Discord Detection Concepts and Methods

Discord = Most unusual subsequence Sliding window = tk − 2δ to tk + 2δ Subset Tk? = Most different from its similar subset Max min distance = Finding distance between subsequences

tk = Central time point δ = Fixed parameter for window size Tk = Defined time series subsequence xTi = Element in time series subsequence

Most unusual subsequence = Discord d(xTi, xTj) = Distance function Arg max = Finding the maximum value Intersection = Common elements between subsets

<p>Tk = tk − 2δ, tk + 2δ = Defines the range of subsequences Fixed δ = Controls the width of the window Time series = Sequence of data points Subset = Part of a larger set of elements</p> Signup and view all the answers

<p>Brute-force search = Compares all pairs of subsets to find discord subsets HOT-SAX algorithm = Uses heuristics and pruning for efficient detection Distance-based approach = Compares subsequences to a reference subsequence Clustering = Method to obtain the reference subsequence</p> Signup and view all the answers

<p>Determine discord subset = Identify most different subsequence Define subsequences = Use sliding window approach Arg max operation = Maximize distance to similar segments Time series analysis = Examine sequences over time</p> Signup and view all the answers

<p>Predefined window width δ = Fixed size used for analysis in detection methods Most unusual sequence = Sequence determined by discord detection Pairwise comparison = Method of comparing subsequences against each other Normal subsequence x̂ = Reference subsequence used in distance-based detection</p> Signup and view all the answers

<p>Brute-force search = Exhaustive comparison of all subset pairs HOT-SAX algorithm = Implements optimizations to reduce comparisons Distance-based outlier detection = Focuses on subsequence comparison Clustering = Groups similar subsequences to identify a reference</p> Signup and view all the answers

<p>Discord detection = Identifies outliers in time series data Pairwise comparison = Analyzes an entire set of subsequences against each other Heuristics = Employs rule-of-thumb techniques for improved efficiency Outlier detection = Identifying data points that deviate significantly from the norm</p> Signup and view all the answers

<p>d(xTi , x̂) &gt; τ = Condition to determine discord based on distances Reference x̂ = A normal subsequence for comparison Window width δ = Determines the length of subsequences considered #discords = Indicates the quantity of unusual sequences identified</p> Signup and view all the answers

<p>Clustering = Grouping similar data points based on features Feature-based classification = Identifying data based on specific attributes Distance-based approach = Assessing similarities using distance metrics Outlier detection = Identifying data points that deviate significantly from others</p> Signup and view all the answers

<p>Reference from the same time series = Clustering Reference from external time series = Feature-based classification Reference for collective outlier detection = Mean absolute deviation Reference using seasonal average = Heartbeat analysis</p> Signup and view all the answers

<p>Length of the subsequence = Determines if subsequences are consistent in size Representation of the subsequence = Involves models or transformations applied to data Periodicity of subsequence outliers = Examines if patterns are consistent over time Fixed-length versus variable-length = Categorizes subsequences based on their size variation</p> Signup and view all the answers

<p>Distance-based approaches = Utilizes reference values to analyze time series Time series clustering = Groups data points based on similarity Collective outlier detection = Identifies multiple anomalous data points Reference patterns = Compares time series data against established models</p> Signup and view all the answers

<p>Non-periodic sequences = Do not exhibit repeating patterns over time Periodic sequences = Have consistent repetitions over intervals Fixed-length subsequences = All subsequences are of the same length Variable-length subsequences = Subsequences can vary in length from each other</p> Signup and view all the answers

<p>Reference value = A baseline used for comparison Time series = Sequential data points collected over time Median = A statistic used to summarize central tendency Seasonal average = Typical value across a season or period</p> Signup and view all the answers

<p>Discord detection = Focuses on single-outlier subsequences Distance-based approaches = Utilize spatial distance to identify anomalies Model-based approaches = Apply statistical models to capture data trends Collective outliers = Groups of data points that deviate collectively</p> Signup and view all the answers

<p>Clustering = Identifying groups within data Feature-based classification = Sorting data based on features Outlier detection = Finding data anomalies Distance calculation = Measuring dissimilarity between data points</p> Signup and view all the answers

<p>Blázquez-García et al., 2021 = Research on collective outlier detection frameworks Gupta et al., 2014 = Contributions to the understanding of temporal anomalies Kristian Hovde Liland = Author of the course on outlier detection Norwegian University of Life Sciences = Institution conducting research on data anomalies</p> Signup and view all the answers

<p>Mean absolute deviation = Distance-based collective outlier detection Seasonal averages = Analyzing heartbeat data Feature extraction = Identifying relevant characteristics of data Time series analysis = Investigating data trends over intervals</p> Signup and view all the answers

<p>Models = Statistical algorithms used for prediction Transformations = Methods altering data for better fitting Subsequences = Slices of the dataset analyzed as units Anomalies = Outliers that do not fit the expected data pattern</p> Signup and view all the answers

<p>Discord detection = Identifying subsets that differ significantly from the trend 1-nearest neighbor distance = The shortest distance between a point and the nearest point in another set Non-overlapping subsets = Groups of data that do not share any common elements Single linkage = A method of clustering that uses the shortest distance between clusters</p> Signup and view all the answers

<p>Clustering analysis = Grouping similar time series Classification analysis = Assigning time series to categories Distance analysis = Calculating similarity between time points Pattern recognition = Identifying recurring sequences in data</p> Signup and view all the answers

<p>$d(x_{Ti}, x_{Tj})$ = Distance between points in subsets $T_i$ = Subset containing selected points $T_j$ = Another subset that does not overlap with $T_i$ $arg ext{ max}$ = The value that maximizes a given function</p> Signup and view all the answers

<p>Collective outliers = Important for understanding data discrepancies Subsequences = Core to the analysis of time-dependent data ECG signals = An example dataset used in analysis Data periodicity = Key for identifying trends over intervals</p> Signup and view all the answers

<p>Reference from same time series = Clustering External references = Feature-based classification Distance-based techniques = Measuring time series similarity Outlier detection methods = Analyzing deviations from expected patterns</p> Signup and view all the answers

<p>Fixed-length subsequence = Consistent size required for analysis Variable-length subsequence = Adaptable size that varies Length = Crucial for defining subsequence characteristics Representation = Necessary for modeling subsequences accurately</p> Signup and view all the answers

<p>Value = Represents the distance calculated Time = Indicates the analysis duration for detection Min = The smallest computed distance among a set Intersection ($T_j igcap T_i$) = Defines overlap conditions between subsets</p> Signup and view all the answers

<p>K-nearest neighbors = Classification and regression tasks Hierarchical clustering = Group data into a tree of clusters Outlier detection = Finding anomalies in datasets Time series analysis = Analyzing data points indexed in time order</p> Signup and view all the answers

<p>Subset $T_i$ = A defined group for analysis Subset $T_j$ = Another defined group, non-overlapping with $T_i$ Distance function $d(.,.)$ = A method for measuring distance between data points Analysis phase = Step where data is evaluated for patterns or anomalies</p> Signup and view all the answers

<p>Euclidean distance = Straight-line distance between two points Manhattan distance = Distance calculated along grid lines Cosine similarity = Measure of angle between two vectors Hamming distance = Count of differing elements in strings or sequences</p> Signup and view all the answers

<p>Mean = Average value of a data set Variance = Measure of data spread Standard deviation = Square root of the variance Outlier = A data point that deviates significantly from other observations</p> Signup and view all the answers

<p>Finance = Risk analysis and modeling Healthcare = Patient data analysis and trends Retail = Customer behavior analysis Telecommunications = Network data monitoring and anomaly detection</p> Signup and view all the answers

<p>Predictive model = A model that estimates future values based on training data Distance-based approach = Measures the deviation between predictions and actual values Interval forecasting = Predicts multiple steps ahead in time Outlier detection = Identifies data points that significantly differ from other observations</p> Signup and view all the answers

<p>Training set = The historical data used to train a predictive model Forecasted values = The projected outputs of a predictive model over a specific time Time series = A sequence of data points indexed in time order Threshold (τ) = The predefined limit used to determine significant deviations in predictions</p> Signup and view all the answers

<p>$x_i$ = Actual value at time $i$ $ar{x}_i$ = Predicted value at time $i$ $t$ = Current time step in the prediction process $ au$ = Value that defines tolerable prediction error</p> Signup and view all the answers

<p>Model training = The process of creating a predictive model from data Model prediction = Estimating future values from the trained model Forecast interval = A time period over which predictions are made Error measurement = Quantifying the difference between predicted and actual values</p> Signup and view all the answers

<p>Historical reference = Provides necessary context for predictions Model accuracy = Indicates the effectiveness of the predictions Collective outlier detection = Assesses groups of data points for anomalies Seasonal naive model = A baseline model that can be used for comparison with advanced models</p> Signup and view all the answers

<p>Naive model = Simplicity in predicting without complex patterns Seasonal model = Accounts for repetitive patterns in data over time Collective model = Focuses on aggregating multiple predictions to identify trends Predictive analytics = Utilizes historical data to forecast future trends</p> Signup and view all the answers

<p>Prediction function = Used to generate expected future outcomes Deviance calculation = Measures the discrepancy between predicted and actual values Optimization = Enhances model parameters for better accuracy Validation = Confirms model performance using separate test data</p> Signup and view all the answers

<p>Training phase = Initial phase represented in Figure 7 Forecast phase = Future predictions shown in Figure 8 Distance threshold = Concept illustrated alongside prediction accuracy Collective detection = Outlier assessment highlighted in model visuals</p> Signup and view all the answers