatically?

I've been doing machine learning. I have done lots of learning related to data analysis and ML algorithms, and I've got very good results and I understand the algorithms. However, my approaches are ...
3
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1answer
106 views

Test for difference between time-series measurements

I have an experiment where the response to a treatment is measured over time. I now want to test for if the response profile differ between the treated group and the control group. There are ...
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1answer
171 views

Orthogonal and stationary basis of projection

Consider a set of $p$ stationary correlated time signals of identical duration $T$. I would like to de-correlate them by projection on an orthogonal basis but preserving stationarity. Without the ...
2
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1answer
267 views

Multivariate multiple non linear regression

I know there are already two questions on this topic, but neither has an answer. I have a set of $N$ experiments. For each experiment, denoted by a vector of predictors $\mathbf{x}$, I measure $m$ ...
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1answer
602 views

Splines for repeated measures?

I have a dataset which has repeated measures for each subject. And the linear-mixed effect model doesn't work well for the dataset. I want to know if there is any smoothing methods (e.g. splines) that ...
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0answers
22 views

Optimal policy finding with given constraint

I'm trying to solve for the optimal policy function $h^*(x)$ over the domain of all policy functions $u_t = h(x_t)$ for the following problem. \begin{equation} \min_{h(x)} \, \mathbb{E}[\sum_{t=0}^{\...
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0answers
119 views

Continuous response variable with zeros (Functional Data Analysis)

I am using functional linear model for scalar response. It is that I have i.e. data frame with five columns. Every value in these columns is pressure estimation to certain time ( let's say every 0.04 ...
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2answers
370 views

R: Regression between Two related Dependent Variables (not paired)

I have two dependent variables that are measured during an experiment, they both change in time (independent variable). The measurements for both variables do not always coincide in time (so they are ...
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2answers
2k views

From a statistical perspective: Fourier transform vs regression with Fourier basis

I am trying to understand whether discrete Fourier transform gives the same representation of a curve as a regression using Fourier basis. For example, ...
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0answers
230 views

Smooth hazard function at given knots in R

Is there a way to obtain a smooth estimate of the hazard function at specific x coordinates in R? My problem is related to functional data analysis where I have a number of hazard function estimates (...
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1answer
767 views

How to select the optimal number principal components in functional principal components analysis?

I am interested in the selecting the optimal number of principal components in functional principal component analysis (FPCA). There are various techniques to do that for example AIC, BIC etc. (I am ...
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2answers
99 views

Confusion about when to use least-squares regression analysis

I am going through an article titled On the misuse of regression in earth science. On page 65, the author say as follows about the least-squares method. It is usual to require that the independent ...
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1answer
466 views

How to select the number of basis functions and smoothing parameter in functional data analysis?

I am confused over the selection of number of basis and smoothing parameter for particular data set in functional data analysis. I have two data sets (A) Daily temperature data set of England of 228 ...
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2answers
263 views

Forecasting ranges for multiple observations with quarterly data

I have 90 markets with quarterly results, with data from 2014 Q1 to 2016 Q2. I'd like to predict 2016 Q4 results. With a time-series in R, as I understand, you need a single observation over multiple ...
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1answer
317 views

How to consider different samples in functional data clustering?

In the engineering context several data sources like different kinds of measurement signals (for example distances, angles and efficiencies) are very common. If it would be possible to observe these ...
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1answer
50 views

confirmation and validation of a lab environment versus real life scenario

I'm having some trouble trending turbofan jet engines exhaust gas temperatures (EGT). Data collected shown that EGT measured in the test cell versus EGT measured on-wing while flying is different. ...
3
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1answer
298 views

Multinomial Count Models

Is it possible to model a dependent variable which is both multinomial and count? If so, how would one do so with a tool such as R? For example, suppose that my dependent variable looks like this: ...
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1answer
71 views

Can I validate results after statistical hypothesis testing?

I have data from one clinical test for 450 patients. Depending upon my objective, I divided data into 7 different categories to compare two groups, in each category (inherited from parents and not ...
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1answer
244 views

Canonical Correlation Analysis in R

I have a dataset of temperature readings of different burner parts which determine the final temperature of the burner and time to set off burner So my dataset looks like this: ...
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0answers
33 views

Question about example in Linear Models for Functional Responses

I am reading Chapter 10 Linear Models for Functional Responses of Functional Data Analysis with R and Matlab by Ramsay. On page 148, the book mentions the model for "Climate Region Effects on ...
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1answer
65 views

Alternate terms, or definition for functional logistic regression

I have recently come upon a paper discussing "functional logistic regression." I could not find literature related to functional logistic regression. Is there a different name for this kind of ...
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1answer
426 views

Functional clustering with R [closed]

I have a time series data in R, and I am using functional clustering. I would like to interpret a figure that is output below the code. Furthermore, I would like to control line colors and thickness ...