workflow cluster-calendar template: define-unit -> contextualise -> characterise -> loop(define-unit (similarity-based) -> characterise (groups) -> visualise -> abstract -> assess) -> generate-knowledge description: "Identify and analyse recurring daily patterns in time series data through interactive clustering and calendar-based visualisation; detect standard patterns and exceptional days" # ============================================================================ # INPUT # ============================================================================ artifact D_hour : entities origin: given internal structure: elementary embedment: time features: - id: f_value value structure: atomic value type: numeric description: "Measured value" description: "Time series measurements at regular intervals over extended period" artifact D_calendar entities origin: given internal structure: elementary embedment: time features: - id: f_temporal_coords value structure: vector value type: {categorical, numeric} description: "Month, day of week, day number" description: "Calendar structure providing temporal context with month and weekday organisation" # ============================================================================ # STEP 1: PARTITION INTO DAILY EPISODES # ============================================================================ transform T_partition : intent: define-unit manner: "time-partitioning into daily episodes" input: D_hour output: D_day actor: machine description: "Organise time series into daily episodes, each containing measurements for one 24-hour period" artifact D_day : entities internal structure: episode embedment: time features: - id: f_day_index value structure: atomic value type: ordinal description: "Sequential position of day in the year" description: "Daily episodes consisting of all measurements within each 24-hour period" # ============================================================================ # STEP 2: ARRANGE DAYS IN A CALENDAR CONTEXT # ============================================================================ transform T_arrange : intent: contextualise manner: "calendar-based" input: D_day, D_calendar output: A_calendar actor: machine description: "Arrange daily episodes in calendar context according to their temporal position" artifact A_calendar : arrangement(D_day) context: D_calendar principle: "calendar date mapping to grid position" description: "Calendar-based arrangement where each day occupies its corresponding calendar cell" # ============================================================================ # STEP 3: EXTRACT DAILY TEMPORAL PROFILES # ============================================================================ transform T_profile : intent: characterize manner: "extract temporal profile" input: D_day output: F_day_profile actor: machine description: "Represent each day by its measurement sequence" artifact F_day_profile : feature(D_day) value structure: vector value type: numeric description: "Daily temporal profile: sequence of measurements within each day" # ============================================================================ # SPECIFICATION FOR CLUSTERING (initial loop artifact) # ============================================================================ artifact S_clustering : specification origin: given representation form: "parameter settings" description: "Initial parameters for hierarchical clustering: number of clusters (dendrogram cut level), distance measure (geometric, normalised, shift-invariant, max-based), time interval focus" # ============================================================================ # STEP 4: CLUSTERING LOOP -- INTERACTIVELY DISCOVER PATTERNS # ============================================================================ loop L_clustering: purpose: "Iteratively explore cluster structure to identify meaningful and interpretable daily patterns" until: "Clusters provide clear, interpretable decomposition of daily patterns; standard patterns and exceptional days are identified" body: transform T_cluster : intent: define-unit manner: "hierarchical clustering by similarity" input: D_day, F_day_profile, S_clustering output: D_cluster, F_cluster_label actor: hyrbid description: "Apply hierarchical clustering to group days with similar profiles; user selects cut through dendrogram to determine clusters" artifact D_cluster : entities internal structure: group/cluster embedment: set features: - id: cluster_size value structure: atomic value type: numeric description: "Number of days in cluster" description: "Groups of days with similar daily profiles selected from hierarchical clustering tree" artifact F_cluster_label : feature(D_day) value structure: atomic value type: categorical description: "Cluster membership identifier for each day" transform T_aggregate : intent: characterise manner: "aggregate profiles per cluster" input: D_cluster, F_day_profile output: F_cluster_profile actor: machine description: "Compute average daily profile for each cluster to represent typical pattern" artifact F_cluster_profile : feature(D_cluster) value structure: vector value type: numeric description: "Cluster-level average daily profiles representing typical patterns for each group" transform T_calendar_vis : intent: visualise manner: "calendar grid with colour-coded clusters" input: A_calender, F_cluster_label output: V_calendar actor: machine description: "Display days on calendar grid, coloured by cluster membership" artifact V_calendar : visualisation(A_calendar, F_cluster_label) layout: "calendar grid (months as rows, weekdays as columns)" form: "coloured cells" encoding: "position from A_calendar; colour from F_cluster_label" description: "Calendar view showing temporal distribution of cluster patterns across year and week" transform T_profile_vis : intent: visualise manner: "line graphs of cluster profiles" input: F_cluster_profile, D_cluster output: V_profiles actor: machine description: "Display average daily profile for each cluster as line graph" artifact V_profiles : visualisation(F_cluster_profile, D_cluster) layout: "time axis (hour of day)" form: "line graphs (one per cluster)" encoding: "x-position: time within day; y-position: average measurement value; colour: cluster identity matching calendar colours" description: "Line graphs showing characteristic temporal patterns for each cluster" transform T_interpret : intent: abstract manner: "interpret cluster meanings" input: V_calendar, V_profiles output: P_patterns actor: human description: "Interpret cluster patterns: identify behavioural meaning of each cluster type" artifact P_patterns : pattern(D_cluster, F_cluster_profile) representation form: "textual labels and descriptions" description: "Interpreted meanings of daily patterns (e.g., 'typical weekday', 'weekend', 'holiday', 'summer Friday', 'exceptional event')" transform T_assess_clusters : intent: assess manner: "evaluate cluster quality and interpretability" input: V_calendar, V_profiles, P_patterns output: K_cluster_quality actor: human description: "Assess whether clusters provide meaningful decomposition: patterns are interpretable, clusters well-separated, standard vs. exceptional days identified" artifact K_cluster_quality : knowledge(D_cluster) representation form: "quality judgment" description: "Assessment of cluster quality: interpretability, separation, coverage of pattern types, and whether refinement with adjusted parameters is needed" if K_cluster_quality indicates satisfactory clustering: then: exit loop L_clustering else: transform T_adjust_clustering : intent: generate-knowledge manner: "adjust clustering parameters based on assessment" input: K_cluster_quality, V_calendar, V_profiles, S_clustering output: S_clustering_r actor: human description: "Adjust clustering parameters: modify number of clusters, select different distance measure, or change time interval focus" artifact S_clustering_r : specification representation form: "parameter settings" description: "Updated clustering parameters after analyst refinement" assign: S_clustering := S_clustering_r end loop L_clusterng # ============================================================================ # STEP 5: SYNTHESISE FINDINGS # ============================================================================ transform T_synthesise : intent: generate-knowledge manner: "formulate statements about temporal patterns" input: P_patterns, V_calendar, V_profiles, K_cluster_quality output: K_findings actor: human description: "Synthesise findings: document discovered patterns, their temporal distribution, correlations with external events, and exceptional occurrences" artifact K_findings : knowledge(P_patterns) representation form: "statements and explanations" description: "Understanding of temporal patterns: standard daily patterns identified, their distribution over week and year, correlation with calendar events, exceptional patterns and their causes"