95 releases (6 stable)
Uses new Rust 2021
|new 1.0.5||Jan 16, 2022|
|1.0.2||Dec 29, 2021|
|0.9.5||Dec 23, 2021|
|0.9.4||Nov 19, 2021|
|0.5.9||Oct 6, 2020|
#6 in Machine learning
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Used in tid2013stats
rstats = "^1" in the
Cargo.toml file, under
Use in source files any of the following structs, as needed:
and any of the following helper functions:
and any of the following traits:
It is highly recommended to read and run
tests/tests.rs, which shows examples of usage.
To run all the tests, use single thread in order to produce the results in the right order:
cargo test --release -- --test-threads=1 --nocapture --color always
Rstats is primarily about characterising multidimensional sets of points, with applications to Machine Learning and Big Data Analysis. It uses
non analytical statistics, where the 'random variables' are replaced by vectors of real data. Probabilities densities and other parameters are always obtained from the data, not from some assumed distributions.
This crate begins with basic statistical measures and vector algebra, which provide self-contained tools for the multidimensional algorithms but can also be used in their own right.
Our treatment of multidimensional sets of points (vectors) is constructed from the first principles. Some original concepts, not found elsewhere, are introduced and implemented here. Specifically, the new simple multidimensional (geometric) median algorithm. Also, the
comediance matrix as a replacement for the covariance matrix. It is obtained simply by supplying
covar with the geometric median instead of the usual centroid (mean vector).
Zero median vectors are generally preferable to the commonly used zero mean vectors.
Most authors 'cheat' by using quasi medians (1-d medians along each axis). Quasi medians are a poor start to stable characterisation of multidimensional data. In a highly dimensional space, they are not even any quicker to compute.
Specifically, all 1-d measures are sensitive to the choice of axis and thus are affected by rotation.
In contrast, analyses based on the true geometric median (gm) are axis (rotation) independent. They are computed here by the novel methods
gmedian and their weighted versions
The main constituent parts of Rstats are its traits. The selection of traits (to import) is primarily determined by the types of objects to be handled. These are mostly vectors of arbitrary length (dimensionality). The main traits are implementing methods applicable to a single vector (of numbers) -
Stats, methods (of vector algebra) for two vectors -
Vecg, methods for n vectors -
VecVec, and methods for n vectors with another generic argument -
In other words, the traits and their methods operate on arguments of their required categories. In classical statistical parlance, the main categories correspond to the number of 'random variables'. However, the vectors' end types (for the actual data) are mostly generic: usually some numeric type. There are also some traits specialised for input end types
u8 and some that take mutable self. End type
f64 is most commonly used for the results.
For more detailed comments, plus some examples, see the source. You may have to unclick the 'implementations on foreign types' somewhere near the bottom of the page in the rust docs to get to it.
struct Medto hold median and quartiles
struct MStatsto hold mean and standard deviation
struct MinMaxre exported from crate
indxvecto hold min and max values of a vector and their indices. It is returned by function
i64tof64, tof64, here, wsum, wi, wv, printvv, genvec, genvecu8.
One dimensional statistical measures implemented for all numeric end types.
Its methods operate on one slice of generic data and take no arguments.
s.amean() returns the arithmetic mean of the data in slice
Some of these methods are checked and will report all kinds of errors, such as an empty input. This means you have to call
.unwrap() or something better on their results.
Included in this trait are:
- means (arithmetic, geometric and harmonic),
- standard deviations,
- linearly weighted means (useful for time dependent data analysis),
- median and quartiles,
- probability density function (pdf)
- autocorrelation, entropy
- linear transformation to [0,1],
- other measures and vector algebra operators
A few of the
Stats methods are reimplemented under this trait
(only for f64), so that they mutate
This is more efficient and convenient in some circumstances, such as in
vector iterative methods.
Vector algebra operations between two slices
&[U] of any length (dimensionality):
- Vector additions, subtractions and products (scalar, kronecker, outer),
- Other relationships and measures of difference,
- Pearson's, Spearman's and Kendall's correlations,
Median correlation, which we define analogously to Pearson's, as cosine of an angle between two zero median vectors (instead of zero mean vectors).
- Joint pdf, joint entropy, statistical dependence (mutual information).
This trait is unchecked (for speed), so some caution with data is advisable.
A handful of methods from
Vecg, specialised to an argument of known end type
Mutable vector addition, subtraction and multiplication.
This is for efficiency and convenience. Specifically, in
vector iterative methods.
MutVecf64 is to be used in preference, when the end type of
self is known to be
f64. Beware that these methods work by side-effect and do not return anything, so they can not be functionally chained.
Some vector algebra as above that can be more efficient when the end type happens to be u8 (bytes). They have u8 appended to their names to avoid confusion with Vecg methods.
- Relationships between two vectors (of bytes)
- Frequency count of bytes by their values (histogram, pdf, jointpdf)
- Entropy, jointentropy, dependence (different algorithms to those in Vecg)
Relationships between n vectors (in d dimensions). This is the main original contribution of this library. True geometric median is found by fast and stable iteration, using improved Weiszfeld's algorithm
gmedian, optionally boosted by a secant method
gsmedian. These algorithms both solve Weiszfeld's convergence and stability problems in the neighbourhood of existing set points.
- sums of distances, eccentricity (radius) measure,
- centroid, medoid, outliers, true geometric median,
- characterisations of sets of multidimensional points (of d random variables): means, stds, medians
- transformation to zero geometric median data,
- multivariate trend (regression) between two sets of nd points,
- covariance and comediance matrices (weighted and unweighted).
Trait VecVec is entirely unchecked, so check your data upfront.
Methods which take an additional generic vector argument, such as a vector of weights for computing the weighted geometric medians.
Centroid\Centre\Meanis the (generally non member) point that minimises the sum of squares of distances to all member points. Thus it is susceptible to outliers. Specifically, it is the n-dimensional arithmetic mean. By drawing physical analogy with gravity, it is sometimes called 'the centre of mass'. Centroid can also sometimes mean the member of the set which is the nearest to the Centre. Here we follow the common (if somewhat confusing) usage: Centroid = Centre = Arithmetic Mean.
Quasi\Marginal Medianis the point minimising sums of distances separately in each dimension (its coordinates are 1-d medians along each axis). It is a mistaken concept which we do not use here.
Tukey Medianis the point maximising
Tukey's Depth, which is the minimum number of (outlying) points found in a hemisphere in any direction. Potentially useful concept but not yet implemented here, as its advantages over
gmare not clear.
Medoidis the member of the set with the least sum of distances to all other members.
Outlieris the member of the set with the greatest sum of distances to all other members.
Median or the true geometric median (gm), is the point (generally non member), which minimises the sum of distances to all members. This is the one we want. It is much less susceptible to outliers than centroid. In addition, unlike quasi median,
gmis rotation independent.
Zero median vectoris obtained by subtracting the geometric median. This is a proposed alternative to the commonly used
zero mean vector, obtained by subtracting the centroid.
Comedianceis similar to
covariance, except zero median vectors are used to compute it, instead of zero mean vectors.
Version 1.0.5 Dependence is now the same as mutual information. Added 1D
median correlation, which we define analogously to Pearson's, as cosine of the angle between two zero median vectors (instead of zero mean vectors). This is more robust. Added
correlationswhich efficiently map these relationships of a single given vector (typically of outcomes), to a set of vectors (typically features vectors).
Version 1.0.4 Added joint pdf, joint entropy and dependence for a set of n vectors.
Version 1.0.3 Better implementations of joint probability and joint entropy. Code style and testing improvements.
Version 1.0.2 Updated the dependency
indxvecto version 1. A few minor changes to this document.
Version 1.0.1 Minor change:
wsortedeccsnow take gm as an argument for more efficient repeated use. Vecvec test improved.
Version 1.0.0 Rstats reaches stability (of sorts)! Some code simplifications:
wsmedianare now just slightly more accurate than
wgmedianrespectively, otherwise their performance is very similar. Sometimes a bit slower, at other times, especially on 'difficult' data, they can be a bit faster.
Version 0.9.5 Improved
smedian. Also added a weighted version of it:
Version 0.9.4 Organisation improvements. Added trait
Vecf64and moved into it relevant methods from
Vecg. Added a few functions to MutVecf64 trait. Simplified
Version 0.9.3 Added
hwmeanstd- harmonic weighted mean and standard deviation. Tidied up readme badges and some tests. Simplified random number generation. Weights for the weighted means are now ascending (more intuitive).
Version 0.9.2 Fixed some tests broken by moved functions. Added harmonic standard deviation, harmonic centroid and more tests.
Version 0.9.1 Made the auxiliary functions more visible by moving them to
lib.rs(the top level of the crate).
Version 0.9.0 Added