Developer Guide and Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

Multivariate Outlier Detection

In multivariate outlier detection methods, the observation point is the entire feature vector.

Details

Given a set
X
of
n
feature vectors LaTex Math image. of dimension
p
, the problem is to identify the vectors that do not belong to the underlying distribution (see [Ben2005] for exact definitions of an outlier).
The multivariate outlier detection method takes into account dependencies between features. This method can be parametric, assumes a known underlying distribution for the data set, and defines an outlier region such that if an observation belongs to the region, it is marked as an outlier. Definition of the outlier region is connected to the assumed underlying data distribution.
The following is an example of an outlier region for multivariate outlier detection:
LaTex Math image.
where LaTex Math image. and Sigma_n are (robust) estimates of the vector of means and variance-covariance matrix computed for a given data set, LaTex Math image. is the confidence coefficient, and LaTex Math image. defines the limit of the region.

Batch Processing

Algorithm Input
The multivariate outlier detection algorithm accepts the input described below. Pass the
Input ID
as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.
Input ID
Input
data
Pointer to the LaTex Math image. numeric table with the data for outlier detection. The input can be an object of any class derived from the
NumericTable
class.
location
Pointer to the LaTex Math image. numeric table with the vector of means. The input can be an object of any class derived from
NumericTable
except
PackedSymmetricMatrix
and
PackedTriangularMatrix
.
scatter
Pointer to the LaTex Math image. numeric table that contains the variance-covariance matrix. The input can be an object of any class derived from
NumericTable
except
PackedTriangularMatrix
.
threshold
Pointer to the LaTex Math image. numeric table with the non-negative number that defines the outlier region. The input can be an object of any class derived from
NumericTable
except
PackedSymmetricMatrix
and
PackedTriangularMatrix
.
If you do not provide at least one of the
location
,
scatter
,
threshold
inputs, the library will initialize all of them with the following default values:
location
A set of
0.0
scatter
A numeric table with diagonal elements equal to
1.0
and non-diagonal elements equal to
0.0
threshold
3.0
Algorithm Parameters
The multivariate outlier detection algorithm has the following parameters:
Parameter
Default Value
Description
algorithmFPType
float
The floating-point type that the algorithm uses for intermediate computations. Can be
float
or
double
.
method
defaultDense
Performance-oriented computation method.
Algorithm Output
The multivariate outlier detection algorithm calculates the result described below. Pass the
Result ID
as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.
Result ID
Result
weights
Pointer to the LaTex Math image. numeric table of zeros and ones. Zero in the
i
-th position indicates that the
i
-th feature vector is an outlier.
By default, the result is an object of the
HomogenNumericTable
class, but you can define the result as an object of any class derived from
NumericTable
except the
PackedSymmetricMatrix
,
PackedTriangularMatrix
, and
CSRNumericTable
.

Examples

C++ (CPU)
Java*
There is no support for Java on GPU.
Batch Processing:
Python*

Performance Considerations

To get the best overall performance of multivariate outlier detection:
  • If input data is homogeneous, provide input data and store results in homogeneous numeric tables of the same type as specified in the
    algorithmFPType
    class template parameter.
  • If input data is non-homogeneous, use AOS layout rather than SOA layout.
  • For the default outlier detection method (
    defaultDense
    ), you can benefit from splitting the input data set into blocks for parallel processing.
Optimization Notice
Intel’s compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.
Notice revision #20110804

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.