Novelty detection with missing parameters

A method of determining and displaying an index of novelty representing the state of a system based on measurement of a plurality of different parameters of the system, the system being a physical system or a biological system, the method being performed by a processor, and the method comprising the steps of:

• receiving a data set comprising a plurality of sets of values each value being a measurement of a different one of said plurality of parameters, each set of values defining a data point in measurement space of dimension D, where D is a positive integer greater than one;
• calculating a provisional index of novelty for each data point by comparing the position in said measurement space of dimension D of each data point to a set of prototype data points comprising measurements of said parameters representative of the system being in a normal state;
• calculating a relationship, in said measurement space of dimension D, between the provisional index of novelty and the probability of different states of the system to find a probability value representing the probability of the system being at least as close to said normal state as the state represented by a data point having that provisional index of novelty,
• using said calculated relationship to find for each data point of the data set the probability value corresponding to its provisional index of novelty;
• using a further predefined relationship between the probability of different states of the system and an index of novelty defined in a space of dimension L, where L is a positive integer less than D, and based on comparing the distance between a data point and said normal state of the system, to find for each data point of the data set the index of novelty corresponding in the space of dimension L to said probability value;
• and
• displaying the index of novelty so found as the index of novelty for that data point.

A method of detecting sensor malfunction amongst a plurality of different sensors each measuring a parameter of the system, the plurality of parameters defining respective dimensions of a D-dimensional measurement space, where D is equal to the number of sensors, the method comprising the steps of:

• receiving sets of values, each value in a set being a measurement from a different one of said sensors, each set defining a data point in said D-dimensional measurement space;
• calculating an index of novelty for each data point by comparing its position in said D-dimensional measurement space to a set of prototype data points comprising measurements of said parameters representative of the system being in a normal state;
• using a predefined relationship, calculated for said D-dimensional measurement space, between the index of novelty and the probability of different states of the system to find a probability value representing the probability of the system being at least as close to said normal state as the state represented by the data point;
• calculating for each data point at least one marginal novelty index by ignoring one parameter value from said set of values and comparing the position of the data point in a D-1 dimensional space to the set of prototype data points also in the D-1 dimensional space, the D-1 dimensional space omitting the dimension corresponding to the ignored parameter;
• using a further predefined relationship, calculated for said D-1 dimensional space, between the marginal index of novelty and the marginal probability of different states of the system to find a marginal probability value representing the probability of the system being at least as close to said normal state as the state represented by the marginal novelty index;
• comparing said probability value and said marginal probability value;
• and
• in the event of the probability value and marginal probability value differing by more than a predefined threshold, outputting an alert for malfunction of the sensor whose parameter value was ignored.